Lihat sumber Daftar masalah matematika yang belum terpecahkan

Ada banyak permasalahan matematika yang telah dinyatakan tetapi belum ada yang terpecahkan. Masalah tersebut berasal dari [[cabang matematika|cabang-cabang matematika]] seperti [[fisika]], [[ilmu komputer]], [[aljabar]], [[Analisis matematis|analisis]], [[kombinatorika]], [[geometri aljabar]], [[geometri diferensial]], [[geometri diskret]], [[geometri Euklides]], [[teori graf]], [[teori grup]], [[teori model]], [[teori bilangan]], [[teori himpunan]], [[teori Ramsey]], [[sistem dinamika]], dan [[persamaan diferensial parsial]]. Beberapa masalah dapat dikelompokkan dan dipelajari dalam banyak bidang ilmu yang berbeda. Hadiah sering sering kali diberikan untuk seseorang yang memecahkan masalah yang belum terpecahkan, dan daftar-daftar masalah yang belum terpecahkan (seperti daftar [[Masalah Milenium|Masalah Hadiah Millenium]]) mendapatkan perhatian yang lebih.

Artikel ini mengumpulkan berbagai masalah yang didapat dari berbagai sumber, termasuk namun tidak terbatas pada daftar-daftar yang terpercaya. Masalah-masalah dalam artikel ini memiliki tingkat kesulitan yang beragam, maupun tingkat kepentingannya bagi matematika dan sains secara umum.  Daftar ini belum tentu lengkap atau terbarukan ketika <!-- Anda -->membacanya saat ini.

== Masalah-masalah yang dikompilasi ==
Berbagai matematikawan dan organisasi telah menyusun masalah-masalah matematika yang belum terpecahkan dalam bentuk daftar dan memromosikannya. Dalam beberapa kasus, nama daftar-daftar tersebut juga digunakan untuk merujuk hadiah yang diberikan bagi penemu penyelesaiannya.
{| class="wikitable"
|+
!Daftar
!Jumlah masalah
!Jumlah yang belum terpecahkan atau belum terselesaikan sepenuhnya
!Diusulkan oleh
!Diusulkan pada tahun
|-
|[[Masalah Hilbert]]<ref>{{citation|last=Thiele|first=Rüdiger|chapter=On Hilbert and his twenty-four problems|title=Mathematics and the historian's craft. The Kenneth O. May Lectures|pages=243–295|isbn=978-0-387-25284-1|editor-last=Van Brummelen|editor-first=Glen|year=2005|series=[[Canadian Mathematical Society|CMS]] Books in Mathematics/Ouvrages de Mathématiques de la SMC|volume=21|title-link=Kenneth May}}</ref>
|23
| 15
|[[David Hilbert]]
|1900
|-
|[[Masalah Landau]]<ref>{{citation|title=Unsolved Problems in Number Theory|first=Richard|last=Guy|author-link=Richard K. Guy|edition=2nd|publisher=Springer|year=1994|page=vii|url=https://books.google.com/books?id=EbLzBwAAQBAJ&pg=PR7|isbn=978-1-4899-3585-4|access-date=2016-09-22|archive-url=https://web.archive.org/web/20190323220345/https://books.google.com/books?id=EbLzBwAAQBAJ&pg=PR7|archive-date=2019-03-23|url-status=live}}.</ref>
|4
| 4
|[[Edmund Landau]]
|1912
|-
|[[Masalah Tanimaya]]<ref>{{cite journal|last=Shimura|first=G.|author-link=Goro Shimura|year=1989|title=Yutaka Taniyama and his time|url=http://blms.oxfordjournals.org/content/21/2/186|journal=Bulletin of the London Mathematical Society|volume=21|issue=2|pages=186–196|doi=10.1112/blms/21.2.186|archive-url=https://web.archive.org/web/20160125085046/http://blms.oxfordjournals.org/content/21/2/186|archive-date=2016-01-25|access-date=2015-01-15|url-status=dead}}</ref>
|36
| -
|[[Yutaka Taniyama]]
|1955
|-
|24 pertanyaan Thurston<ref>{{Cite web|title=Archived copy|url=http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/friedl/papers/dmv_091514.pdf|archive-url=https://web.archive.org/web/20160208034601/http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/friedl/papers/dmv_091514.pdf|archive-date=2016-02-08|access-date=2016-01-22|url-status=dead}}</ref><ref>{{cite web|title=THREE DIMENSIONAL MANIFOLDS, KLEINIAN GROUPS AND HYPERBOLIC GEOMETRY|url=http://www.ams.org/journals/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf|archive-url=https://web.archive.org/web/20160410172024/http://www.ams.org/journals/bull/1982-06-03/S0273-0979-1982-15003-0/S0273-0979-1982-15003-0.pdf|archive-date=2016-04-10|access-date=2016-02-09|url-status=live}}</ref>
|24
| -
|[[William Thurston]]
|1982
|-
|[[Masalah Smale]]
|18
|14
|[[Stephen Smale]]
|1998
|-
|[[Masalah Millenium|Masalah Hadiah Millenium]]
|7
|6<ref name="auto12">{{cite web|title=Millennium Problems|url=http://claymath.org/millennium-problems|archive-url=https://web.archive.org/web/20170606121331/http://claymath.org/millennium-problems|archive-date=2017-06-06|access-date=2015-01-20|url-status=dead}}</ref>
|[[Clay Mathematics Institute]]
|2000
|-
|[[Masalah Simon]]
|15
|<12<ref>{{cite web|date=2014-08-13|title=Fields Medal awarded to Artur Avila|url=http://www2.cnrs.fr/en/2435.htm?debut=8&theme1=12|website=[[Centre national de la recherche scientifique]]|archive-url=https://web.archive.org/web/20180710010437/http://www2.cnrs.fr/en/2435.htm?debut=8&theme1=12|archive-date=2018-07-10|access-date=2018-07-07|url-status=dead}}</ref><ref name="guardian">{{cite web|last=Bellos|first=Alex|date=2014-08-13|title=Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained|url=https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/aug/13/fields-medals-2014-maths-avila-bhargava-hairer-mirzakhani|website=[[The Guardian]]|archive-url=https://web.archive.org/web/20161021115900/https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/aug/13/fields-medals-2014-maths-avila-bhargava-hairer-mirzakhani|archive-date=2016-10-21|access-date=2018-07-07|url-status=live}}</ref>
|[[Barry Simon]]
|2000
|-
|[[Masalah yang Belum Terpecahkan dalam Matematika pada Abad ke-21]]<ref>{{cite book|last1=Abe|first1=Jair Minoro|last2=Tanaka|first2=Shotaro|year=2001|url=https://books.google.com/books?id=yHzfbqtVGLIC&q=unsolved+problems+in+mathematics|title=Unsolved Problems on Mathematics for the 21st Century|publisher=IOS Press|isbn=978-9051994902}}</ref>
|22
| -
|Jair Minoro Abe, Shotaro Tanaka
|2001
|-
|[[Tantangan matematika DARPA]]<ref>{{cite web|date=2008-10-14|title=DARPA invests in math|url=http://edition.cnn.com/2008/TECH/science/10/09/darpa.challenges/index.html|publisher=[[Cable News Network|CNN]]|archive-url=https://web.archive.org/web/20090304121240/http://edition.cnn.com/2008/TECH/science/10/09/darpa.challenges/index.html|archive-date=2009-03-04|access-date=2013-01-14}}</ref><ref>{{cite web|date=2007-09-10|title=Broad Agency Announcement (BAA 07-68) for Defense Sciences Office (DSO)|url=http://www.math.utk.edu/~vasili/refs/darpa07.MathChallenges.html|publisher=DARPA|archive-url=https://web.archive.org/web/20121001111057/http://www.math.utk.edu/~vasili/refs/darpa07.MathChallenges.html|archive-date=2012-10-01|access-date=2013-06-25}}</ref>
|23
| -
|DARPA
|2007
|}

=== Masalah Millenium Prize ===
[[Berkas:Riemann-Zeta-Func.png|jmpl|[[Fungsi zeta Riemann]], yang dikenal luas dan memiliki pengaruh penting, adalah subjek dari masalah [[hipotesis Riemann]] yang belum terpecahkan.]]
[[Masalah Milenium|Masalah Millenium Prize]] adalah daftar berisi tujuh masalah matematika yang diumumkan oleh [[Clay Mathematics Institute]] pada tahun 2000. Hadiah sebesar satu juta [[Dolar Amerika Serikat|dollar Amerika Serikat]] akan diberikan bagi penemu solusi benar untuk sembarang masalah pada daftar tersebut. Keenam masalah yang masih belum terpecahkan adalah:<ref name="auto12"/>

* [[Masalah P versus NP]]
* [[Konjektur Hodge]]
* [[Hipotesis Riemann]]
* [[Keberadaan Yang–Mills dan celah massa]]
* [[Keberadaan dan kemulusan Navier–Stokes]]
* [[Konjektur Birch dan Swinnerton-Dyer]]

Masalah ketujuh, [[konjektur Poincaré]], berhasil dipecahkan.<ref>{{cite web|title=Poincaré Conjecture|url=http://www.claymath.org/millenium-problems/poincar%C3%A9-conjecture|website=Clay Mathematics Institute|archive-url=https://web.archive.org/web/20131215120130/http://www.claymath.org/millenium-problems/poincar%C3%A9-conjecture|archive-date=2013-12-15}}</ref> Namun, perumuman masalah tersebut, yang dikenal sebagai [[Konjektur Poincaré yang diperumum|konjektur Poincaré dimensi empat yang mulus]] belum terpecahkan. Perumuman ini menanyakan apakah sebuah bola topologis empat dimensi dapat memiliki dua atau lebih [[struktur mulus]] yang tidak ekuivalen.<ref>{{cite web|title=Smooth 4-dimensional Poincare conjecture|url=http://www.openproblemgarden.org/?q=op/smooth_4_dimensional_poincare_conjecture|archive-url=https://web.archive.org/web/20180125203721/http://www.openproblemgarden.org/?q=op%2Fsmooth_4_dimensional_poincare_conjecture|archive-date=2018-01-25|access-date=2019-08-06|url-status=live}}</ref>

== Masalah yang belum terpecahkan berdasarkan bidang ==
=== Aljabar ===
[[File:Regular_tetrahedron_inscribed_in_a_sphere.svg|pra=https://en.wikipedia.org/wiki/File:Regular_tetrahedron_inscribed_in_a_sphere.svg|ka|jmpl|Dalam [[bola Bloch]] yang mewakili [[qubit]], sebuah [[SIC-POVM]] akan membentuk sebuah [[Tetrahedron|tetrahedron beraturan]]. Zauner menduga bahwa struktur yang analog juga ada di [[ruang Hilbert]] kompleks dari semua dimensi terhingga.]]Dalam bentuk paling umum, [[aljabar]] adalah ilmu yang mempelajari simbol-simbol matematika dan aturan untuk memanipulasi simbol-simbol tersebut. Dalam bidang ini, terdapat kompilasi Buku Catatan Dneister (''Dnestrovskaya Tetrad'') yang berisi kumpulan beberapa ratusan masalah-masalah aljabar, khususnya [[teori gelanggang]] dan [[Modulus (teori bilangan aljabar)|teori modulus]],<ref>{{citation|year=1993|title=Dnestrovskaya notebook|publisher=The Russian Academy of Sciences|language=ru|url=http://math.nsc.ru/LBRT/a1/files/dnestr93.pdf}}{{citation|url=https://math.usask.ca/~bremner/research/publications/dniester.pdf|title=Dneister Notebook: Unsolved Problems in the Theory of Rings and Modules|website=[[University of Saskatchewan]]|access-date=2019-08-15}}</ref> dan Buku Catatan Erlagol (''Erlagolskaya Tetrad'') yang berisi masalah-masalah dalam aljabar dan teori model.<ref>{{citation|year=2018|title=Erlagol notebook|publisher=The Novosibirsk State University|language=ru|url=http://uamt.conf.nstu.ru/erl_note.pdf}}</ref> Masalah-masalah dalam bidang ini meliputi:

* Keberadaan [[kuboid sempurna]] dan [[konjektur kuboid]] yang terkait
* [[Konjektur basis Rota]]
* [[Konjektur Birch–Tate]]
* [[Konjektur Bombien–Lang]]
* [[Konjektur Bost]]
* [[Konjektur Crouzeix]]
* [[Konjektur Eilenberg–Ganea]]
* [[Konjektur Farrell–Jones]]
* [[Konjektur Hadamard]]
* [[Konjektur homologis dalam aljabar komutatif]]
* [[Konjektur Green]]
* [[Konjektur Jacobson]]
* [[Konjektur Kaplansky]]
* [[Konjektur kegandaan Serre]]
* [[Konjektur kelengkungan-p Grothendieck–Katz]]
* [[Konjektur Köthe]]
* [[Konjektur Kummer–Vandiver]]
* [[Konjektur Pierce–Birkhoff]]
* [[Konjektur Sendov]]
* [[Konjektur seragam]]
* [[Konjektur Serre II]]
* [[Konjektur Zariski–Lipman]]
* Konjektur Zauner: keberadaan [[SIC-POVM]] di semua dimensi
* [[Masalah keenambelas Hilbert]]
* [[Masalah kelimabelas Hilbert]]
* [[Masalah liar]], yang membahas mengenai penggolongan pasangan matriks <math>n\!\times\!n</math> dalam konjugasi secara simultan dan masalah-masalah lain yang mengandung masalah ini (seperti banyak masalah penggolongan pada umumnya)
* [[Masalah pembenaman Connes]] dalam teori [[aljabar von Neumann]]
* [[Masalah wakilan kekisi hingga]]

=== Analisis ===
[[Berkas:Gamma-area.svg|jmpl|Luas dari daerah berwarna biru konvergen dengan [[konstanta Euler–Mascheroni]], yang dapat atau tidak dapat menjadi sebuah bilangan rasional.]][[Analisis matematis|Analisis]] adalah cabang matematika yang berurusan dengan [[limit]] dan beberapa konsep yang berkaitan dengannya, seperti [[Turunan|diferensiasi]], [[integral]], [[Ukuran (matematika)|ukuran]], [[Deret (matematika)|deret]], [[barisan]], dan [[fungsi analitik]]. Masalah-masalah dalam bidang ini meliputi:

* [[Konjektur empat eksponensial]] membahas transendensi dari setidaknya salah satu dari empat eksponensial gabungan irasional<ref name="waldschmidt2">{{citation|pages=14, 16|url=https://books.google.com/books?id=Wrj0CAAAQBAJ&pg=PA14|title=Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables|first=Michel|last=Waldschmidt|publisher=Springer|year=2013|isbn=9783662115695}}</ref>
* [[Konjektur Lehmer]] membahas ukuran polinomial siklotomik Mahler<ref>{{citation|first=Chris|last=Smyth|chapter=The Mahler measure of algebraic numbers: a survey|pages=322–349|editor1-first=James|editor1-last=McKee|editor2-last=Smyth|editor2-first=Chris|title=Number Theory and Polynomials|series=London Mathematical Society Lecture Note Series|volume=352|publisher=[[Cambridge University Press]]|year=2008|isbn=978-0-521-71467-9}}</ref>
* Masalah Pompeiu membahas topologi domain untuk yang beberapa fungsi taknol memiliki integral lenyap pada setiap salinan kongruen<ref>{{SpringerEOM|title=Pompeiu problem|id=Pompeiu_problem&oldid=14506|author-last1=Berenstein|author-first1=Carlos A.}}</ref>
* [[Konjektur Schanuel]] membahas derajat transenden dari eksponensial irasional bebas linear<ref name="waldschmidt2"/>
* Apakah <math>\gamma</math> ([[konstanta Euler–Mascheroni]]), <math>\pi+e</math>, <math>\pi-e</math>, <math>\pi e</math>, <math>\tfrac{\pi}{e}</math>, <math>\pi^e</math>, <math>\pi^\sqrt 2</math>, <math>\pi^\pi</math>, <math>e^{\pi^2}</math>, <math>\ln \pi</math>, <math>2^e</math>, <math>e^e</math>, [[konstanta Catalan]], maupun [[konstanta Khinchin]] termasuk bilangan rasional, irasional [[Bilangan aljabar|aljabar]], atau [[Bilangan transenden|transendental]]? Berapa [[ukuran keirasionalan]] dari setiap bilangan-bilangan ini?<ref>For background on the numbers that are the focus of this problem, see articles by Eric W. Weisstein, on pi ( {{Cite web |url=http://mathworld.wolfram.com/Pi.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-12-06 |archive-url=https://web.archive.org/web/20141206023912/http://mathworld.wolfram.com/Pi.html |dead-url=unfit }}), e ( {{Cite web |url=http://mathworld.wolfram.com/e.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-11-21 |archive-url=https://web.archive.org/web/20141121122615/http://mathworld.wolfram.com/e.html |dead-url=unfit }}), Khinchin's Constant ( {{Cite web |url=http://mathworld.wolfram.com/KhinchinsConstant.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-11-05 |archive-url=https://web.archive.org/web/20141105201509/http://mathworld.wolfram.com/KhinchinsConstant.html |dead-url=unfit }}), irrational numbers ( {{Cite web |url=http://mathworld.wolfram.com/IrrationalNumber.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2015-03-27 |archive-url=https://web.archive.org/web/20150327024040/http://mathworld.wolfram.com/IrrationalNumber.html |dead-url=unfit }}), transcendental numbers ( {{Cite web |url=http://mathworld.wolfram.com/TranscendentalNumber.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-11-13 |archive-url=https://web.archive.org/web/20141113174913/http://mathworld.wolfram.com/TranscendentalNumber.html |dead-url=unfit }}), and irrationality measures ( {{Cite web |url=http://mathworld.wolfram.com/IrrationalityMeasure.html |title=Salinan arsip |access-date=2021-01-27 |archive-date=2015-04-21 |archive-url=https://web.archive.org/web/20150421203736/http://mathworld.wolfram.com/IrrationalityMeasure.html |dead-url=unfit }}) at Wolfram ''MathWorld'', all articles accessed 15 December 2014.</ref><ref>Michel Waldschmidt, 2008, "An introduction to irrationality and transcendence methods," at The University of Arizona The Southwest Center for Arithmetic Geometry 2008 Arizona Winter School, March 15–19, 2008 (Special Functions and Transcendence), see  {{Cite web |url=http://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/AWSLecture5.pdf |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-12-16 |archive-url=https://web.archive.org/web/20141216004531/http://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/AWSLecture5.pdf |dead-url=unfit }}, accessed 15 December 2014.</ref><ref>John Albert, posting date unknown, "Some unsolved problems in number theory" [from Victor Klee & Stan Wagon, "Old and New Unsolved Problems in Plane Geometry and Number Theory"], in University of Oklahoma Math 4513 course materials, see  {{Cite web |url=http://www2.math.ou.edu/~jalbert/courses/openprob2.pdf |title=Salinan arsip |access-date=2021-01-27 |archive-date=2014-01-17 |archive-url=https://web.archive.org/web/20140117150133/http://www2.math.ou.edu/~jalbert/courses/openprob2.pdf |dead-url=unfit }}, accessed 15 December 2014.</ref>
* [[Kapasitas analitik#Konjektur Vitushkin|Konjektur Vitushkin]]
* [[Masalah subruang invarian]]
* [[Konjektur Kung–Traub]]<ref>{{citation|last1=Kung|first1=H. T.|last2=Traub|first2=Joseph Frederick|author-link1=H. T. Kung|author-link2=Joseph F. Traub|title=Optimal order of one-point and multipoint iteration|journal=[[Journal of the ACM]]|year=1974|volume=21|number=4|pages=643–651|doi=10.1145/321850.321860|s2cid=74921}}</ref>
* Keteraturan dari penyelesaian [[persamaan Vlasov–Maxwell]]
* Keteraturan dari penyelesaian [[Persamaan Euler (dinamika fluida)|persamaan Euler]]
* Kekonvergenan deret Flint Hills

=== Kombinatorika ===
* [[Konjektur himpunan gabungan tertutup]] Franki: untuk setiap keluarga himpunan ditutup dalam jumlah, terdapat sebuah elemen (dari ruang pendasar) milik setengah atau lebih dari himpunan-himpunan tersebut<ref>{{citation|last1=Bruhn|url=http://www.zaik.uni-koeln.de/~schaudt/UCSurvey.pdf|archive-date=2017-08-08|archive-url=https://web.archive.org/web/20170808104232/http://www.zaik.uni-koeln.de/~schaudt/UCSurvey.pdf|access-date=2017-07-18|s2cid=17531822|arxiv=1309.3297|year=2015|volume=31|title=The journey of the union-closed sets conjecture|first1=Henning|pages=2043–2074|mr=3417215|journal=Graphs and Combinatorics|issue=6|doi=10.1007/s00373-014-1515-0|first2=Oliver|last2=Schaudt|url-status=live}}</ref>
* [[Masalah dalam persegi Latin]] – masalah terbuka yang melibatkan [[persegi Latin]]
* [[Konjektur pelari kesepian]]: jika <math>k+1</math> pelari berpasangan dengan kecepatan yang berbeda berlari mengitari lintasan panjang satuan, apakah setiap pelari akan "kesepian" (yaitu, setidaknya sebuah jarak <math>\tfrac{1}{k+1}</math> dari setiap pelari lainnya) pada suatu waktu?<ref>{{cite arxiv|first=Terence|last=Tao|author-link=Terence Tao|title=Some remarks on the lonely runner conjecture|year=2017|eprint=1701.02048|mode=cs2|class=math.CO}}</ref>
* Mencari sebuah fungsi untuk memodelkan n-langkah [[langkah hindar-diri]]<ref>{{Cite journal|last1=Liśkiewicz|first1=Maciej|last2=Ogihara|first2=Mitsunori|last3=Toda|first3=Seinosuke|date=2003-07-28|title=The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes|journal=Theoretical Computer Science|volume=304|issue=1|pages=129–156|doi=10.1016/S0304-3975(03)00080-X}}</ref>
* [[Konjektur 1/3–2/3]]: apakah setiap [[himpunan terurut parsial]] terhingga yang bukan [[terurut total]] berisi dua elemen <math>x</math> dan <math>y</math> sehingga probabilitasnya bahwa <math>x</math> sebelum <math>y</math> dalam sebuah [[pengembangan linear]] acak di antara 1/3 dan 2/3?<ref>{{citation|last1=Brightwell|first1=Graham R.|last2=Felsner|first2=Stefan|last3=Trotter|first3=William T.|doi=10.1007/BF01110378|mr=1368815|issue=4|journal=[[Order (journal)|Order]]|pages=327–349|title=Balancing pairs and the cross product conjecture|volume=12|year=1995|citeseerx=10.1.1.38.7841|s2cid=14793475}}.</ref>
* Memberikan sebuah interpretasi kombinatorial dari [[koefisien Kronecker]].<ref>{{citation|last=Murnaghan|first=F. D.|doi=10.2307/2371542|issue=1|journal=American Journal of Mathematics|mr=1507301|pages=44–65|title=The Analysis of the Direct Product of Irreducible Representations of the Symmetric Groups|volume=60|year=1938|pmc=1076971|pmid=16577800|jstor=2371542}}</ref>
* [[Masalah-masalah dalam persegi Latin|Pertanyaan terbuka]] mengenai [[persegi Latin]]
* Nilai dari [[bilangan Dedekind]] <math>M(n)</math> untuk <math>n \ge 9</math>.<ref>{{Cite web |url=http://www.sfu.ca/~tyusun/ThesisDedekind.pdf |title=Dedekind Numbers and Related Sequences |access-date=2021-01-27 |archive-date=2015-03-15 |archive-url=https://web.archive.org/web/20150315021125/http://www.sfu.ca/~tyusun/ThesisDedekind.pdf |dead-url=yes }}</ref>
* Nilai dari [[bilangan Ramsey]], khususnya <math>R(5,5)</math>
* Nilai dari [[bilangan Van der Waerden]]

=== Sistem dinamikal ===
[[Berkas:Mandel zoom 07 satellite.jpg|jmpl|Sebuah{{Pranala mati|date=April 2021 |bot=InternetArchiveBot |fix-attempted=yes }} detail dari [[himpunan Mandelbrot]]. Ini tidak tahu apakah himpunan Mandebrot [[Ruang terhubung lokal|terhubung lokal]] atau tidak.]]
* [[Konjektur Collatz]] (konjektur <math>3n+1 </math>)
* [[Fungsi Lyapunov|Metode kedua Lyapunov untuk kestabilan]] – Untuk apa kelas [[persamaan diferensial biasa]], yang menjelaskan sistem dinamika, apakah metode kedua Lyapunov yang dirumuskan dalam bentuk klasik dan kekanonisan yang dirampat menentukan syarat perlu dan cukup untuk kestabilan (asimtotis) gerak?
* Konjektur [[Hillel Furstenberg|Furstenberg]] – apakah setipa ukura nyang invarian dan [[ergodik]] untuk tindakan <math>\times 2</math>, <math>\times 3</math> pada lingkaran Lebesgue atau atomik?
* Konjektur [[Grigory Margulis|Margulis]] – Pengglongan ukuran untuk tindakan terdiagonalkan dalam grup peringkat tinggi
* [[Himpunan Mandelbrot#Keterhubungan lokal|Konjektur MLC]] – apakah himpunan Mandelbrot terhubung lokal?
* [[Konjektur Weinstein]]  – Apakah sebuah [[himpunan aras]] [[tipe kontak]] kompak beraturan dari sebuah [[Mekanika Hamiltonian|Hamilton]] pada sebuah [[manifold simplektik]] membawa setidaknya satu orbit berkala dari alir Hamilton?
* [[Konjektur Arnold–Givental]] dan [[Simplektomorfisme#Konjektur Arnold|konjektur Arnold]] – berkaitan geometri simplektik dengan teori Morse
* Konjektur Eremenko bahwa setiap komponen dari [[himpunan pelepasan]] sebuah fungsi transendental menyeluruh tidak terbatas
* Apakah setiap [[automaton seluler terbalikkan]] dalam tiga dimensi atau lebih secara lokal terbalikkan?<ref>{{citation|last=Kari|first=Jarkko|author-link=Jarkko Kari|contribution=Structure of reversible cellular automata|doi=10.1007/978-3-642-03745-0_5|page=6|publisher=Springer|series=[[Lecture Notes in Computer Science]]|title=Unconventional Computation: 8th International Conference, UC 2009, Ponta Delgada, Portugal, September 7ÔÇô11, 2009, Proceedings|volume=5715|year=2009|bibcode=2009LNCS.5715....6K|isbn=978-3-642-03744-3|doi-access=free}}</ref>
* [[Konjektur Birkhoff]]: jika sebuah tabel terintegralkan dan cembung sempurna, apakah batasnya yang semestinya sebuah elips?<ref>{{cite journal|last1=Kaloshin|first1=Vadim|last2=Sorrentino|first2=Alfonso|year=2018|title=On the local Birkhoff conjecture for convex billiards|journal=[[Annals of Mathematics]]|volume=188|pages=315–380|arxiv=1612.09194|doi=10.4007/annals.2018.188.1.6|author-link1=Vadim Kaloshin|number=1|s2cid=119171182}}</ref>
* Banyak masalah berkaitan dengan sebuah biliar luar, sebagai contoh menunjukkan bahwa [[Biliar luar#Masalah luar|biliar luar]] relatif dengan hampir setiap poligon cembung memiliki orbit-orbit yang tidak terbatas.
* [[Konjektur ergodisitas tunggal kuantum]]<ref>{{citation|last=Sarnak|first=Peter|author-link=Peter Sarnak|title=Recent progress on the quantum unique ergodicity conjecture|journal=[[Bulletin of the American Mathematical Society]]|volume=48|issue=2|year=2011|pages=211–228|doi=10.1090/S0273-0979-2011-01323-4|mr=2774090|doi-access=free}}</ref>
* [[Kekacauan kuantum#Konjektur Berry–Tabor|Konjektur Berry–Tabor]]
* [[Konjektur Painlevé]]

=== Permainan dan teka-teki ===

==== Permainan kombinatorial ====
* [[Sudoku]]:
** Berapa [[Matematika Sudoku#Jumlah maksimum yang diberikan|jumlah maksimum yang diberikan]] untuk sebuah teka-teki [[Glosarium Sudoku#Terminologi lainnya|minimal]]?<ref name="openq2">[http://english.log-it-ex.com/2.html http://english.log-it-ex.com] {{Webarchive|url=https://web.archive.org/web/20171110030932/http://english.log-it-ex.com/2.html|date=2017-11-10}} Ten open questions about Sudoku (2012-01-21).</ref>
** Berapa banyak teka-teki yang seharusnya memiliki satu penyelesaian?<ref name="openq2"/>
** Berapa banyak teka-teki dengan tepatnya satu penyelesaian merupakan minimal<ref name="openq2"/>
* [[Variasi silang-bulat-silang]]:
** Diberikan sebuah lebar papan silang-bulat-silang, berapa dimensi paling terkecil sehingga <math>X</math> dijamin sebuah strategi kemenangan?<ref>{{cite web|date=2017-09-21|title=Higher-Dimensional Tic-Tac-Toe|url=https://www.youtube.com/watch?v=FwJZa-helig|website=[[PBS Digital Studios|PBS Infinite Series]]|publisher=[[YouTube]]|archive-url=https://web.archive.org/web/20171011000653/https://www.youtube.com/watch?v=FwJZa-helig|archive-date=2017-10-11|access-date=2018-07-29|url-status=live}}</ref>
* Apa status [[kelengkapan Turing]] dari semua [[Automata seluler elementer|Permainan dengan]]  tunggal?

==== Permainan dengan informasi yang tidak sempurna ====
* [[Persoalan pertemuan]]

=== Geometri ===
==== Geometri aljabar ====

* [[Konjektur limpahan]]
* [[Konjektur Bass]]
* [[Pierre Deligne#Konsep yang dinamakan oleh Deligne|Konjektur Deligne]]
* [[Konjektur Dixmier]]
* [[Konjektur Fröberg]]
* [[Konjektur Fujita]]
* [[Konjektur Hartshorne]]<ref>{{cite journal|last1=Barlet|first1=Daniel|last2=Peternell|first2=Thomas|last3=Schneider|first3=Michael|year=1990|title=On two conjectures of Hartshorne's|journal=[[Mathematische Annalen]]|volume=286|issue=1–3|pages=13–25|doi=10.1007/BF01453563|s2cid=122151259}}</ref>
* [[Konjektur Jacobi]]
* [[Konjektur Manin]]
* [[Konjektur Maulik–Nekrasov–Okounkov–Pandharipande]] pada sebuah kesetaraan antara [[teorema Gromov–Witten]] and [[teorema Donaldson–Thomas]] <ref>{{citation|last1=Maulik|first1=Davesh|last2=Nekrasov|first2=Nikita|author-link2=Nikita Nekrasov|last3=Okounov|first3=Andrei|author-link3=Andrei Okounov|last4=Pandharipande|first4=Rahul|author-link4=Rahul Pandharipande|title=Gromov–Witten theory and Donaldson–Thomas theory, I|arxiv=math/0312059|date=2004-06-05|bibcode=2003math.....12059M}}</ref>
* [[Konjektur Nakai]]
* [[Resolusi kesingularan]] dalam karateristik <math>p</math>
* [[Konjektur standar]] pada siklus aljabar
* [[Konjektur bagian]]
* [[Konjektur Tate]]
* [[Pembalikan (matematika)|Penghentian pembalikan]]
* [[Konjektur Virasoro]]
* [[Konjektur monodromi bobot]]
* [[Konjektur kegandaan Zariski]]<ref>{{cite journal|last=Zariski|first=Oscar|author-link=Oscar Zariski|year=1971|title=Some open questions in the theory of singularities|journal=[[Bulletin of the American Mathematical Society]]|volume=77|issue=4|pages=481–491|doi=10.1090/S0002-9904-1971-12729-5|mr=0277533|doi-access=free}}</ref>

==== Peliputan dan pengepakan ====

* [[Masalah Borsuk]] pada btas atas dan bawah untuk bilangan himpunan bagian diamater yang terkecil dibutuhkan utuk liputan sebuah himpunan <math>n</math> dimensi [[Himpunan terbatas|terbatas]].
* [[Masalah pengepakan Rado]]: jika gabungan persegi yang bayak memilki luas satuan, seberpa kecil dapat luas terbesaar diliputi oleh sebuah himpunan bagian lepas persegi-persegi?<ref>{{citation|last1=Bereg|first1=Sergey|last2=Dumitrescu|first2=Adrian|last3=Jiang|first3=Minghui|doi=10.1007/s00453-009-9298-z|issue=3|journal=Algorithmica|mr=2609053|pages=538–561|title=On covering problems of Rado|volume=57|year=2010|s2cid=6511998}}</ref>
* [[Pengepakan lingkaran dalam sebuah segitiga sama sisi|Konjektur Erdős–Oler]] yang ketika <math>n</math> merupakan sebuah [[bilangan segitiga]], pengepakan lingkaran <math>n-1</math> dalam sebuah [[segitiga sama sisi]] membutuhkan sebuah segitiga dari ukuran yang sama sebagai pengepakan lingkaran <math>n</math><ref>{{citation|last=Melissen|first=Hans|doi=10.2307/2324212|issue=10|journal=American Mathematical Monthly|mr=1252928|pages=916–925|title=Densest packings of congruent circles in an equilateral triangle|volume=100|year=1993|jstor=2324212}}</ref>
* [[Masalah bilangan ciuman]] untuk dimensi selain 1, 2, 3, 4, 8 dan 24<ref>{{citation|first=John H.|last=Conway|author-link=John Horton Conway|author2=Neil J.A. Sloane|author-link2=Neil Sloane|year=1999|title=Sphere Packings, Lattices and Groups|edition=3rd|publisher=Springer-Verlag|location=New York|isbn=978-0-387-98585-5|pages=[https://books.google.com/books?id=upYwZ6cQumoC&pg=PA21 21–22]}}</ref>
* [[Konjektur Reinhardt]] bahwa oktagon yang mulus memiliki kerapatan pengepakan maksimum terendah dari semua himpunan bidang simetris pusat<ref>{{citation|last=Hales|first=Thomas|author-link=Thomas Callister Hales|arxiv=1703.01352|title=The Reinhardt conjecture as an optimal control problem|year=2017}}</ref>
* Masalah[[pengepakan bola]], termasuk kerapatan dari pengepakan terapat dalam dimensi selain 1, 2, 3, 8, dan 24, dan perilaku asimtotiknya untuk dimensi yang tinggi.
* [[Pengepakan persegi dalam sebuah persegi]]: berapa rata-rata pertumbuhan asimtotik dari ruang yang terbuang?<ref>{{citation|last1=Brass|first1=Peter|last2=Moser|first2=William|last3=Pach|first3=János|author3-link=János Pach|isbn=978-0387-23815-9|mr=2163782|page=45|publisher=Springer|location=New York|title=Research Problems in Discrete Geometry|url=https://books.google.com/books?id=WehCspo0Qa0C&pg=PA45|year=2005}}</ref>
* [[Konjektur pengepakan Ulam]] mengenai identitas dari padatan cembung pengepakan terburuk<ref>{{citation|last=Gardner|first=Martin|date=1995|title=New Mathematical Diversions (Revised Edition)|location=Washington|publisher=Mathematical Association of America|page=251}}</ref>

==== Geometri diferensial ====
* The [[Konjektur luas pengisi]], yang sebuah setengah bola memiliki luas minimum disekitar among permukaan bebas pintas dalam [[ruang Euklides]] yang perbatasannya membentuk sebuah kurva tertutub dari panjang yang diberikan<ref>{{citation|last=Katz|first=Mikhail G.|doi=10.1090/surv/137|isbn=978-0-8218-4177-8|mr=2292367|page=57|publisher=American Mathematical Society, Providence, RI|series=Mathematical Surveys and Monographs|title=Systolic geometry and topology|url=https://books.google.com/books?id=R5_zBwAAQBAJ&pg=PA57|volume=137|year=2007}}</ref>
* [[Konjektur Hopf]] mengaitkan kelengkungan dan karaterisitk Euler dari manifold Riemann dimensi yang lebih tinggi<ref>{{citation|last=Rosenberg|first=Steven|doi=10.1017/CBO9780511623783|isbn=978-0-521-46300-3|location=Cambridge|mr=1462892|pages=62–63|publisher=Cambridge University Press|series=London Mathematical Society Student Texts|title=The Laplacian on a Riemannian Manifold: An introduction to analysis on manifolds|url=https://books.google.com/books?id=gzJ6Vn0y7XQC&pg=PA62|volume=31|year=1997}}</ref>
* The [[Masalah Bernstein bola]], sebuah rampat kemungkinan dari [[masalah Bernstein]] yang asli.
* [[Konjektur Cartan–Hadamard]]: Dapatkah [[pertidaksamaan isoperimetrik]] klasik untuk himpunan bagian ruang Euklides diperpanjang menjadi ruang kelengkungan takpositif, dikenal sebagai [[Manifold Hadamard|manifold Cartan–Hadamard]]?
* [[Konjektur Carathéodory]]
* [[Konjektur Chern (geometri afin)]]
* [[Konjektur Chern untuk hiperpermukaan dalam bola]]
* [[Konjektur Yau]]
* [[Konjektu Yau pada eigenniiai pertama]]
* [[Masalah kurva tertutup]]: Carilah syarat perlu dan cukup (eksplisit) yang menentukan ketika, diberikan dua fungsi berkalai dengan periode yang sama, kurva integral tertutup.<ref>{{citation|last=Barros|first=Manuel|jstor=2162098|journal=[[Proceedings of the American Mathematical Society]]|pages=1503–1509|title=General Helices and a Theorem of Lancret|volume=125|issue=5|year=1997|doi=10.1090/S0002-9939-97-03692-7|doi-access=free}}</ref>

==== Geometri diskret ====
[[Image:Kissing-3d.png|thumb|right|250px|Dalam tiga dimensi, [[bilangan ciuman]]<nowiki/>n<nowiki/>ya adalah 12, karena 12 bola satuan taktumpang tindih dapat ditaruh menjadi kontak dengan sebuah bola satuan pusat. (Disini, pusat-pusat bola luar membentuk puncak [[Ikosahedron reguler|ikosahedron regular]].) Bilangan ciuman hanya dikenal persis dalam dimensi 1, 2, 3, 4, 8 dan 24.]]
* Menyelesaikan [[masalah akhir yang bahagia]] untuk sembarang <math>n</math><ref>{{citation
 | last1 = Morris | first1 = Walter D.
 | last2 = Soltan | first2 = Valeriu
 | doi = 10.1090/S0273-0979-00-00877-6
 | issue = 4
 | journal = Bull. Amer. Math. Soc.
 | mr = 1779413
 | pages = 437–458
 | title = The Erdős-Szekeres problem on points in convex position—a survey
 | volume = 37
 | year = 2000| doi-access = free
 }}; {{citation
 | last = Suk | first = Andrew
 | arxiv = 1604.08657
 | doi = 10.1090/jams/869
 | journal = J. Amer. Math. Soc.
 | title = On the Erdős–Szekeres convex polygon problem
 | year = 2016
 | volume=30
 | issue = 4
 | pages=1047–1053| s2cid = 15732134
 }}</ref>
* Mencari pemadanan batas atas dan bawah untuk [[Himpunan-k (geometri)|himpunan-''k'']] dan membagi garis<ref>{{citation
 | last = Dey | first = Tamal K. | author-link = Tamal Dey
 | doi = 10.1007/PL00009354
 | journal = Discrete Comput. Geom.
 | mr = 1608878
 | pages = 373–382
 | title = Improved bounds for planar ''k''-sets and related problems
 | volume = 19
 | issue = 3
 | year = 1998| doi-access = free
 }}; {{citation
 | last = Tóth | first = Gábor
 | doi = 10.1007/s004540010022
 | issue = 2
 | journal = Discrete Comput. Geom.
 | mr = 1843435
 | pages = 187–194
 | title = Point sets with many ''k''-sets
 | volume = 26
 | year = 2001| doi-access = free
 }}.</ref>
* [[Hadwiger conjecture (combinatorial geometry)|Konjektur Hadwiger]] pada peliputan benda cembung ''n''-dimensi dengan paling banyak <math>2^n</math> salinan yang lebih kecil?<ref>{{citation|title=Results and Problems in Combinatorial Geometry|first1=V.|last1=Boltjansky|first2=I.|last2=Gohberg|publisher=Cambridge University Press|year=1985|contribution=11. Hadwiger's Conjecture|pages=44–46}}.</ref>
* [[Masalah segitiga Kobon]] pada segitiga dalam garis urutan garis<ref>{{MathWorld|urlname=KobonTriangle|title=Kobon Triangle}}</ref>
* [[Masalah Kusner]] yang paling banyak <math>2d</math> titik dapat berjarak sama dalam ruang <math>L^1</math><ref>{{citation
 | last = Guy | first = Richard K. | authorlink = Richard K. Guy
 | issue = 3
 | journal = [[American Mathematical Monthly]]
 | mr = 1540158
 | pages = 196–200
 | title = An olla-podrida of open problems, often oddly posed
 | jstor = 2975549
 | volume = 90
 | year = 1983
 | doi = 10.2307/2975549 }}</ref>
* [[Masalah McMullen]] pada himpunan transformasi dengan cara proyeksi dari dua titik menjadi [[posisi cekung]]<ref>{{citation
 | last = Matoušek | first = Jiří | author-link = Jiří Matoušek (mathematician)
 | doi = 10.1007/978-1-4613-0039-7
 | isbn = 978-0-387-95373-1
 | mr = 1899299
 | page = 206
 | publisher = Springer-Verlag, New York
 | series = Graduate Texts in Mathematics
 | title = Lectures on discrete geometry
 | volume = 212
 | year = 2002}}</ref>
* [[Pengepakan penyanggah berkaki tiga]]<ref>{{citation|last1=Aronov|first1=Boris|author1-link=Boris Aronov|last2=Dujmović|first2=Vida|last3=Morin|first3=Pat|author3-link= Pat Morin |last4=Ooms|first4=Aurélien|last5=Schultz Xavier da Silveira|first5=Luís Fernando|issue=1|journal=[[Electronic Journal of Combinatorics]]|page=P1.8|title=More Turán-type theorems for triangles in convex point sets|url=https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p8|volume=26|year=2019|bibcode=2017arXiv170610193A|arxiv=1706.10193|access-date=2019-02-18|archive-url=https://web.archive.org/web/20190218082023/https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p8|archive-date=2019-02-18|url-status=live|doi-access=free|doi=10.37236/7224}}</ref>
* [[Grafik jarak satuan#Menghitung jarak satuan|Berapa banyak jarak satuan]] yang dapat ditentukan oleh sebuah himpunan dari <math>n</math> titik dalam bidang Euclides?<ref>{{citation
 | last1 = Brass | first1 = Peter
 | last2 = Moser | first2 = William
 | last3 = Pach | first3 = János
 | contribution = 5.1 The Maximum Number of Unit Distances in the Plane
 | isbn = 978-0-387-23815-9
 | mr = 2163782
 | pages = 183–190
 | publisher = Springer, New York
 | title = Research problems in discrete geometry
 | year = 2005}}</ref>
*[[Masalah hutan buram]]
*Meningkatkan batas bawah dan atas untuk [[masalah segitiga Heilbronn]].
* [[Konjektur 3^d Kalai]] pada jumlah kemungkinan terkecil dari sisi [[politop]] [[Titik simetri|simetrik terpusat]].<ref name="kalai">{{citation
 | last = Kalai | first = Gil | author-link = Gil Kalai
 | doi = 10.1007/BF01788696
 | issue = 1
 | journal = [[Graphs and Combinatorics]]
 | mr = 1554357
 | pages = 389–391
 | title = The number of faces of centrally-symmetric polytopes
 | volume = 5
 | year = 1989| s2cid = 8917264 }}.</ref>

==== Geometri Euklides ====
* [[Konjektur Atiyah pada konfigurasi]]<ref>{{Citation | last1=Atiyah | first1=Michael | author1-link=Michael Atiyah | title=Configurations of points | doi=10.1098/rsta.2001.0840 | mr=1853626  | year=2001 | journal= Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences| issn=1364-503X | volume=359 | issue=1784 | pages=1375–1387| bibcode=2001RSPTA.359.1375A | s2cid=55833332 }}</ref>
* [[Belmann tersesat dalam sebuah hutan]] – carilah jalan terpendek yang dijamin mendekati batasnya dari sebuah bentuk yang diberikan, dimulai pada titik yang takdiketahui dari bentuk dengna orientasi yang takdiketahui<ref>{{citation|last1=Finch|first1=S. R.|last2=Wetzel|first2=J. E.|title=Lost in a forest|volume=11|issue=8|year=2004|journal=[[American Mathematical Monthly]]|pages=645–654|mr=2091541|doi=10.2307/4145038|jstor=4145038}}</ref>
* Gelanggang Borromean — apakah tiga kurva ruang taktersimpul, bukan semua tiga lingkaran, yang tidak dapat disusun untuk membentuk tautan ini?<ref>{{citation
 | last = Howards | first = Hugh Nelson
 | arxiv = 1406.3370
 | doi = 10.1142/S0218216513500831
 | issue = 14
 | journal = Journal of Knot Theory and Its Ramifications
 | mr = 3190121
 | page = 1350083, 15
 | title = Forming the Borromean rings out of arbitrary polygonal unknots
 | volume = 22
 | year = 2013| s2cid = 119674622
 }}</ref>
* Masalah Danzer dan masalah lalat mati Conway – apakah [[himpunan Danzer]] dari kerapatan yang dibatasi atau pemisahan yang dibatasi ada?<ref>{{citation|last1=Solomon|first1=Yaar|last2=Weiss|first2=Barak|arxiv=1406.3807|doi=10.24033/asens.2303|issue=5|journal=Annales Scientifiques de l'École Normale Supérieure|mr=3581810|pages=1053–1074|title=Dense forests and Danzer sets|volume=49|year=2016|s2cid=672315}}; {{citation|last=Conway|first=John H.|author-link=John Horton Conway|access-date=2019-02-12|publisher=[[On-Line Encyclopedia of Integer Sequences]]|title=Five $1,000 Problems (Update 2017)|url=https://oeis.org/A248380/a248380.pdf|archive-url=https://web.archive.org/web/20190213123825/https://oeis.org/A248380/a248380.pdf|archive-date=2019-02-13|url-status=live}}</ref>
* Pembedahan ke ortoskema – apakah mungkin untuk [[Simpleks|simpleks-simpleks]] dari setiap dimensi?<ref>{{citation|last1=Brandts|first1=Jan|last2=Korotov|first2=Sergey|last3=Křížek|first3=Michal|last4=Šolc|first4=Jakub|doi=10.1137/060669073|issue=2|journal=SIAM Review|mr=2505583|pages=317–335|title=On nonobtuse simplicial partitions|volume=51|year=2009|url=https://pure.uva.nl/ws/files/836396/73198_315330.pdf|bibcode=2009SIAMR..51..317B|access-date=2018-11-22|archive-url=https://web.archive.org/web/20181104211116/https://pure.uva.nl/ws/files/836396/73198_315330.pdf|archive-date=2018-11-04|url-status=live}}. See in particular Conjecture 23, p. 327.</ref>
* {{not a typo|[[Masalah einstein]]}} – apakah terdapat sebuah bentuk dua dimensi yang membentuk [[prototile]] untuk sebuah [[pengubinan aperiodik]], tapi bukan untuk suatu pengubinan periodik?<ref>{{citation|last1=Socolar|first1=Joshua E. S.|last2=Taylor|first2=Joan M.|arxiv=1009.1419|doi=10.1007/s00283-011-9255-y|issue=1|journal=The Mathematical Intelligencer|mr=2902144|pages=18–28|title=Forcing nonperiodicity with a single tile|volume=34|year=2012|s2cid=10747746}}</ref>
* [[Konjektur Falconer]] bahwa himpunan dimensi Hausdorff lebih besar daripada <math>d/2</math> di <math>\mathbb{R}^d</math> harus memiliki sebuah himpunan jarak [[ukuran Lebesgue]]<ref>{{citation|last1=Arutyunyants|first1=G.|last2=Iosevich|first2=A.|editor-last=Pach|editor-first=János|editor-link=János Pach|contribution=Falconer conjecture, spherical averages and discrete analogs|doi=10.1090/conm/342/06127|mr=2065249|pages=15–24|publisher=Amer. Math. Soc., Providence, RI|series=Contemp. Math.|title=Towards a Theory of Geometric Graphs|volume=342|year=2004|isbn=9780821834848|doi-access=free}}</ref>
* [[Masalah persegi dalam]], juga dikenal sebagai [[konjektur Toeplitz]] – apakah setiap [[kurva Jordan]] memilik sebuah persegi dalam?<ref name="matschke">{{citation|last=Matschke|first=Benjamin|date=2014|title=A survey on the square peg problem|journal=[[Notices of the American Mathematical Society]]|volume=61|issue=4|pages=346–352|doi=10.1090/noti1100|doi-access=free}}</ref>
* [[Konjektur Kakeya]] – apakah himpunan <math>n</math>-dimensi yang berisi sebuah ruas garis satuan dalam setiap arah selalu memiliki [[dimensi Hausdorff]] dan [[dimensi Minkowski]] sama dengan <math>n</math>?<ref>{{citation|last1=Katz|first1=Nets|author1-link=Nets Katz|last2=Tao|first2=Terence|author2-link=Terence Tao|department=Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000)|doi=10.5565/PUBLMAT_Esco02_07|issue=Vol. Extra|journal=Publicacions Matemàtiques|mr=1964819|pages=161–179|title=Recent progress on the Kakeya conjecture|year=2002|citeseerx=10.1.1.241.5335|s2cid=77088}}</ref>
* Masalah Kelvin pada partisi luas permukaan minimum dari ruang ke sel volume yang sama, dan and the optimalitas dari [[struktur Weaire–Phelan]] sebagai sebuah penyelesaian untuk masalah Kelvin<ref>{{citation|title=The Kelvin Problem|editor-first=Denis|editor-last=Weaire|editor-link=Denis Weaire|publisher=CRC Press|year=1997|isbn=9780748406326|page=1|url=https://books.google.com/books?id=otokU4KQnXIC&pg=PA1}}</ref>
* [[Masalah peliputan semesta Lebesgue]] pada bentuk cembung luas minimum dalam bidang yang dapat meliputi suatu bentuk diameter<ref>{{citation|last1=Brass|first1=Peter|last2=Moser|first2=William|last3=Pach|first3=János|location=New York|mr=2163782|page=457|publisher=Springer|title=Research problems in discrete geometry|url=https://books.google.com/books?id=cT7TB20y3A8C&pg=PA457|year=2005|isbn=9780387299297}}</ref>
* [[Konjektur Mahler]] pada darab dari volume [[benda cembung]] [[Titik simetri|simetrik terpusat]] dan [[Himpunan polar|polar]]<nowiki/>nya.<ref>{{Cite journal|last1=Mahler|first1=Kurt|title=Ein Minimalproblem für konvexe Polygone|journal=Mathematica (Zutphen) B|pages=118–127|year=1939}}</ref>
* [[Masalah cacing Moser]] – berapakah luasterkecil dari sebuah bentuk yang dapat meliputi setiap kurva panjang satuan dalam bidang?<ref>{{citation|last1=Norwood|first1=Rick|author1-link=Rick Norwood|last2=Poole|first2=George|last3=Laidacker|first3=Michael|doi=10.1007/BF02187832|issue=2|journal=[[Discrete and Computational Geometry]]|mr=1139077|pages=153–162|title=The worm problem of Leo Moser|volume=7|year=1992|doi-access=free}}</ref>
* [[Masalah sofa bergerak]] – berapa luas terbesar dari sebuah bentuk yang dapat diarahkan melalui sebuah lebar satuan koridor berbentuk huruf L?<ref>{{citation|last=Wagner|first=Neal R.|date=1976|title=The Sofa Problem|journal=The American Mathematical Monthly|doi=10.2307/2977022|jstor=2977022|volume=83|issue=3|pages=188–189|url=http://www.cs.utsa.edu/~wagner/pubs/corner/corner_final.pdf|access-date=2014-05-14|archive-url=https://web.archive.org/web/20150420160001/http://www.cs.utsa.edu/~wagner/pubs/corner/corner_final.pdf|archive-date=2015-04-20|url-status=live}}</ref>
* [[Masalah Shephard|Masalah Shephard (atau konjektur Dürer)]] – apakah setiap [[polihedron cembung]] memiliki sebuah [[Jaring (polihedron)|jaring]], atau pembukaan lipatan tepi yang sederhana?<ref>{{citation|last1=Demaine|first1=Erik D.|author1-link=Erik Demaine|last2=O'Rourke|first2=Joseph|author2-link=Joseph O'Rourke (professor)|date=2007|title=Geometric Folding Algorithms: Linkages, Origami, Polyhedra|title-link=Geometric Folding Algorithms|publisher=Cambridge University Press|contribution=Chapter 22. Edge Unfolding of Polyhedra|pages=306–338}}</ref><ref>{{Cite journal|last=Ghomi|first=Mohammad|date=2018-01-01|title=D &quot;urer&apos;s Unfolding Problem for Convex Polyhedra|journal=Notices of the American Mathematical Society|volume=65|issue=1|pages=25–27|doi=10.1090/noti1609|issn=0002-9920|doi-access=free}}</ref>
* [[Masalah Thomson]] – berapa konfigurasi energi minimum dari partikel pengelakan satu sama lain <math>n</math> pada sebuah bola satuan?<ref>{{citation|last=Whyte|first=L. L.|doi=10.2307/2306764|journal=The American Mathematical Monthly|mr=0050303|pages=606–611|title=Unique arrangements of points on a sphere|volume=59|issue=9|year=1952|jstor=2306764}}</ref>
* [[Seragam 5 politop]] – carilah dan golongkan himpunan sempurna dari bentuk-bentuk ini<ref>{{citation|url=http://www.openproblemgarden.org/op/convex_uniform_5_polytopes|work=Open Problem Garden|title=Convex uniform 5-polytopes|access-date=2016-10-04|date=May 24, 2012|author=ACW|archive-url=https://web.archive.org/web/20161005164840/http://www.openproblemgarden.org/op/convex_uniform_5_polytopes|archive-date=October 5, 2016|url-status=live}}.</ref>

=== Teori graf ===
==== Lintasan dan siklus dalam graf ====
* [[Konjektur Barnette]] bahwa setiap graf planar tiga terhubung dwipihak kubik memiliki sebuah siklus Hamilton<ref>{{citation
 | last = Florek | first = Jan
 | doi = 10.1016/j.disc.2010.01.018
 | issue = 10–11
 | journal = Discrete Mathematics
 | mr = 2601261
 | pages = 1531–1535
 | title = On Barnette's conjecture
 | volume = 310
 | year = 2010}}.</ref>
* [[Kekerasan graf|Konjektur kekerasan Chvátal]], bahwa terdapat sebuah bilangan <math>t</math> sehingga setiap graf keras-<math>t</math> adalah Hamilton<ref>{{citation
 | last1 = Broersma | first1 = Hajo
 | last2 = Patel | first2 = Viresh
 | last3 = Pyatkin | first3 = Artem
 | doi = 10.1002/jgt.21734
 | issue = 3
 | journal = Journal of Graph Theory
 | mr = 3153119
 | pages = 244–255
 | title = On toughness and Hamiltonicity of $2K_2$-free graphs
 | volume = 75
 | year = 2014}}</ref>
* [[Konjektur peliputan ganda siklus]] bahwa setiap yang tanpa jembatan, memiliki sebuah keluarga siklus yang termasuk setiap tepi dua kali<ref>{{citation
 | last = Jaeger | first = F.
 | contribution = A survey of the cycle double cover conjecture
 | doi = 10.1016/S0304-0208(08)72993-1
 | pages = 1–12
 | series = North-Holland Mathematics Studies
 | title = Annals of Discrete Mathematics 27 – Cycles in Graphs
 | volume = 27
 | year = 1985| isbn = 9780444878038
 }}.</ref>
* [[Konjektur Erdős–Gyárfás]] pada siklus dengan panjang pangkat dari dua dalam graf kubik<ref>{{citation|title=Erdös-Gyárfás conjecture for cubic planar graphs|first1=Christopher Carl|last1=Heckman|first2=Roi|last2=Krakovski|volume=20|issue=2|year=2013|at=P7|journal=Electronic Journal of Combinatorics|doi-access=free|doi=10.37236/3252}}.</ref>
* Konjektur [[arborisitas linear]] pada penguraian graf menjadi gabungan lepas lintasan menurut derajat maksimumnya<ref>{{citation
 | last1 = Akiyama | first1 = Jin | author1-link = Jin Akiyama
 | last2 = Exoo | first2 = Geoffrey
 | last3 = Harary | first3 = Frank
 | doi = 10.1002/net.3230110108
 | issue = 1
 | journal = Networks
 | mr = 608921
 | pages = 69–72
 | title = Covering and packing in graphs. IV. Linear arboricity
 | volume = 11
 | year = 1981}}.</ref>
* [[Konjektur Lovász]] pada lintasan Hamilton dalam graf simetrik<ref>[[László Babai|L. Babai]], [http://www.cs.uchicago.edu/research/publications/techreports/TR-94-10 Automorphism groups, isomorphism, reconstruction] {{Webarchive|url=https://web.archive.org/web/20070613201449/http://www.cs.uchicago.edu/research/publications/techreports/TR-94-10|date=2007-06-13}}, in ''Handbook of Combinatorics'', Vol. 2, Elsevier, 1996, 1447–1540.</ref>
* [[Masalah Oberwolfach]] di mana 2 graf beraturan memilik sifat bahwa sebuah graf sempurna pada jumlah puncak yang sama dapat diuraikan menjadi salinan tepi-lepas dari graf yang diberikan.<ref>{{citation
 | last1 = Lenz | first1 = Hanfried
 | last2 = Ringel | first2 = Gerhard
 | doi = 10.1016/0012-365X(91)90416-Y
 | issue = 1–3
 | journal = Discrete Mathematics
 | mr = 1140782
 | pages = 3–16
 | title = A brief review on Egmont Köhler's mathematical work
 | volume = 97
 | year = 1991}}</ref>
* [[Konjektur Szymanski]]

==== Pewarnaan and pelabelan graf ====
[[Image:Erdős–Faber–Lovász conjecture.svg|thumb|upright=1.2|Sebuah contoh dari konjektur Erdős–Faber–Lovász: sebuah graf dibentuk dari empat klik mengenai empat setiap verteks, suatu dua yang memotong dalam sebuah verteks tunggal, dapat menjadi empat berwarna.]]
* [[Konjektur Cereceda]] pada diameter dari ruang pewarnaan graf merosot<ref>{{citation
 | last1 = Bousquet | first1 = Nicolas
 | last2 = Bartier | first2 = Valentin
 | editor1-last = Bender | editor1-first = Michael A.
 | editor2-last = Svensson | editor2-first = Ola
 | editor3-last = Herman | editor3-first = Grzegorz
 | contribution = Linear Transformations Between Colorings in Chordal Graphs
 | doi = 10.4230/LIPIcs.ESA.2019.24
 | pages = 24:1–24:15
 | publisher = Schloss Dagstuhl - Leibniz-Zentrum für Informatik
 | series = LIPIcs
 | title = 27th Annual European Symposium on Algorithms, ESA 2019, September 9-11, 2019, Munich/Garching, Germany
 | volume = 144
 | year = 2019| s2cid = 195791634
 }}</ref>
* [[Konjektur Erdős–Faber–Lovász]] pada gabungan pewarnaan klik<ref>{{citation
 | last1 = Chung | first1 = Fan | author-link1 = Fan Chung
 | last2 = Graham | first2 = Ron | author-link2 = Ronald Graham
 | title = Erdős on Graphs: His Legacy of Unsolved Problems
 | year = 1998
 | publisher = A K Peters
 | pages = 97–99}}.</ref>
* [[Konjektur Gyárfás–Sumner]] pada keterbatasan <math>\chi</math> dari graf dengan sebuah pohon terimbas yang dliarang<ref>{{citation
 | last1 = Chudnovsky | first1 = Maria | author1-link = Maria Chudnovsky
 | last2 = Seymour | first2 = Paul | author2-link = Paul Seymour (mathematician)
 | doi = 10.1016/j.jctb.2013.11.002
 | journal = [[Journal of Combinatorial Theory]]
 | mr = 3171779
 | pages = 11–16
 | series = Series B
 | title = Extending the Gyárfás-Sumner conjecture
 | volume = 105
 | year = 2014| doi-access = free
 }}</ref>
* [[Konjektur Hadwiger (teori graf)|Konjektur Hadwiger]] mengaitkan pewarnaan untuk minor klik<ref>{{citation
 | last = Toft | first = Bjarne
 | journal = Congressus Numerantium
 | mr = 1411244
 | pages = 249–283
 | title = A survey of Hadwiger's conjecture
 | volume = 115
 | year = 1996}}.</ref>
* [[Masalah Hadwiger–Nelson]] pada bilangan kromatik dari graf jarak satuan<ref>{{citation
 | last1 = Croft | first1 = Hallard T.
 | last2 = Falconer | first2 = Kenneth J.
 | last3 = Guy | first3 = Richard K. | author-link3 = Richard K. Guy
 | title = Unsolved Problems in Geometry
 | publisher = Springer-Verlag
 | year = 1991}}, Problem G10.</ref>
* [[Konjektur pewarnaan Jaeger's Petersen]] bahwa setiap grafik kubik takberjembantan memiliki sebuah pemetaan siklus-kontinu ke graf Petersen<ref>{{citation
 | last1 = Hägglund
 | first1 = Jonas
 | last2 = Steffen
 | first2 = Eckhard
 | issue = 1
 | journal = Ars Mathematica Contemporanea
 | mr = 3047618
 | pages = 161–173
 | title = Petersen-colorings and some families of snarks
 | url = http://amc-journal.eu/index.php/amc/article/viewFile/288/247
 | volume = 7
 | year = 2014
 | doi = 10.26493/1855-3974.288.11a
 | access-date = 2016-09-30
 | archive-url = https://web.archive.org/web/20161003070647/http://amc-journal.eu/index.php/amc/article/viewFile/288/247
 | archive-date = 2016-10-03
 | url-status = live
 | doi-access = free
 }}.</ref>
* [[Daftar pewarnaan konjektur]] bahwa, untuk setiap grad, daftar kromatik indeks sama dengan indeks kromatik<ref>{{citation|last1=Jensen|first1=Tommy R.|last2=Toft|first2=Bjarne|year=1995|title=Graph Coloring Problems|location=New York|publisher=Wiley-Interscience|isbn=978-0-471-02865-9|chapter=12.20 List-Edge-Chromatic Numbers|pages=201–202}}.</ref>
* [[Konjektur pewarnaan total]] Behzad dan Vizing bahwa bilangan kromatik total paling banyak dua ditambah derajat maksimum<ref>{{citation
 | last1 = Molloy | first1 = Michael
 | last2 = Reed | first2 = Bruce | author1-link = Bruce Reed (mathematician)
 | doi = 10.1007/PL00009820
 | issue = 2
 | journal = [[Combinatorica]]
 | mr = 1656544
 | pages = 241–280
 | title = A bound on the total chromatic number
 | volume = 18
 | year = 1998| citeseerx = 10.1.1.24.6514
 | s2cid = 9600550
 }}.</ref>

==== Gambaran graf ====
* [[Konjektur Albertson]] yang bilangan penyilangan dapat menjadi bawah terbatas oleh bilangan penyilangan mengenai sebuah [[graf lengkap]]<nowiki/>dengan [[bilangan kromatik]] yang sama<ref>{{citation|first1=János|last1=Barát|first2=Géza|last2=Tóth|year=2010|title=Towards the Albertson Conjecture|arxiv=0909.0413|journal=Electronic Journal of Combinatorics|volume=17|issue=1|page=R73|bibcode=2009arXiv0909.0413B|doi-access=free|doi=10.37236/345}}.</ref>
* [[Konjektur Blankenship–Oporowski]] pada ketebalam buku mengenai subpembagian<ref>{{citation|url=http://www.openproblemgarden.org/op/book_thickness_of_subdivisions|work=Open Problem Garden|title=Book Thickness of Subdivisions|access-date=2013-02-05|date=January 19, 2009|first=David|last=Wood|archive-url=https://web.archive.org/web/20130916170733/http://www.openproblemgarden.org/op/book_thickness_of_subdivisions|archive-date=September 16, 2013|url-status=live}}.</ref>
* [[Konjektur thrackle Conway|Konjektur ''thrackle'' Conway]]<ref>{{citation |last1=Fulek |first1=R. |last2=Pach |first2=J. |title=A computational approach to Conway's thrackle conjecture|journal= Computational Geometry |volume=44 |year=2011|issue=6–7 |pages=345–355 |mr=2785903 |doi=10.1007/978-3-642-18469-7_21|arxiv=1002.3904 }}.</ref>
* [[Konjektur Harborth]] bahwa setiap graf planar dapat digabar dengan panjang sisi bilangan bulat<ref>{{citation|title=Pearls in Graph Theory: A Comprehensive Introduction|title-link= Pearls in Graph Theory |series=Dover Books on Mathematics|last1=Hartsfield|first1=Nora|last2=Ringel|first2=Gerhard|author2-link=Gerhard Ringel|publisher=Courier Dover Publications|year=2013|isbn=978-0-486-31552-2|at=[https://books.google.com/books?id=VMjDAgAAQBAJ&pg=PA247 p. 247]|mr=2047103}}.</ref>
* [[Konjektur Negami]] pada pembenaman graf-projektif mengenai graf dengan liput planar<ref>{{citation | last = Hliněný | first = Petr | doi = 10.1007/s00373-010-0934-9 | issue = 4 | journal = [[Graphs and Combinatorics]] | mr = 2669457 | pages = 525–536 | title = 20 years of Negami's planar cover conjecture | url = http://www.fi.muni.cz/~hlineny/papers/plcover20-gc.pdf | volume = 26 | year = 2010 | citeseerx = 10.1.1.605.4932 | s2cid = 121645 | access-date = 2016-10-04 | archive-url = https://web.archive.org/web/20160304030722/http://www.fi.muni.cz/~hlineny/papers/plcover20-gc.pdf | archive-date = 2016-03-04 | url-status = live }}.</ref>
* [[Konjektur Papadimitriou–Ratajczak kuat]] bahwa setiap graf polihedral memiliki sebuah pembenaman serakah cembung<ref>{{citation | last1 = Nöllenburg | first1 = Martin | last2 = Prutkin | first2 = Roman | last3 = Rutter | first3 = Ignaz | doi = 10.20382/jocg.v7i1a3 | issue = 1 | journal = [[Journal of Computational Geometry]] | mr = 3463906 | pages = 47–69 | title = On self-approaching and increasing-chord drawings of 3-connected planar graphs | volume = 7 | year = 2016| arxiv = 1409.0315 }}</ref>
* [[Masalah pabrik batu bata Turán]] – Apakah terdapat sebuah gambaran mengenai suatu graf dwipihak lengkap dengan penyilangan lebih sedikit daripada bilangan yang diberikan oleh Zarankiewicz?<ref>{{citation | last1 = Pach | first1 = János | author1-link = János Pach | last2 = Sharir | first2 = Micha | author2-link = Micha Sharir | contribution = 5.1 Crossings—the Brick Factory Problem | pages = 126–127 | publisher = [[American Mathematical Society]] | series = Mathematical Surveys and Monographs | title = Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures | volume = 152 | year = 2009}}.</ref>
* [[Himpunan titik semesta]] mengenai ukuran subkuadrat untuk graf planar<ref>{{citation | last1 = Demaine | first1 = E. | author1-link = Erik Demaine | last2 = O'Rourke | first2 = J. | author2-link = Joseph O'Rourke (professor) | contribution = Problem 45: Smallest Universal Set of Points for Planar Graphs | title = The Open Problems Project | url = http://cs.smith.edu/~orourke/TOPP/P45.html | year = 2002–2012 | access-date = 2013-03-19 | archive-url = https://web.archive.org/web/20120814154255/http://cs.smith.edu/~orourke/TOPP/P45.html | archive-date = 2012-08-14 | url-status = live }}.</ref>
==== Wakilan kata graf ====
*Mengkarakteristik [[graf planar]] [[Graf kata terwakilkan|kata (tak-)terwakilkan]]<ref name="KL15"/><ref name="K17">[[arxiv:1705.05924|S. Kitaev. A comprehensive introduction to the theory of word-representable graphs. In: É. Charlier, J. Leroy, M. Rigo (eds), Developments in Language Theory. DLT 2017. Lecture Notes Comp. Sci. 10396, Springer, 36−67.]]</ref><ref name="KP18"/><ref name="KP18-2"/>
*Mengkarakteristik [[Graf kata terwakilkan|kata terwakilkan]] triangulasi dekat berisi graf lengkap <math>K_4</math> (seperti sebuah karakterisasi dikenal untuk graf planar <math>K_4</math><ref name="Glen2019">{{cite arxiv |eprint=1605.01688|author1=Marc Elliot Glen|title=Colourability and word-representability of near-triangulations|class=math.CO|year=2016}}</ref>)
*Menggolongkan graf dengan bilangan wakilan 3, yaitu, graf yang dapat [[Graf kata terwakilkan|diwakili]] menggunakan 3 salinan setiap huruf, tapi tidak dapat diwakili menggunakan 2 salinan setiap huruf <ref name="Kit2013-3-repr">[[arxiv:1403.1616|S. Kitaev. On graphs with representation number 3, J. Autom., Lang. and Combin. 18 (2013), 97−112.]]</ref>
*Apakah [[graf garis]] mengenai sebuah [[Graf kata terwakilkan|graf kata takterwakilkan]] selalu [[Grup kata terwakilkan|kata takterwakilkan]]? <ref name="KL15"/><ref name="K17"/><ref name="KP18"/><ref name="KP18-2"/>
*Apakah terdapat suatu graf pada <math>n</math> verteks yang [[Grup kata wakilan|wakilannya]] membutuhkan lebih dari <math>\left \lfloor \frac{n}{2} \right \rfloor</math> salinan setiap huruf? <ref name="KL15"/><ref name="K17"/><ref name="KP18"/><ref name="KP18-2">[http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=da&paperid=894&option_lang=rus С. В. Китаев, А. В. Пяткин. Графы, представимые в виде слов. Обзор результатов, Дискретн. анализ и исслед. опер., 2018, том 25,номер 2, 19−53]</ref>
*Apakah benar bahwa dari semua [[graf mahkota]], [[graf dwipihak]] membutuhkan kata terwakilkan terpanjang? <ref name="GKP18">{{cite journal|url = https://www.sciencedirect.com/science/article/pii/S0166218X18301045 | doi=10.1016/j.dam.2018.03.013 | volume=244 | title=On the representation number of a crown graph | year=2018 | journal=Discrete Applied Mathematics | pages=89–93 | last1 = Glen | first1 = Marc | last2 = Kitaev | first2 = Sergey | last3 = Pyatkin | first3 = Artem| s2cid=46925617 }}</ref>
*Mengkarakteristik [[graf kata terwakilkan]] dalam hal subgraf terlarang (terimbas).<ref name="KL15"/><ref name="K17"/><ref name="KP18"/><ref name="KP18-2"/>
*Masalah (sulit) mana pada graf dapat diterjemahkan ke kata yang [[Graf kata terwakilkan|mewakilkan]]<nowiki/>nya dan diselesaikan pada kata-kata (dengan efisien)? <ref name="KL15">[https://www.springer.com/la/book/9783319258577 S. Kitaev and V. Lozin. Words and Graphs, Springer, 2015.]</ref><ref name="K17"/><ref name="KP18">[https://link.springer.com/article/10.1134/S1990478918020084 S. Kitaev and A. Pyatkin. Word-representable graphs: a Survey, Journal of Applied and Industrial Mathematics 12(2) (2018) 278−296.]</ref><ref name="KP18-2"/>

==== Teori graf lainnya ====
* [[Masalah 99-graf Conway]]: apakah ada sebuah [[graf beraturan kuat]] dengan parameter <math>(99,14,1,2)</math>?<ref>{{citation
 | last = Conway
 | first = John H.
 | author-link = John Horton Conway
 | access-date = 2019-02-12
 | publisher = Online Encyclopedia of Integer Sequences
 | title = Five $1,000 Problems (Update 2017)
 | url = https://oeis.org/A248380/a248380.pdf
 | archive-url = https://web.archive.org/web/20190213123825/https://oeis.org/A248380/a248380.pdf
 | archive-date = 2019-02-13
 | url-status = live
 }}</ref>
* [[Konjektur Erdős–Hajnal]] pada klik besar atau himpunan bebas dalam graf dengan sebuah subgraf terimbas terlarang<ref>{{citation
 | last = Chudnovsky
 | first = Maria
 | author-link = Maria Chudnovsky
 | arxiv = 1606.08827
 | doi = 10.1002/jgt.21730
 | issue = 2
 | journal = Journal of Graph Theory
 | mr = 3150572
 | zbl = 1280.05086
 | pages = 178–190
 | title = The Erdös–Hajnal conjecture—a survey
 | url = http://www.columbia.edu/~mc2775/EHsurvey.pdf
 | volume = 75
 | year = 2014
 | s2cid = 985458
 | access-date = 2016-09-22
 | archive-url = https://web.archive.org/web/20160304102611/http://www.columbia.edu/~mc2775/EHsurvey.pdf
 | archive-date = 2016-03-04
 | url-status = live
 }}.</ref>
* [[Konjektur GNRS]] mengenai apakah keluarga graf minor tertutup memiliki pembenaman <math>\ell_1</math> dengan distorsi terbatas<ref>{{citation
 | last1 = Gupta | first1 = Anupam
 | last2 = Newman | first2 = Ilan
 | last3 = Rabinovich | first3 = Yuri
 | last4 = Sinclair | first4 = Alistair | author4-link = Alistair Sinclair
 | doi = 10.1007/s00493-004-0015-x
 | issue = 2
 | journal = [[Combinatorica]]
 | mr = 2071334
 | pages = 233–269
 | title = Cuts, trees and <math>\ell_1</math>-embeddings of graphs
 | volume = 24
 | year = 2004| citeseerx = 10.1.1.698.8978
 | s2cid = 46133408
 }}</ref>
* [[Konjektur kerikil Graham]] pada bilangan kerikil mengenai produk Cartesius dari graf<ref>{{citation
 | last = Pleanmani | first = Nopparat
 | doi = 10.1142/s179383091950068x
 | issue = 6
 | journal = Discrete Mathematics, Algorithms and Applications
 | mr = 4044549
 | page = 1950068, 7
 | title = Graham's pebbling conjecture holds for the product of a graph and a sufficiently large complete bipartite graph
 | volume = 11
 | year = 2019}}</ref>
* Konjektur graf implisit pada keberadaan mengenai wakilan implisit untuk [[Sifat turunan#Dalam teori graf|keluarga graf turunan]] yang bertumbuh dengan menurun<ref>{{citation|first=Jeremy P.|last=Spinrad|title=Efficient Graph Representations|year=2003|isbn=978-0-8218-2815-1|chapter=2. Implicit graph representation|pages=17–30|chapter-url=https://books.google.com/books?id=RrtXSKMAmWgC&pg=PA17}}.</ref>
* Konjektur Jørgensen bahwa setiap graf minor bebas <math>K_6</math> terhubung 6 verteks adalah sebuah [[graf puncak]]<ref>{{citation|url=http://www.openproblemgarden.org/op/jorgensens_conjecture|title=Jorgensen's Conjecture|work=Open Problem Garden|access-date=2016-11-13|archive-url=https://web.archive.org/web/20161114232136/http://www.openproblemgarden.org/op/jorgensens_conjecture|archive-date=2016-11-14|url-status=live}}.</ref>
* Konjektur Meyniel bahwa [[bilangan polisi]] adalah <math>O(\sqrt n)</math><ref>{{citation
 | last1 = Baird | first1 = William
 | last2 = Bonato | first2 = Anthony
 | arxiv = 1308.3385
 | doi = 10.4310/JOC.2012.v3.n2.a6
 | issue = 2
 | journal = Journal of Combinatorics
 | mr = 2980752
 | pages = 225–238
 | title = Meyniel's conjecture on the cop number: a survey
 | volume = 3
 | year = 2012| s2cid = 18942362
 }}</ref>
* Apakah sebuah [[graf Moore]] dengan ketebalan 5 dan derajat 57 ada?<ref>{{citation|last=Ducey|first=Joshua E.|doi=10.1016/j.disc.2016.10.001|issue=5|journal=[[Discrete Mathematics (journal)|Discrete Mathematics]]|mr=3612450|pages=1104–1109|title=On the critical group of the missing Moore graph|volume=340|year=2017|arxiv=1509.00327|s2cid=28297244}}</ref>
* Berapa kemungkinan terbesar [[lebar lintasan]] [[graf kubik]] verteks-<math>n</math>?<ref>{{citation
 | last1 = Fomin | first1 = Fedor V.
 | last2 = Høie | first2 = Kjartan
 | doi = 10.1016/j.ipl.2005.10.012
 | issue = 5
 | journal = Information Processing Letters
 | mr = 2195217
 | pages = 191–196
 | title = Pathwidth of cubic graphs and exact algorithms
 | volume = 97
 | year = 2006}}</ref>
* [[Konjektur rekonstruksi]] dan [[konjektur rekonstruksi digraf baru]] mengenai apakah sebuah graf secara unik ditentukan oleh subgraf verteks terhapuskannya.<ref>{{citation|first=Allen|last=Schwenk|title=Some History on the Reconstruction Conjecture|year=2012|url=http://faculty.nps.edu/rgera/conjectures/jmm2012/Schwenk,%20%20Some%20History%20on%20the%20RC.pdf|work=Joint Mathematics Meetings|access-date=2018-11-26|archive-url=https://web.archive.org/web/20150409233306/http://faculty.nps.edu/rgera/Conjectures/jmm2012/Schwenk,%20%20Some%20History%20on%20the%20RC.pdf|archive-date=2015-04-09|url-status=live}}</ref><ref>{{citation
 | last = Ramachandran | first = S.
 | doi = 10.1016/S0095-8956(81)80019-6
 | issue = 2
 | journal = Journal of Combinatorial Theory
 | mr = 630977
 | pages = 143–149
 | series = Series B
 | title = On a new digraph reconstruction conjecture
 | volume = 31
 | year = 1981| doi-access = free
 }}</ref>
* [[Masalah lingkungan kedua]]: apakah setiap graf terorientasi berisi sebuah verteks untuk yang terdapat setidaknya verteks lainnya di jarak dua sebagai di jarak satu?<ref>[https://faculty.math.illinois.edu/~west/openp/2ndnbhd.html Seymour's 2nd Neighborhood Conjecture] {{Webarchive|url=https://web.archive.org/web/20190111175310/https://faculty.math.illinois.edu/~west/openp/2ndnbhd.html|date=2019-01-11}}, Open Problems in Graph Theory and Combinatorics, [[Douglas West (mathematician)|Douglas B. West]].</ref>
* Apaskah terdapat [[graf geodetik]] [[Graf beraturan kuat|beraturan kuat]], atau suatu graf geodetik beraturan kuat yang bukan merupakan graf Moore?<ref>{{citation
 | last1 = Blokhuis | first1 = A.
 | last2 = Brouwer | first2 = A. E. | author-link = Andries Brouwer
 | doi = 10.1007/BF00191941
 | issue = 1–3
 | journal = [[Geometriae Dedicata]]
 | mr = 925851
 | pages = 527–533
 | title = Geodetic graphs of diameter two
 | volume = 25
 | year = 1988| s2cid = 189890651
 }}</ref>
* [[Konjektur Sumner]]: apakah setiap turnamen <math>(2n-2)</math>-verteks berisi sebuah subgraf setiap pohon berorientasi verteks-<math>n</math>?<ref>{{citation
 | last1 = Kühn | first1 = Daniela | author1-link = Daniela Kühn
 | last2 = Mycroft | first2 = Richard
 | last3 = Osthus | first3 = Deryk
 | arxiv = 1010.4430
 | doi = 10.1112/plms/pdq035
 | issue = 4
 | journal = Proceedings of the London Mathematical Society | series = Third Series
 | mr = 2793448 | zbl=1218.05034
 | pages = 731–766
 | title = A proof of Sumner's universal tournament conjecture for large tournaments
 | volume = 102
 | year = 2011| s2cid = 119169562 }}.</ref>
* Konjektur Tutte bahwa setiap graf tanpa jembatan memiliki sebuah [[Alir nol di mana-mana|5-alir nol di mana-mana]] dan setiap graf tanpa jembatan bebas-[[Minor graf|minor]]-[[Graf Petersen|Petersen]] memiliki sebuah 4-alir nol di mana-mana<ref>[http://www.openproblemgarden.org/op/4_flow_conjecture 4-flow conjecture] {{Webarchive|url=https://web.archive.org/web/20181126134908/http://www.openproblemgarden.org/op/4_flow_conjecture |date=2018-11-26 }} and [http://www.openproblemgarden.org/op/5_flow_conjecture 5-flow conjecture] {{Webarchive|url=https://web.archive.org/web/20181126134833/http://www.openproblemgarden.org/op/5_flow_conjecture |date=2018-11-26 }}, Open Problem Garden</ref>
* [[Konjektur Vizing]] pada [[bilangan dominasi]] mengenai [[produk Cartesius dari graf]]<ref>{{citation
 | last1 = Brešar | first1 = Boštjan
 | last2 = Dorbec | first2 = Paul
 | last3 = Goddard | first3 = Wayne
 | last4 = Hartnell | first4 = Bert L.
 | last5 = Henning | first5 = Michael A.
 | last6 = Klavžar | first6 = Sandi
 | last7 = Rall | first7 = Douglas F.
 | doi = 10.1002/jgt.20565
 | issue = 1
 | journal = Journal of Graph Theory
 | mr = 2864622
 | pages = 46–76
 | title = Vizing's conjecture: a survey and recent results
 | volume = 69
 | year = 2012| citeseerx = 10.1.1.159.7029
 }}.</ref>
* [[Masalah Zarankiewicz]]

=== [[Teori grup]] ===
[[File:FreeBurnsideGroupExp3Gens2.png|thumb|350px|right|[[Grup Burnside bebas]] <math>B(2,3)</math> adalah terhingga; dalam [[graf Cayley]]<nowiki/>nya, ditunjukkan disini, setiap 27 unsur diwakili oleh sebuah verteks. Pertanyaannya yang mana grup <math>B(m,n)</math> lainnya terhingga tetap terbuka.]]
* Apakah setiap [[grup periodik]] [[Grup disajikan hingga|disajikan hingga]] adalah terhingga?
* [[Masalah Galois balikan]]: apakah setiap grup hingga adalah grup Galois mengenai sebuah perluasan Galois dari rasional?
* Untuk yang bilangan bulat positif <math>m</math>, <math>n</math> adalah [[grup Burnside bebas]] <math>B(m,n)</math> terhingga? Khususnya, apakah <math>B(2,5)</math> terhingga?
* Apakah setiap grup [[Grup surjungtif|surjungtif]]?
* [[Konjektur Andrews–Curtis]]
* [[Konjektur Herzog–Schönheim]]
* Apakah [[Cahaya bulan mengerikan#Cahaya bulan rampat|cahaya bulan rampat]] ada?
* Apakah terdapat bilangan takhingga mengenai [[grup Leinster]]?
* [[Konjektur Guralnick–Thompson]]<ref>{{citation |last=Aschbacher |first=Michael |author-link=Michael Aschbacher |title=On Conjectures of Guralnick and Thompson |journal=[[Journal of Algebra]] |volume=135 |issue=2 |pages=277–343 |year=1990 |doi=10.1016/0021-8693(90)90292-V}}</ref>
* [[Masalah dalam teori gelung dan teori kuasigrup]] menganggap rampat grup
* ''[[Kourovka Notebook]]'' merupakan sebuah kumpulan masalah yang belum terpecahkan dalam teori grup, diterbitkan pertama pada tahun 1965 dan diperbarui berkali-kali sejak.<ref>{{citation
 | last1 = Khukhro | first1 = Evgeny I.
 | last2 = Mazurov | first2 = Victor D. |author-link2 = Victor Mazurov
 | arxiv = 1401.0300v16
 | title = Unsolved Problems in Group Theory. The Kourovka Notebook
 | year = 2019}}</ref>

=== Teori model dan bahasa formal ===
* [[Konjektur Vaught]]
* [[Grup stabil|Konjektur Cherlin–Zilber]] : Sebuah grup sederhana yang teori tingkat pertama adalah [[Teori stabil|stabil]] di <math>\aleph_0</math> merupakan sebuah grup aljabar sederhana atas sebuah medan tertutup secara aljabar.
* Konjektur Celah Utama, misalnya untuk [[teori tingkat pertama]] taktercacahkan, untuk [[kelas elementer abstrak]], dan untuk model jenuh <math>\aleph_1</math> mengenai sebuah teori tercacahkan.<ref name=":0">Shelah S, ''Classification Theory'', North-Holland, 1990</ref>
* Menentukan struktur tingkat Keisler<ref>{{cite journal | last1 = Keisler | first1 = HJ | year = 1967 | title = Ultraproducts which are not saturated | journal = J. Symb. Log. | volume = 32 | issue = 1| pages = 23–46 | doi=10.2307/2271240| jstor = 2271240 }}</ref><ref>[[Maryanthe Malliaris|Malliaris M]], [[Saharon Shelah|Shelah S]], "A dividing line in simple unstable theories." https://arxiv.org/abs/1208.2140 {{Webarchive|url=https://web.archive.org/web/20170802171447/https://arxiv.org/abs/1208.2140|date=2017-08-02}}</ref>
* Konjektur medan stabil: setiap medan takhingga dengan sebuah teori tingkat pertama [[Teori stabil|stabil]] tertutup secara terpisah.
* Apakah teori dari medan deret Laurent atas <math>\mathbb{Z}_p</math> [[Decidability (logic)|terputuskan]]? dari medan polinomial atas <math>\mathbb{C}</math>?
* Apakah teori monadik Borel dari terputuskan tingkat real? Apakah teori monadik mengenai terputuskan secara konsisten urutan rapi?<ref>Gurevich, Yuri, "Monadic Second-Order Theories," in [[Jon Barwise|J. Barwise]], [[Solomon Feferman|S. Feferman]], eds., ''Model-Theoretic Logics'' (New York: Springer-Verlag, 1985), 479–506.</ref>
* Konjektur Bercabang Dua Stabil untuk teori sederhana<ref>{{cite journal | last1 = Peretz | first1 = Assaf | year = 2006 | title = Geometry of forking in simple theories | url = https://archive.org/details/sim_journal-of-symbolic-logic_2006-03_71_1/page/347 | journal =  Journal of Symbolic Logic| volume = 71 | issue = 1| pages = 347–359 | doi=10.2178/jsl/1140641179| arxiv = math/0412356| s2cid = 9380215 }}</ref>
* Untuk yang medan bilangan apakah [[masalah kesepuluh Hilbert]] berlaku?
* Asumsi <math>K</math> adalah kelas model teori tingkat pertama tercacahkan menghilangkan banyajk [[Tipe (teori model)|tipe]] tercacah. Jika <math>K</math> memilki sebuah model kekardinalan <math>\aleph_{\omega_1}</math>, apakah ini mempunyai sebuah model kontinum kekardinalan?<ref>{{cite journal |last=Shelah |first=Saharon |author-link=Saharon Shelah |date=1999 |title=Borel sets with large squares |journal=[[Fundamenta Mathematicae]] |arxiv=math/9802134 |volume=159 |issue=1 |pages=1–50|bibcode=1998math......2134S |doi=10.4064/fm-159-1-1-50 |s2cid=8846429 }}</ref>
* Konjektur akhir kategoritas Shelah: Untuk setiap kardinal <math>\lambda</math>, terdapat sebuah kardinal <math>\mu(\lambda)</math> sehingga jika sebuah [[kelas elementer abstrak]] <math>K</math> dengan <math>\mathrm{LS}(K) \le \lambda</math> adalah  kategoris dalam sebuah kardinal di atas <math>\mu(\lambda)</math>, maka kategorisnya dalam semua kardinal di atas <math>\mu(\lambda)</math>.<ref name=":0" /><ref>{{Cite book
| title = Classification theory for abstract elementary classes
| last = Shelah
| first = Saharon
| publisher = College Publications
| year = 2009
| isbn = 978-1-904987-71-0
}}</ref>
* Konjektur kategoris Shelah untuk <math>L_{\omega_1,\omega}</math>:  Jika sebuah kalimat adalah kategoris di atas bilangan Hanf, maka kategorisnya di atas bilangan Hanf.<ref name=":0" />
* Apakah ada sebuah logika <math>L</math> yang memenuhi kedua sifat Beth dan interpolasi-<math>\Delta</math>, adalah kompak tapi tidak memenuhi sifat interpolasi?<ref>Makowsky J, "Compactness, embeddings and definability," in ''Model-Theoretic Logics'', eds Barwise and Feferman, Springer 1985 pps. 645–715.</ref>
* Jika kelas model atomik teori tingkat pertama lengkap adalah [[Kategoris (teori model)|kategoris]] dalam <math>\aleph_n</math>, apakah kategoris dalam setiap kardinal?<ref>{{cite book |last=Baldwin |first=John T. |date=July 24, 2009 |title=Categoricity |publisher=[[American Mathematical Society]] |isbn=978-0-8218-4893-7 |url=http://www.math.uic.edu/~jbaldwin/pub/AEClec.pdf |access-date=February 20, 2014 |archive-url=https://web.archive.org/web/20100729073738/http://www.math.uic.edu/%7Ejbaldwin/pub/AEClec.pdf |archive-date=July 29, 2010 |url-status=live }}</ref><ref>{{cite journal |last=Shelah |first=Saharon |title=Introduction to classification theory for abstract elementary classes |url=http://front.math.ucdavis.edu/0903.3428 |bibcode=2009arXiv0903.3428S |year=2009 |arxiv=0903.3428 }}{{Pranala mati|date=April 2021 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>
* Apakah setiap takhingga, medan minimal mengenai nol karakteristik [[Medan tertutup secara aljabar|tertutup secara aljabar]]? (Disini, "minimal" berarti bahwa setiap himpunan bagian terdefinisikan dari struktur adalah hingga atau ko-hingga.)
* Konjektur Kueker<ref>{{cite journal | last1 = Hrushovski | first1 = Ehud | year = 1989 | title = Kueker's conjecture for stable theories | url = https://archive.org/details/sim_journal-of-symbolic-logic_1989-03_54_1/page/207 | journal = Journal of Symbolic Logic | volume = 54 | issue = 1| pages = 207–220 | doi=10.2307/2275025| jstor = 2275025 }}</ref>
* Apakah terdapat sebuah teori tingkat pertama [[minimal-o]] dengan fungsi trans-eksponensial (bertumbuh dengan cepat)?
* Apakah sebuah struktur homogen disajikan untuk sebuah bahasa relasional hingga memiliki [[Pengurangan (teori model)|pengurangan]] ?
* Apakah [[graf Henson]] memiliki [[sifat model hingga]]?
* Masalah keuniversalan untuk graf bebas-<math>C</math>: Untuk yang himpunan hingga <math>C</math> mengenai graf, apakah kelas graf tercacahkan bebas-<math>C</math>memiliki sebuah anggota semesta terhadap pembenaman kuat?<ref>{{cite journal |last1=Cherlin |first1=G. |last2=Shelah |first2=S. |date=May 2007 |title=Universal graphs with a forbidden subtree |journal=[[Journal of Combinatorial Theory, Series B]] |arxiv=math/0512218 |doi=10.1016/j.jctb.2006.05.008 |volume=97 |issue=3 |pages=293–333|s2cid=10425739 }}</ref>
* Masalah spektrum keuniversalan: Apakah terdapat sebuah teori tingkat pertama yang spektrum keuniversalan adalah minimum?<ref>Džamonja, Mirna, "Club guessing and the universal models." ''On PCF'', ed. M. Foreman, (Banff, Alberta, 2004).</ref>
* [[Masalah tinggi bintang rampat]]
* [[Masalah fungsi eksponensial Tarski]]

=== Teori bilangan ===
==== Umum ====
[[File:Perfect number Cuisenaire rods 6.png|thumb|6 adalah sebuah [[bilangan sempurna]] karena ini adalah jumlah pembagi positif wajarnya, 1, 2 dan 3. Ini tidak diketahui berapa banyak bilangan sempurna, atau jika suatu dari mereka adalah ganjil.]]
*Apakah 10 sebuah [[Bilangan ramah#Bilangan sendirian|bilangan sendirian]]?
* Apakah π sebuah [[bilangan normal]] (digitnya "secara acak")?<ref>{{cite web|title=Are the Digits of Pi Random? Berkeley Lab Researcher May Hold Key|url=http://www2.lbl.gov/Science-Articles/Archive/pi-random.html|archive-url=https://web.archive.org/web/20160327035021/http://www2.lbl.gov/Science-Articles/Archive/pi-random.html|archive-date=2016-03-27|access-date=2016-03-18|url-status=live}}</ref>
* Apakah ada [[bilangan aneh]] ganjil?
* Apakah ada [[bilangan kuasisempurna]]?
* Apakah ada [[bilangan Lychrel]]?
* Apakah ada [[bilangan sempurna]] ganjil?
* Apakah ada bilangan [[Bilangan Taxicab rampat|Taxicab(5, 2, n)]] untuk <math>n>1</math>?
* Apakah terdapat pasangan [[bilangan bersahabat]] yang memiliki paritas yang berlawanan?
* Apakah terdapat suatu pasangan [[bilangan bersahabat]] [[Koprima (bilangan)|relatif prima]]?
* Apakah terdapat tak hingga banyaknya [[bilangan bersahabat]]?
* Apakah terdapat tak hingga banyaknya [[bilangan bertunangan]]?
* Apakah terdapat tak hingga banyaknya [[bilangan sempurna]]?
* Apakah terdapat suatu [[bilangan bertunangan]] yang memiliki paritas yang sama?
* Apakah terdapat sebuah [[sistem peliputan]] dengan moduli berbeda ganjil?<ref>{{citation|last1=Guo|first1=Song|last2=Sun|first2=Zhi-Wei|doi=10.1016/j.aam.2005.01.004|issue=2|journal=Advances in Applied Mathematics|mr=2152886|pages=182–187|title=On odd covering systems with distinct moduli|volume=35|year=2005|arxiv=math/0412217|s2cid=835158}}</ref>
* Bilangan bulat mana yang dapat ditulis sebagai [[Jumlah tiga kubik|jumlah tiga kubik sempurna]]?<ref>{{Cite arxiv|eprint=1604.07746v1|last1=Bruhn|first1=Henning|title=Newer sums of three cubes|last2=Schaudt|first2=Oliver|class=math.NT|year=2016}}</ref>
* [[Hipotesis Riemann]]
** [[Hipotesis Riemann Besar]]
** [[Hipotesis Riemann rampat]]
* [[Hipotesis Lindelöf]] dan akibatnya, [[hipotesis kerapatan]] untuk nol dari fungsi zeta Riemann (ilhat [[teorema Bombieri–Vinogradov]])
* [[Konjektur Beilinson]]
* [[Konjektur Casas–Alvero]]
* [[Barisan alikuot#Konjektur Catalan–Dickson|Konjektur Catalan–Dickson pada barisan alikuot]]
* [[Konjektur Erdős–Straus]]
* [[Konjektur fungsi phi Carmichael]]
* [[Konjektur Grimm]]
* [[Konjektur Goormaghtigh]]
* [[Konjektur Hall]]
* [[Konjektur Hilbert–Pólya]]
* [[Konjektur korelasi pasangan Montgomery]]
* [[Konjektur Keating–Snaith]] mengenai asimtotik integral melibatkan fungsi zeta Riemann<ref>{{citation|last=Conrey|first=Brian|author-link=Brian Conrey|doi=10.1090/bull/1525|title=Lectures on the Riemann zeta function (book review)|journal=[[Bulletin of the American Mathematical Society]]|volume=53|number=3|pages=507–512|year=2016|doi-access=free}}</ref>
* [[Bilangan Markov#Sifat-sifat lainnya|Konjektur ketunggalan untuk bilangan Markov]]<ref>{{citation|last=Aigner|first=Martin|doi=10.1007/978-3-319-00888-2|isbn=978-3-319-00887-5|location=Cham|mr=3098784|publisher=Springer|title=Markov's theorem and 100 years of the uniqueness conjecture|year=2013}}</ref>
* [[Konjektur Leopoldt]]
* [[Konjektur Littlewood]]
* [[Konjektur Newman]]
* [[Konjektur n|Konjektur ''n'']]
** [[Konjektur abc|Konjektur ''abc'']]
** [[Konjektur Szpiro]]
* [[Konjektur Pillai]]
* [[Metode Van der Corput#Pasangan eksponen|Konjektur pasangan eksponen]]
* [[Konjektur Sato–Tate]]
* [[Konjektur Scholz]]
* [[Konjektur Singmaster]]: apakah terdapat sebuah batas atas hingga pada perkalian dari entri-entri lebih besar dari 1 dalam [[segitiga Pascal]]?<ref>{{citation|last=Singmaster|first=D.|author-link=David Singmaster|doi=10.2307/2316907|mr=1536288|issue=4|journal=[[American Mathematical Monthly]]|pages=385–386|title=Research Problems: How often does an integer occur as a binomial coefficient?|volume=78|year=1971|jstor=2316907}}.</ref>
* [[Konjektur Vojta]]
* Masalah Erdős–Moser: apakah <math>1^1 + 2^1 = 3^1</math> hanyalah penyelesaian untuk [[persamaan Erdős–Moser]]?
* [[Masalah Brocard]]: keberadaan bilangan bulat, <math>(n,m)</math>, sehingga <math>n! + 1 = m^2</math> selain <math>n = 4, 5, 7</math>
* [[Masalah kesembilan Hilbert]]
* [[Masalah kesebelas Hilbert]]
* [[Masalah keduabelas Hilbert]]
* [[Masalah Erdős–Ulam]]
* [[Masalah bilangan kongruen]] (sebuah korolari untuk [[konjektur Birch and Swinnerton-Dyer]], per [[teorema Tunnell]])
* [[Masalah phi Lehmer]]: jika <math>\varphi(n)</math> membagi <math>n-1</math>, haruskah <math>n</math> menjadi bilangan prima?
* [[Masalah lingkaran Gauss]] – seberapa jauh jumlah titik bilangan bulat dalam sebuah lingkaran terpusat di asalnya dari luas lingkaran?
* Mencari nilai [[tetapan de Bruijn–Newman]]
* [[Fungsi penjumlahan pembagi#Masalah pembagi Piltz|Piltz divisor problem]], termasuk juga [[masalah pembagi Dirichlet]]

==== Teori bilangan aditif ====
{{See also|Masalah yang melibatkan barisan arimetik}}
* [[Konjektur Beal]]
* [[Konjektur Fermat–Catalan]]
* [[Konjektur Goldbach]]
* [[Konjektur Lemoine]]
* Nilai <math>g(k)</math> dan <math>G(k)</math> dalam [[masalah Waring]]
* [[Konjektur Lander, Parkin, dan Selfridge]]
* [[Konjektur Gilbreath]]
* [[Konjektur Erdős pada barisan aritmetik]]
* [[Konjektur Erdős–Turán pada dasar aditif]]
* [[Konjektur bilangan oktahedral Pollock]]
* [[Masalah Skolem]]
* Menentukan laju pertumbuhan <math>r_k(N)</math> (lihat [[teorema Szemerédi]])
* [[Masalah bertindih minimum]]
* Apakah [[bilangan Ulam]] memiliki sebuah kerapatan positif?

==== Teori bilangan aljabar ====
* Apakah terdapat banyaknya [[Masalah bilangan kelas#Medan kuadrat real|medan bilangan kuadrat]] dengan [[faktorisasi tunggal]] ([[Masalah bilangan kelas]])?
* Mencirikan semua medan bilangan aljabar yang memiliki suatu [[basis pangkat]].
* [[Konjektur Stark]] (termasuk [[konjektur Brumer–Stark]])
* [[Konjektur Kummer–Vandiver]]
* [[Konjektur Greenberg]]
* [[Masalah Hermite]]

==== Teori bilangan komputasi ====
* [[Faktorisasi bilangan bulat]]: Dapatkah faktorisasi bilangan bulat diselesaikan dalam waktu polinomial?

==== Bilangan prima ====
[[Image:Goldbach partitions of the even integers from 4 to 50 rev4b.svg|thumb=Goldbach_partitions_of_the_even_integers_from_4_to_28_300px.png|[[Konjektur Goldbach]] menyatakan bahwa semua bilangan bulat genap yang lebih besar daripada 2 dapat ditulis sebagai jumlah dua bilangan prima. Disini diilustrasikan untuk bilangan bulat genap dari 4 sampai dengan 28.]]
[[Bilangan prima]] adalah [[bilangan asli]] lebih besar daripada 1 dan tidak dapat ditulis sebagai perkalian dua bilangan asli yang lebih kecil dari bilangan tersebut. Bilangan prima berperan penting dalam teori bilangan karena [[teorema dasar aritmetika]] menyatakan bahwa setiap bilangan asli lebih besar daripada 1, dapat merupakan bilangan prima atau dapat difaktorkan sebagai perkalian bilangan-bilangan prima yang unik.

Beberapa masalah mengenai bilangan prima membahas tentang banyaknya bilangan prima yang memenuhi sifat tertentu. Secara spesifik, daftar berikut bertanya apakah jenis bilangan-bilangan prima berikut memiliki jumlah yang tak hingga:

{{columns-list|*[[bilangan prima Cullen]]
*[[bilangan prima Euklides]]
*[[bilangan prima Fibonacci]]
*[[bilangan prima kembar-tiga]]
*[[bilangan prima kembar-empat]]
*[[bilangan prima kluster]]
*[[bilangan prima Kummer]]
*[[bilangan prima Lucas]]
*[[bilangan prima Mersenne]]
*[[bilangan prima Newman–Shanks–Williams]]
*[[bilangan prima palindromik]] pada setiap basis
*[[bilangan prima Pell]]
*[[bilangan prima Pierpont]]
*[[bilangan prima reguler]] dan densitas relatifnya 
*[[bilangan prima seimbang]]
*[[bilangan prima seksi]]
*[[bilangan prima sepupu]]
*[[bilangan prima Sophie Germain]] dan [[bilangan prima aman|amannya]]
*[[bilangan prima Wagstaff]]
*[[bilangan prima Wieferich]]
*[[bilangan prima Wilson]]
*[[bilangan prima Wolstenholme]]
*[[bilangan prima Woodall]]
|colwidth=20em}}

Sedangkan beberapa masalah lain lebih dikenal dari nama konjekturnya, seperti:

{{columns-list|* [[Konjektur Agoh–Giuga]]
* [[Konjektur Artin pada akar-akar primitif]]
* [[Konjektur Brocard]]
* [[Konjektur Bunyakovsky]]
* [[Konjektur Dickson]]
* [[Konjektur Dubner]]
* [[Konjektur Elliott–Halberstam]]
*[[Konjektur Erdős–Mollin–Walsh]]
* [[Konjektur Feit–Thompson]]
* Konjektur Fortune (tidak ada [[bilangan Fortunate]] komposit)
* [[Konjektur Gillie]]
* [[Konjektur Goldbach]]
* [[Hipotesis H Schinzel]]
* [[Konjektur Mersenne Catalan]]
* [[Konjektur Mersenne#Konjektur Mersenne terbaru|Konjektur Mersenne terbaru]]
* [[Konjektur prima kembar]]
* [[Konjektur Polignac]]|colwidth=20em}}

Atau terlalu spesifik untuk mendapatkan nama khusus, seperti:
* Apakah 509,203 merupakan [[bilangan Riesel]] terendah?
* Apakah 78,557 merupakan [[bilangan Sierpiński]] terendah (disebut [[konjektur Selfridge]])?
* Apakah ada bilangan komposit <math>c</math> yang memenuhi <math>2^{c - 1} \equiv 1 \pmod {c^2}</math>?
* Apakah ada [[bilangan prima Wall–Sun–Sun]]?
* Apakah ada bilangan Wieferich dalam basis 47?
* Apakah konvers dari [[teorema Wolstenholme]] juga berlaku untuk semua bilangan asli?
* Apakah semua [[bilangan Euklides]] [[Bilangan kuadrat-bebas|kuadrat-bebas]]?
* Apakah semua [[bilangan Fermat]] kuadrat-bebas?
* Apakah semua bilangan Fermat <math>2^{2^n}+1</math> komposit untuk <math>n > 4</math>?
* Apakah semua [[bilangan prima Mersenne]] dengan indeks bilangan prima bersifat kuadrat-bebas?
* Apakah semua bilangan prima muncul di [[barisan Euclid–Mullin]]?
* Dapatkah sebuah bilangan prima <math>p</math> memenuhi <math>2^{p - 1} \equiv 1 \pmod {p^2}</math> dan <math>3^{p - 1} \equiv 1 \pmod {p^2}</math> secara serentak?<ref>{{cite arxiv|last=Dobson|first=J. B.|date=1 April 2017|title=On Lerch's formula for the Fermat quotient|eprint=1103.3907v6|page=23|mode=cs2|class=math.NT}}</ref>
* [[Masalah Landau]]
* Masalah [[parit Gauss]]: apakah mungkin untuk menemukan sebuah barisan takhingga dari [[bilangan prima Gauss]] yang berbeda sehingga beda di antara bilangan berurutan dalam barisan adalah terbatas?
* Masalah yang terkait dengan [[teorema Linnik]]
* Mencari [[bilangan Skewes]] terkecil
* Untuk suatu bilangan bulat <math>b</math> yang bukan sebuah pangkat sempurna dan bukan dari bentuk <math>-4k^4</math> untuk bilangan bulat <math>k</math>, apakah terdapat bilangan prima [[satuan berulang]] banyak untuk basis <math>b</math>?
* Untuk sembarang bilangan bulat <math>a>0</math>, apakah terdapat tak hingga banyaknya bilangan prima <math>p</math> sehingga <math>a^{p-1} \equiv 1 \pmod {p^2}</math>?<ref>{{cite book |last=Ribenboim |first=P. |author-link=Paulo Ribenboim |date=2006 |title=Die Welt der Primzahlen |edition=2nd |language=de |publisher=Springer |doi=10.1007/978-3-642-18079-8 |isbn=978-3-642-18078-1 |pages=242–243 |url=https://books.google.com/books?id=XMyzh-2SClUC&q=die+folgenden+probleme+sind+ungel%C3%B6st&pg=PA242|series=Springer-Lehrbuch }}</ref>
* Untuk sembarang bilangan bulat <math>a>0</math>, apakah terdapat tak hingga banyaknya [[bilangan prima Lucas–Wieferich]] yang berasosiasi dengan pasangan <math>(a, -1)</math>?
* Untuk sembarang bilangan bulat <math>a</math> non-kuadrat dan tidak sama dengan <math>-1</math>, apakah terdapat tak hingga banyaknya bilangan prima dengan <math>a</math> sebagai salah satu akar primitifnya?
* Untuk sembarang bilangan bulat <math>k\ge 1</math>, <math>b \ge 2</math>, <math>c \ne 0</math>, yang memenuhi <math>\gcd(k,c) = 1</math> dan <math>\gcd(b,c) = 1</math>, apakah terdapat tak hingga banyaknya bilangan prima yang memiliki bentuk <math display="inline">\frac{k \cdot b^n + c}{\gcd(k+c,b-1)}</math> dengan <math>n \ge 1</math> merupakan bilangan bulat?

=== Teori himpunan ===
* Masalah mencari [[model teras]], salah satunya yang berisi semua [[Sifat kardinal besar|kardinal besar]].
* Jika <math>\aleph_\omega</math> merupakan sebuah kardinal limit kuat, maka <math>2^{\aleph_\omega} < \aleph_{\omega_1}</math> (lihat [[Hipotesis kardinal tunggal]]). Batas terbaik, <math>\aleph_{\omega_4}</math>, diperoleh oleh [[saharon Shelah|Shelah]] menggunakan [[teori kofinalitas mungkin]]<nowiki/>nya.
* [[Logika-Ω|Hipotesis-Ω]] [[W. Hugh Woodin|Woodin]].
* Apakah [[kekonsistenan]] dari keberadaan [[kardinal kompak kuat]] menyiratkan keberadaan konsisten dari sebuah [[kardinal superkompak]]?
* ([[W. Hugh Woodin|Woodin]]) Apakah [[Hipotesis Kontinum Rampat]] di bawah sebuah [[kardinal kompak kuat]] menyiratkan [[Hipotesis Kontinum Rampat]] di mana-mana?
* Apakah ada sebuah [[Kardinal Jónsson|aljabar Jónsson]] pada <math>\aleph_\omega</math>?
* Tanpa mengasumsi [[aksioma pemilihan]], dapatkah sebuah [[Kardinal Reinhardt|pembenaman elementer taktrivial]] <math>V \to V</math> ada?
* Apakah [[Hipotesis Kontinum Rampat]] memerlukan [[Diamondsuit|<math>{\diamondsuit(E^{\lambda^+}_{\operatorname{cf}(\lambda)}})</math>]] untuk setiap [[kardinal tunggal]] <math>\lambda</math>?
* Apakah [[Hipotesis Kontinum Rampat]] menyiratkan keberadaan [[Pohon Suslin|pohon Suslin-ℵ<sub>2</sub>]]?
*Apakah [[aksioma pewarnaan buka]] konsisten dengan <math>2^{\aleph_{0}}>\aleph_{2}</math>?

=== Topologi ===
[[Image:Ochiai_unknot.svg|right|thumb|250px|[[Masalah ketaksimpulan]] menanyakan apakah terdapat sebuah algoritme yang efisien untuk mengidentifikasikan ketika bentuknay disajikan dalam sebuah [[diagram simpul]] sebenarnya [[tak simpul]] (''unknot'').]]

*[[Konjektur Baum–Connes]]
*[[Konjektur Bing–Borsuk]]
* [[Konjektur Borel]]
* [[Konjektur Hilbert–Smith]]
* [[Konjektur Mazur]]<ref>{{citation|last=Mazur|first=Barry|author-link=Barry Mazur|title=The topology of rational points|journal=[[Experimental Mathematics (journal)|Experimental Mathematics]]|volume=1|number=1|year=1992|pages=35–45|doi=10.1080/10586458.1992.10504244|url=https://projecteuclid.org/euclid.em/1048709114|access-date=2019-04-07|archive-url=https://web.archive.org/web/20190407161124/https://projecteuclid.org/euclid.em/1048709114|archive-date=2019-04-07|url-status=live|doi-broken-date=2021-01-14}}</ref>
* [[Konjektur Novikov]]
*[[Konjektur Ravenel|Konjektur teropong]]
* [[Masalah taksimpulan]] (''unknotting problem'')
* [[Konjektur volume]]
* [[Konjektur Whitehead]]
* [[Konjektur Zeeman]]

== Masalah terpecahkan sejak tahun 1995 ==
[[Image:Ricci flow.png|thumb|right|upright|200px|[[Alir Ricci]], yang diilustrasikan sebagai sebuah manifold 2D, merupakan alat utama dalam penyelesaian [[Grigori Perelman]] dari [[Konjektur Poincaré#Solusi|konjektur Poincaré]].]]

=== Aljabar ===
* [[Konjektur Suita]] (Qi'an Guan dan [[Xiangyu Zhou]], 2015) <ref>{{cite journal
 | jstor=24523356
 | last1=Guan
 | first1=Qi'an
 | last2=Zhou
 | first2=Xiangyu
 | author2-link=Xiangyu Zhou
 | title=A solution of an <math>L^2</math> extension problem with optimal estimate and applications
 | url=https://archive.org/details/sim_annals-of-mathematics_2015-05_181_3/page/n332
 | journal=Annals of Mathematics
 | year=2015
 | volume=181
 | issue=3
 | pages=1139–1208
 | doi=10.4007/annals.2015.181.3.6
 | s2cid=56205818
 | arxiv=1310.7169}}
</ref>
* [[Konjektur torsi]] ([[Loïc Merel]], 1996)<ref>{{cite journal
   |last1 = Merel |first1=Loïc
   |year = 1996
   |title ="Bornes pour la torsion des courbes elliptiques sur les corps de nombres" [Bounds for the torsion of elliptic curves over number fields]
   |journal = Inventiones Mathematicae
   |volume = 124
   |issue = 1
   |pages = 437–449
   |bibcode = 1996InMat.124..437M
   |doi = 10.1007/s002220050059
   |mr = 1369424
   |s2cid = 3590991}}</ref>
* [[Konjektur Carlitz–Wan]] ([[Hendrik Lenstra]], 1995)<ref>{{cite journal
 | last1=Cohen
 | first1=Stephen D.
 | last2=Fried
 | first2=Michael D.
 | author2-link=Michael D. Fried
 | doi=10.1006/ffta.1995.1027
 | issue=3
 | journal=Finite Fields and Their Applications
 | mr=1341953
 | pages=372–375
 | title=Lenstra's proof of the Carlitz–Wan conjecture on exceptional polynomials: an elementary version
 | volume=1
 | year=1995
 | doi-access=free}}
</ref>

=== Analisis ===

* [[Masalah Kadison–Singer]] ([[Adam Marcus (matematikawan)|Adam Marcus]], [[Daniel Spielman]] and [[Nikhil Srivastava]], 2013)<ref name="Casazza20062">{{cite book|last1=Casazza|first1=Peter G.|last2=Fickus|first2=Matthew|last3=Tremain|first3=Janet C.|last4=Weber|first4=Eric|date=2006|title=Large Deviations for Additive Functionals of Markov Chains: The 25th Great Plains Operator Theory Symposium, June 7–12, 2005, University of Central Florida, Florida|publisher=American Mathematical Society.|isbn=978-0-8218-3923-2|editor1-last=Han|editor1-first=Deguang|series=Contemporary Mathematics|volume=414|pages=299–355|contribution=The Kadison-Singer problem in mathematics and engineering: A detailed account|doi=10.1090/conm/414/07820|access-date=24 April 2015|editor2-last=Jorgensen|editor2-first=Palle E. T.|editor3-last=Larson|editor3-first=David Royal|contribution-url=https://books.google.com/books?id=9b-4uqEGJdoC&pg=PA299}}</ref><ref name="SIAM02.20142">{{cite news|last1=Mackenzie|first1=Dana|title=Kadison–Singer Problem Solved|url=https://www.siam.org/pdf/news/2123.pdf|work=SIAM News|publisher=[[Society for Industrial and Applied Mathematics]]|issue=January/February 2014|archive-url=https://web.archive.org/web/20141023120958/http://www.siam.org/pdf/news/2123.pdf|archive-date=23 October 2014|access-date=24 April 2015|url-status=live}}</ref> (dan [[Hans Georg Feichtinger#Konjektur Feichtinger|konjektur Feichtinger]], konjektur trotoar Anderson, konjektur <math>KS_r</math> dan <math>KS'_r</math> ahli teori ketakcocokan Weaver, konjektur Bourgain-Tzafriri dan konjektur-<math>R_\epsilon</math>)
* [[Konjektur Ahlfors|Konjektur ukuran Ahlfors]] ([[Ian Agol]], 2004)<ref name="Agol">{{cite arXiv|eprint=math/0405568|last1=Agol|first1=Ian|title=Tameness of hyperbolic 3-manifolds|year=2004}}</ref>
* [[Konjektur gradien]] (Krzysztof Kurdyka, Tadeusz Mostowski, Adam Parusinski, 1999)<ref>{{Cite journal|last1=Kurdyka|first1=Krzysztof|last2=Mostowski|first2=Tadeusz|last3=Parusiński|first3=Adam|date=2000|title=Proof of the gradient conjecture of R. Thom|url=https://archive.org/details/sim_annals-of-mathematics_2000-11_152_3/page/763|journal=Annals of Mathematics|volume=152|issue=3|pages=763–792|arxiv=math/9906212|doi=10.2307/2661354|jstor=2661354|s2cid=119137528}}</ref>

=== Kombinatorika ===

* [[Konjektur jumlah himpunan Erdős]] (Joel Moreira, Florian Richter, Donald Robertson, 2018)<ref>{{Cite journal|last1=Moreira|first1=Joel|last2=Richter|first2=Florian K.|last3=Robertson|first3=Donald|year=2019|title=A proof of a sumset conjecture of Erdős|journal=[[Annals of Mathematics]]|language=en-US|volume=189|pages=605–652|arxiv=1803.00498|doi=10.4007/annals.2019.189.2.4|number=2|s2cid=119158401}}</ref>
* [[Bola simplisial|Konjektur-g McMullen]] pada kemungkinan bilangna sisi dimensi yang berbeda dalam sebuah bola simplisial (juga konjektur Grünbaum , beberapa konjektur mengenai Kühnel) (Karim Adiprasito, 2018)<ref>{{citation|last=Stanley|contribution=A survey of Eulerian posets|volume=440|title=Polytopes: abstract, convex and computational (Scarborough, ON, 1993)|series=NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences|publisher=Kluwer Academic Publishers|pages=301–333|mr=1322068|location=Dordrecht|editor4-first=A. IviÄ‡|first=Richard P.|editor4-last=Weiss|editor3-first=R.|editor3-last=Schneider|editor2-first=P.|editor2-last=McMullen|editor1-first=T.|editor1-last=Bisztriczky|year=1994}}. See in particular [https://books.google.com/books?id=gHjrCAAAQBAJ&pg=PA316 p.&nbsp;316].</ref><ref>{{cite web|last1=Kalai|first1=Gil|date=2018-12-25|title=Amazing: Karim Adiprasito proved the g-conjecture for spheres!|url=https://gilkalai.wordpress.com/2018/12/25/amazing-karim-adiprasito-proved-the-g-conjecture-for-spheres/|archive-url=https://web.archive.org/web/20190216031650/https://gilkalai.wordpress.com/2018/12/25/amazing-karim-adiprasito-proved-the-g-conjecture-for-spheres/|archive-date=2019-02-16|access-date=2019-02-15|url-status=live}}</ref>
* [[Konjektur Hirsch]] ([[Francisco Santos Leal]], 2010)<ref>{{cite journal|last=Santos|first=Franciscos|date=2012|title=A counterexample to the Hirsch conjecture|url=https://archive.org/details/sim_annals-of-mathematics_2012-07_176_1/page/383|journal=Annals of Mathematics|volume=176|issue=1|pages=383–412|arxiv=1006.2814|doi=10.4007/annals.2012.176.1.7|s2cid=15325169}}</ref><ref>{{cite journal|last=Ziegler|first=Günter M.|date=2012|title=Who solved the Hirsch conjecture?|url=http://www.math.uiuc.edu/documenta/vol-ismp/22_ziegler-guenter.html|journal=Documenta Mathematica|volume=Extra Volume "Optimization Stories"|pages=75–85|archive-url=https://web.archive.org/web/20150402161541/http://www.math.uiuc.edu/documenta/vol-ismp/22_ziegler-guenter.html|archive-date=2015-04-02|access-date=2015-03-25|url-status=dead}}</ref>
* [[Konjektur Stanley–Wilf]] ([[Gábor Tardos]] dan [[Adam Marcus (mathematician)|Adam Marcus]], 2004)<ref>{{cite journal|last1=Chung|first1=Fan|last2=Greene|first2=Curtis|last3=Hutchinson|first3=Joan|date=April 2015|title=Herbert S. Wilf (1931–2012)|journal=[[Notices of the AMS]]|volume=62|issue=4|page=358|doi=10.1090/noti1247|issn=1088-9477|oclc=34550461|quote=The conjecture was finally given an exceptionally elegant proof by A. Marcus and G. Tardos in 2004.|doi-access=free}}</ref> (dan juga konjektur Alon–Friedgut)
* [[Konjektur Kemnitz]] ([[Christian Reiher]], 2003, Carlos di Fiore, 2003)<ref>{{cite journal|last1=Savchev|first1=Svetoslav|year=2005|title=Kemnitz' conjecture revisited|journal=Discrete Mathematics|volume=297|issue=1–3|pages=196–201|doi=10.1016/j.disc.2005.02.018|doi-access=free}}</ref>

=== Sistem dinamikal ===

* [[Konjektur Painlevé]] (Jinxin Xue, 2014)<ref name="Xue1">{{Cite document|last=Xue|first=Jinxin|date=2014|title=Noncollision Singularities in a Planar Four-body Problem|url=https://archive.org/details/arxiv-1409.0048|arxiv=1409.0048}}</ref><ref name="Xue2">{{Cite journal|last=Xue|first=Jinxin|date=2020|title=Non-collision singularities in a planar 4-body problem|journal=[[Acta Mathematica]]|volume=224|issue=2|pages=253–388|doi=10.4310/ACTA.2020.v224.n2.a2|s2cid=226420221}}</ref>

=== Teori permainan ===

* [[Masalah malaikat]] (berbagai bukti independen, 2006, 2006)<ref>{{Cite web|last=Bowditch|first=Brian H.|date=2006|title=The angel game in the plane|url=http://homepages.warwick.ac.uk/~masgak/papers/bhb-angel.pdf|publisher=warwick.ac.uk [[Warwick University]]|location=School of Mathematics, [[University of Southampton]]|archive-url=https://web.archive.org/web/20160304185616/http://homepages.warwick.ac.uk/~masgak/papers/bhb-angel.pdf|archive-date=2016-03-04|access-date=2016-03-18|url-status=live}}</ref><ref>{{Cite web|last=Kloster|first=Oddvar|title=A Solution to the Angel Problem|url=http://home.broadpark.no/~oddvark/angel/Angel.pdf|location=SINTEF ICT, Postboks 124 Blindern, 0314 Oslo, Norway|archive-url=https://web.archive.org/web/20160107125925/http://home.broadpark.no/~oddvark/angel/Angel.pdf|archive-date=2016-01-07|access-date=2016-03-18|url-status=dead}}</ref><ref>{{Cite journal|last=Mathe|first=Andras|date=2007|title=The Angel of power 2 wins|url=http://homepages.warwick.ac.uk/~masibe/angel-mathe.pdf|journal=[[Combinatorics, Probability and Computing]]|volume=16|pages=363–374|doi=10.1017/S0963548306008303|archive-url=https://web.archive.org/web/20161013034302/http://homepages.warwick.ac.uk/~masibe/angel-mathe.pdf|archive-date=2016-10-13|access-date=2016-03-18|number=3|s2cid=16892955|url-status=live}}</ref><ref>{{Cite web|last=Gacs|first=Peter|title=THE ANGEL WINS|url=http://www.cs.bu.edu/~gacs/papers/angel.pdf|archive-url=https://web.archive.org/web/20160304030433/http://www.cs.bu.edu/~gacs/papers/angel.pdf|archive-date=2016-03-04|access-date=2016-03-18|url-status=live}}</ref>

=== Geometri ===

==== Abad ke-21 ====

* [[Konjektur Yau]] ([[Antoine Song]], 2018)<ref>https://www.claymath.org/people/antoine-song</ref>
* [[Pengubinan segilima]] (Michaël Rao, 2017)<ref>{{citation|url=https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/|magazine=[[Quanta Magazine]]|title=Pentagon Tiling Proof Solves Century-Old Math Problem|first=Natalie|last=Wolchover|date=July 11, 2017|access-date=July 18, 2017|archive-url=https://web.archive.org/web/20170806093353/https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/|archive-date=August 6, 2017|url-status=dead}}</ref>
* [[Konjektur Willmore]] ([[Fernando Codá Marques]] dan [[André Neves]], 2012)<ref>{{cite journal|last1=Marques|first1=Fernando C.|last2=Neves|first2=André|year=2013|title=Min-max theory and the Willmore conjecture|journal=Annals of Mathematics|volume=179|issue=2|pages=683–782|arxiv=1202.6036|doi=10.4007/annals.2014.179.2.6|s2cid=50742102}}</ref>
* [[Masalah jarak berbeda Erdős]] ([[Larry Guth]], [[Nets Katz|Nets Hawk Katz]], 2011)<ref>{{Cite arxiv|eprint=1011.4105v3|last1=Bruhn|first1=Henning|title=On the Erdos distinct distance problem in the plane|last2=Schaudt|first2=Oliver|class=math.CO|year=2010}}</ref>
* [[Menguadratkan bidang|Konjektur pengubinan heterogen (menguadratkan bidang)]] (Frederick V. Henle dan James M. Henle, 2008)<ref>{{Cite web|title=Archived copy|url=http://www.ww.amc12.org/sites/default/files/pdf/pubs/SquaringThePlane.pdf|archive-url=https://web.archive.org/web/20160324074609/http://www.ww.amc12.org/sites/default/files/pdf/pubs/SquaringThePlane.pdf|archive-date=2016-03-24|access-date=2016-03-18|url-status=live}}</ref>
* [[Konjektur kejinakan]] ([[Ian Agol]], 2004)<ref name="Agol" />
* [[Teorema laminasi akhir]] ([[Jeffrey Brock|Jeffrey F. Brock]], [[Richard Canary|Richard D. Canary]], [[Yair Minsky|Yair N. Minsky]], 2004)<ref>{{Cite journal|last1=Brock|first1=Jeffrey F.|last2=Canary|first2=Richard D.|last3=Minsky|first3=Yair N.|authorlink3=Yair Minsky|date=2012|title=The classification of Kleinian surface groups, II: The Ending Lamination Conjecture|url=https://archive.org/details/sim_annals-of-mathematics_2012-07_176_1/page/1|journal=Annals of Mathematics|volume=176|issue=1|pages=1–149|arxiv=math/0412006|doi=10.4007/annals.2012.176.1.1|doi-access=free}}</ref>
* [[Masalah kaidah Carpenter]] ([[Robert Connelly]], [[Erik Demaine]], Günter Rote, 2003)<ref>{{citation|last1=Connelly|issue=2|year=2003|volume=30|url=http://page.mi.fu-berlin.de/~rote/Papers/pdf/Straightening+polygonal+arcs+and+convexifying+polygonal+cycles-DCG.pdf|title=Straightening polygonal arcs and convexifying polygonal cycles|pages=205–239|mr=1931840|journal=[[Discrete & Computational Geometry]]|doi-access=free|first1=Robert|doi=10.1007/s00454-003-0006-7|first3=Günter|last3=Rote|author2-link=Erik Demaine|first2=Erik D.|last2=Demaine|author1-link=Robert Connelly|s2cid=40382145}}</ref>
* [[Konjektur Nagata]] (Ivan Shestakov, Ualbai Umirbaev, 2003)<ref>{{Cite web|title=Archived copy|url=https://www.ams.org/journals/jams/2004-17-01/S0894-0347-03-00440-5/S0894-0347-03-00440-5.pdf|archive-url=https://web.archive.org/web/20160308201215/http://www.ams.org/journals/jams/2004-17-01/S0894-0347-03-00440-5/S0894-0347-03-00440-5.pdf|archive-date=2016-03-08|access-date=2016-03-23|url-status=live}}</ref>
* [[Konjektur gelembung ganda]] ([[Michael Hutchings (mathematician)|Michael Hutchings]], [[Frank Morgan (mathematician)|Frank Morgan]], Manuel Ritoré, Antonio Ros, 2002)<ref>{{Cite web|title=Archived copy|url=http://www.ugr.es/~ritore/preprints/0406017.pdf|archive-url=https://web.archive.org/web/20160303183909/http://www.ugr.es/~ritore/preprints/0406017.pdf|archive-date=2016-03-03|access-date=2016-03-22|url-status=live}}</ref>

==== Abad ke-20 ====

* [[Konjektur sarang lebah]] ([[Thomas Callister Hales]], 1999)<ref>{{Cite journal|last1=Hales|first1=Thomas C.|date=2001|title=The Honeycomb Conjecture|journal=[[Discrete & Computational Geometry]]|volume=25|pages=1–22|arxiv=math/9906042|doi=10.1007/s004540010071|authorlink1=Thomas Callister Hales|doi-access=free}}</ref>
* [[Konjektur Bogomolov]] ([[Emmanuel Ullmo]], 1998, [[Shou-Wu Zhang]], 1998)<ref>{{cite journal|last1=Ullmo|first1=E|year=1998|title=Positivité et Discrétion des Points Algébriques des Courbes|url=https://archive.org/details/sim_annals-of-mathematics_1998-01_147_1/page/167|journal=Annals of Mathematics|volume=147|issue=1|pages=167–179|arxiv=alg-geom/9606017|doi=10.2307/120987|jstor=120987|zbl=0934.14013|s2cid=119717506}}</ref><ref>{{cite journal|last1=Zhang|first1=S.-W.|year=1998|title=Equidistribution of small points on abelian varieties|url=https://archive.org/details/sim_annals-of-mathematics_1998-01_147_1/page/159|journal=Annals of Mathematics|volume=147|issue=1|pages=159–165|doi=10.2307/120986|jstor=120986}}</ref>
* [[Konjektur Kepler]] (Samuel Ferguson, [[Thomas Callister Hales]], 1998)<ref>{{cite journal|last1=Hales|first1=Thomas|last2=Adams|first2=Mark|last3=Bauer|first3=Gertrud|last4=Dang|first4=Dat Tat|last5=Harrison|first5=John|last6=Hoang|first6=Le Truong|last7=Kaliszyk|first7=Cezary|last8=Magron|first8=Victor|last9=McLaughlin|first9=Sean|date=2017|title=A formal proof of the Kepler conjecture|journal=Forum of Mathematics, Pi|volume=5|pages=e2|arxiv=1501.02155|doi=10.1017/fmp.2017.1|first22=Roland|first18=Nam Trung|last22=Zumkeller|first21=Vu|last21=Ky|first20=Josef|last20=Urban|first19=Thi Diep|last19=Trieu|first13=Steven|last18=Tran|last13=Obua|last10=Nguyen|first10=Tat Thang|last11=Nguyen|first11=Quang Truong|last12=Nipkow|first12=Tobias|last14=Pleso|first17=Thi Hoai An|first14=Joseph|last15=Rute|first15=Jason|last16=Solovyev|first16=Alexey|last17=Ta|doi-access=free}}</ref>
* [[Dodecahedral conjecture|Konjektur bidang dua belas]] ([[Thomas Callister Hales]], Sean McLaughlin, 1998)<ref>{{Cite journal|last1=Hales|first1=Thomas C.|last2=McLaughlin|first2=Sean|date=2010|title=The dodecahedral conjecture|journal=Journal of the American Mathematical Society|volume=23|issue=2|pages=299–344|arxiv=math/9811079|bibcode=2010JAMS...23..299H|doi=10.1090/S0894-0347-09-00647-X|doi-access=free}}</ref>

=== Teori graf ===

* [[Konjektur Kahn–Kalai]] ([[Jinyoung Park (amtematikawan)|Jinyoung Park]] dan Huy Tuan Pham, 2022)<ref>{{cite arXiv
 |last1=Park |first1=Jinyoung
 |last2=Pham |first2=Huy Tuan
 |date=2022-03-31
 |title=A Proof of the Kahn-Kalai Conjecture
 |class=math.CO
 |eprint=2203.17207 }}</ref>
* [[Konjektur Blankenship–Oporowski]] tentang ketebalan subpembagian buku ([[Vida Dujmović]], [[David Eppstein]], Robert Hickingbotham, [[Pat Morin]], dan [[David Wood (mathematician)|David Wood]], 2021)<ref>{{cite journal
 |last1=Dujmović |first1=Vida |author1-link=Vida Dujmović
 |last2=Eppstein |first2=David |author2-link=David Eppstein
 |last3=Hickingbotham |first3=Robert
 |last4=Morin |first4=Pat |author4-link=Pat Morin
 |last5=Wood |first5=David R. |author5-link=David Wood (matematikawan)
 |date=Agustus 2021
 |title=Stack-number is not bounded by queue-number
 |journal=[[Combinatorica]]
 |arxiv=2011.04195
 |doi=10.1007/s00493-021-4585-7
 |s2cid=226281691}}</ref>
* [[Pelabelan anggun|Konjektur Ringel]], membahas tentang pelabelan pohon yang anggun (Richard Montgomery, Benny Sudakov, Alexey Pokrovskiy, 2020)<ref>{{cite journal
 |last1=Huang |first1=C.
 |last2=Kotzig |first2=A. |author2-link=Anton Kotzig
 |last3=Rosa |first3=A.
 |year=1982
 |title=Further results on tree labellings
 |journal=Utilitas Mathematica
 |volume=21 |pages=31–48
 |mr=668845}}.</ref><ref>{{Cite web
 |last=Hartnett |first=Kevin
 |date=19 Februari 2020
 |title=Rainbow Proof Shows Graphs Have Uniform Parts
 |url=https://www.quantamagazine.org/mathematicians-prove-ringels-graph-theory-conjecture-20200219/
 |website=Quanta Magazine
 |language=en
 |access-date=2020-02-29}}</ref>
* Bantahan [[konjektur Hedetniemi]] tentang bilangan kromatik dari darab tensor graf (Yaroslav Shitov, 2019)<ref>{{cite journal
 |last1=Shitov |first1=Yaroslav
 |date=2019-09-01
 |title=Counterexamples to Hedetniemi's conjecture
 |url=https://annals.math.princeton.edu/2019/190-2/p06
 |journal=Annals of Mathematics
 |volume=190 |issue=2 |pages=663–667
 |arxiv=1905.02167 |doi=10.4007/annals.2019.190.2.6
 |jstor=10.4007/annals.2019.190.2.6
 |mr=3997132
 |zbl=1451.05087
 |access-date=2021-07-19 |df=dmy-all
 |s2cid=146120733}}</ref>
* [[Masalah Babai]] (Alireza Abdollahi, Maysam Zallaghi, 2015)<ref>{{cite journal
 |last=Abdollahi A. |first=Zallaghi M.
 |year=2015
 |title=Character sums for Cayley graphs
 |journal=Communications in Algebra
 |volume=43 |issue=12 |pages=5159–5167
 |doi=10.1080/00927872.2014.967398
 |s2cid=117651702}}</ref>
* [[Konjektur Alspach]] (Darryn Bryant, Daniel Horsley, William Pettersson, 2014)
* [[Konjektur Scheinerman]] (Jeremie Chalopin and Daniel Gonçalves, 2009)<ref>{{cite conference
 | last1 = Chalopin | first1 = Jérémie
 | last2 = Gonçalves | first2 = Daniel
 | editor-last = Mitzenmacher | editor-first = Michael
 | contribution = Every planar graph is the intersection graph of segments in the plane: extended abstract
 | doi = 10.1145/1536414.1536500
 | pages = 631–638
 | publisher = ACM
 | title = Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, May 31 - June 2, 2009
 | year = 2009}}</ref>
* [[Konjektur Erdős–Menger]] ([[Ron Aharoni]], Eli Berger 2007)<ref>{{Cite journal
 |last1=Aharoni |first1=Ron |author1-link=Ron Aharoni
 |last2=Berger |first2=Eli
 |date=2009
 |title=Menger's theorem for infinite graphs
 |journal=Inventiones Mathematicae
 |volume=176
 |issue=1
 |pages=1–62
 |arxiv=math/0509397
 |bibcode=2009InMat.176....1A
 |doi=10.1007/s00222-008-0157-3
 |doi-access=free}}</ref>
* [[Konjektur pewarnaan jalanan]] ([[Avraham Trahtman]], 2007)<ref>{{cite news
 |last=Seigel-Itzkovich |first=Judy
 |date=2008-02-08
 |title=Russian immigrant solves math puzzle
 |url=http://www.jpost.com/Home/Article.aspx?id=91431
 |newspaper=The Jerusalem Post
 |access-date=2015-11-12}}</ref>
* [[Teorema Robertson–Seymour]] ([[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]], 2004)<ref>{{cite web
 |title=Graph Theory
 |url=http://www.flooved.com/reader/3447#348
 |archive-url=https://web.archive.org/web/20160308022407/http://www.flooved.com/reader/3447#348
 |archive-date=2016-03-08
 |access-date=2016-03-18
 |url-status=live}}</ref>
* [[Konjektur graf sempurna kuat]] ([[Maria Chudnovsky]], [[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]] and [[Robin Thomas (mathematician)|Robin Thomas]], 2002)<ref>{{cite journal
 |last1=Chudnovsky |first1=Maria
 |last2=Robertson |first2=Neil
 |last3=Seymour |first3=Paul
 |last4=Thomas |first4=Robin
 |year=2002
 |title=The strong perfect graph theorem
 |url=https://annals.math.princeton.edu/2006/164-1/p02
 |journal=Annals of Mathematics
 |volume=164 |pages=51–229
 |arxiv=math/0212070
 |bibcode=2002math.....12070C
 |doi=10.4007/annals.2006.164.51
 |s2cid=119151552}}</ref>

=== Teori grup ===

* [[Konjektur Hanna Neumann]] (Joel Friedman, 2011, Igor Mineyev, 2011)<ref>Joel Friedman, [https://www.cs.ubc.ca/~jf/pubs/web_stuff/shnc_memoirs.pdf "Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture: With an Appendix by Warren Dicks"] Mem. Amer. Math. Soc., 233 (2015), no. 1100.</ref><ref>{{Cite web|title=Archived copy|url=http://www.math.uiuc.edu/~mineyev/math/art/submult-shnc.pdf|archive-url=https://web.archive.org/web/20161007091758/http://www.math.uiuc.edu/~mineyev/math/art/submult-shnc.pdf|archive-date=2016-10-07|access-date=2016-03-18|url-status=live}}</ref>
* [[Teorema kepadatan untuk grup Klein|Teorema kepadatan]] (Hossein Namazi, Juan Souto, 2010)<ref>{{Cite journal|last1=Namazi|first1=Hossein|last2=Souto|first2=Juan|year=2012|title=Non-realizability and ending laminations: Proof of the density conjecture|url=https://www.researchgate.net/publication/228365532|journal=Acta Mathematica|volume=209|issue=2|pages=323–395|doi=10.1007/s11511-012-0088-0|doi-access=free}}</ref>
* [[Klasifikasi grup sederhana hingga]] penuh ([[Koichiro Harada]], [[Ronald Solomon]], 2008)

=== Teori bilangan ===

==== Abad ke-21 ====

* [[Konjektur Duffin–Schaeffer]] (Dimitris Koukoulopoulos, [[James Maynard (mathematician)|James Maynard]], 2019)
* [[Teorema nilai purata Vinogradov|Konjektur utama dalam teorema nilai purata Vinogradov]] ([[Jean Bourgain]], Ciprian Demeter, [[Larry Guth]], 2015)<ref>{{cite journal|last1=Bourgain|first1=Jean|last2=Ciprian|first2=Demeter|last3=Larry|first3=Guth|year=2015|title=Proof of the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three|journal=Annals of Mathematics|volume=184|issue=2|pages=633–682|arxiv=1512.01565|bibcode=2015arXiv151201565B|doi=10.4007/annals.2016.184.2.7|hdl=1721.1/115568|s2cid=43929329}}</ref>
* [[Konjektur lemah Goldbach]] ([[Harald Helfgott]], 2013)<ref>{{cite arXiv|eprint=1305.2897|title=Major arcs for Goldbach's theorem|last=Helfgott|first=Harald A.|class=math.NT|year=2013}}</ref><ref>{{cite arXiv|eprint=1205.5252|title=Minor arcs for Goldbach's problem|last=Helfgott|first=Harald A.|class=math.NT|year=2012}}</ref><ref>{{cite arXiv|eprint=1312.7748|title=The ternary Goldbach conjecture is true|last=Helfgott|first=Harald A.|class=math.NT|year=2013}}</ref>
* [[Celah bilangan prima#Hasil lebih lanjut|Keberadaan celah batas antara bilangan prima]] ([[Yitang Zhang]], [[Polymath Project|Polymath8]], [[James Maynard (mathematician)|James Maynard]], 2013)<ref>{{Cite journal|last=Zhang|first=Yitang|date=2014-05-01|title=Bounded gaps between primes|url=https://doi.org/10.4007/annals.2014.179.3.7|journal=Annals of Mathematics|volume=179|issue=3|pages=1121–1174|doi=10.4007/annals.2014.179.3.7|issn=0003-486X}}</ref><ref>{{Cite web|title=Bounded gaps between primes - Polymath Wiki|url=https://asone.ai/polymath/index.php?title=Bounded_gaps_between_primes|website=asone.ai|access-date=2021-08-27|archive-date=2020-12-08|archive-url=https://web.archive.org/web/20201208045925/https://asone.ai/polymath/index.php?title=Bounded_gaps_between_primes|dead-url=yes}}</ref><ref>{{Cite journal|last=Maynard|first=James|date=2015-01-01|title=Small gaps between primes|url=https://doi.org/10.4007/annals.2015.181.1.7|journal=Annals of Mathematics|pages=383–413|arxiv=1311.4600|doi=10.4007/annals.2015.181.1.7|issn=0003-486X|s2cid=55175056}}</ref>
* [[Konjektur modularitas Serre]] ([[Chandrashekhar Khare]] dan [[Jean-Pierre Wintenberger]], 2008)<ref>{{Citation|last1=Khare|first1=Chandrashekhar|last2=Wintenberger|first2=Jean-Pierre|year=2009|title=Serre's modularity conjecture (I)|journal=Inventiones Mathematicae|volume=178|issue=3|pages=485–504|doi=10.1007/s00222-009-0205-7|bibcode=2009InMat.178..485K|citeseerx=10.1.1.518.4611|s2cid=14846347}}</ref><ref>{{Citation|last1=Khare|first1=Chandrashekhar|last2=Wintenberger|first2=Jean-Pierre|year=2009|title=Serre's modularity conjecture (II)|journal=Inventiones Mathematicae|volume=178|issue=3|pages=505–586|doi=10.1007/s00222-009-0206-6|bibcode=2009InMat.178..505K|citeseerx=10.1.1.228.8022|s2cid=189820189}}</ref><ref>{{cite journal|author=<!--Staff writer(s); no by-line.-->|title=2011 Cole Prize in Number Theory|url=https://www.ams.org/notices/201104/rtx110400610p.pdf|journal=[[Notices of the AMS]]|volume=58|issue=4|pages=610–611|issn=1088-9477|oclc=34550461|archive-url=https://web.archive.org/web/20151106051835/http://www.ams.org/notices/201104/rtx110400610p.pdf|archive-date=2015-11-06|access-date=2015-11-12|url-status=live}}</ref>
* [[Teorema Mihăilescu|Konjektur Catalan]] ([[Preda Mihăilescu]], 2002)<ref>{{cite journal|last=Metsänkylä|first=Tauno|date=5 September 2003|title=Catalan's conjecture: another old diophantine problem solved|url=https://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdf|journal=[[Bulletin of the American Mathematical Society]]|volume=41|issue=1|pages=43–57|doi=10.1090/s0273-0979-03-00993-5|issn=0273-0979|archive-url=https://web.archive.org/web/20160304082755/http://www.ams.org/journals/bull/2004-41-01/S0273-0979-03-00993-5/S0273-0979-03-00993-5.pdf|archive-date=4 March 2016|access-date=13 November 2015|quote=The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu.|url-status=live}}</ref>

==== Abad ke-20 ====

* [[Teorema Lafforgue]] ([[Laurent Lafforgue]], 1998)<ref>{{Citation|last1=Lafforgue|first1=Laurent|title=Chtoucas de Drinfeld et applications|language=fr|trans-title=Drinfelʹd shtukas and applications|url=http://www.math.uni-bielefeld.de/documenta/xvol-icm/07/Lafforgue.MAN.html|mr=1648105|year=1998|journal=Documenta Mathematica|issn=1431-0635|volume=II|pages=563–570|access-date=2016-03-18|archive-url=https://web.archive.org/web/20180427200241/https://www.math.uni-bielefeld.de/documenta/xvol-icm/07/Lafforgue.MAN.html|archive-date=2018-04-27|url-status=live}}</ref>
* [[Teorema Terakhir Fermat]] ([[Andrew Wiles]] dan [[Richard Taylor (mathematician)|Richard Taylor]], 1995)<ref>{{cite journal|last=Wiles|first=Andrew|author-link=Andrew Wiles|year=1995|title=Modular elliptic curves and Fermat's Last Theorem|url=http://math.stanford.edu/~lekheng/flt/wiles.pdf|journal=Annals of Mathematics|volume=141|issue=3|pages=443–551|doi=10.2307/2118559|jstor=2118559|oclc=37032255|archive-url=https://web.archive.org/web/20110510062158/http://math.stanford.edu/%7Elekheng/flt/wiles.pdf|archive-date=2011-05-10|access-date=2016-03-06|citeseerx=10.1.1.169.9076|url-status=live}}</ref><ref>{{cite journal|author=[[Richard Taylor (mathematician)|Taylor R]], [[Andrew Wiles|Wiles A]]|year=1995|title=Ring theoretic properties of certain Hecke algebras|url=https://web.archive.org/web/20050301000000*/http://www.math.harvard.edu/~rtaylor/hecke.ps|journal=Annals of Mathematics|volume=141|issue=3|pages=553–572|doi=10.2307/2118560|jstor=2118560|oclc=37032255|citeseerx=10.1.1.128.531}}</ref>

=== Teori Ramsey ===

* [[Konjektur Burr–Erdős]] (Choongbum Lee, 2017)<ref>{{cite journal|last1=Lee|first1=Choongbum|year=2017|title=Ramsey numbers of degenerate graphs|journal=Annals of Mathematics|volume=185|issue=3|pages=791–829|arxiv=1505.04773|doi=10.4007/annals.2017.185.3.2|s2cid=7974973}}</ref>
* [[Masalah rangkap tiga Pythagoras Boole]] ([[Marijn Heule]], Oliver Kullmann, [[Victor W. Marek]], 2016)<ref>{{cite journal|last=Lamb|first=Evelyn|date=26 May 2016|title=Two-hundred-terabyte maths proof is largest ever|journal=Nature|volume=534|issue=7605|pages=17–18|bibcode=2016Natur.534...17L|doi=10.1038/nature.2016.19990|pmid=27251254|doi-access=free}}</ref><ref>{{cite book|last1=Heule|first1=Marijn J. H.|last2=Kullmann|first2=Oliver|last3=Marek|first3=Victor W.|year=2016|title=Theory and Applications of Satisfiability Testing – SAT 2016|publisher=Springer, [Cham]|isbn=978-3-319-40969-6|editor-last1=Creignou|editor-first1=N.|series=Lecture Notes in Computer Science|volume=9710|pages=228–245|chapter=Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer|arxiv=1605.00723|doi=10.1007/978-3-319-40970-2_15|mr=3534782|editor-last2=Le Berre|editor-first2=D.|s2cid=7912943}}</ref>

=== Ilmu komputer teoritis ===

* [[Model pohon keputusan#Konjektur sensitivitas|Konjektur sensitivitas]] dalam fungsi Boole ([[Hao Huang (mathematician)|Hao Huang]], 2019)  <ref>{{cite web|author=Linkletter, David|date=27 December 2019|title=The 10 Biggest Math Breakthroughs of 2019|url=https://www.popularmechanics.com/science/math/g30346822/biggest-math-breakthroughs-2019/|work=www.[[popularmechanics.com]]|publisher=[[Hearst Digital Media]]|archive-url=|archive-date=|accessdate=20 June 2021}}</ref>

=== Topology ===

* Menentukan apakah [[simpul Conway]] merupakan [[simpul irisan]] ([[Lisa Piccirillo]], 2020)<ref>[https://annals.math.princeton.edu/2020/191-2/p05 The Conway knot is not slice], [[Annals of Mathematics]], volume 191, issue 2, pp. 581–591</ref><ref>[https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/ Graduate Student Solves Decades-Old Conway Knot Problem], [[Quanta Magazine]] 19 May 2020</ref>
* [[Konjektur Haken maya]] ([[Ian Agol]], Daniel Groves, Jason Manning, 2012)<ref>{{Cite journal|last1=Agol|first1=Ian|date=2013|title=The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves, and Jason Manning)|url=https://www.math.uni-bielefeld.de/documenta/vol-18/33.pdf|journal=Documenta Mathematica|volume=18|pages=1045–1087|arxiv=1204.2810v1}}</ref> (dan juga [[konjektur terserat sebenarnya]], karya [[Daniel Wise]])
* [[Konjektur Hsiang–Lawson]] ([[Simon Brendle]], 2012)<ref>{{Cite journal|last1=Brendle|first1=Simon|date=2013|title=Embedded minimal tori in <math>S^3</math> and the Lawson conjecture|journal=Acta Mathematica|volume=211|issue=2|pages=177–190|arxiv=1203.6597|doi=10.1007/s11511-013-0101-2|author1-link=Simon Brendle|doi-access=free}}</ref>
* [[Konjektur Ehrenpreis]] ([[Jeremy Kahn]], [[Vladimir Markovic]], 2011)<ref>{{Cite journal|last1=Kahn|first1=Jeremy|last2=Markovic|first2=Vladimir|author2-link=Vladimir Markovic|date=2015|title=The good pants homology and the Ehrenpreis conjecture|url=https://archive.org/details/sim_annals-of-mathematics_2015-07_182_1/page/1|journal=Annals of Mathematics|volume=182|issue=1|pages=1–72|arxiv=1101.1330|doi=10.4007/annals.2015.182.1.1|author1-link=Jeremy Kahn|doi-access=free}}</ref>
* [[Konjektur Atiyah]] (Austin, 2009)<ref>{{cite journal|last1=Austin|first1=Tim|date=December 2013|title=Rational group ring elements with kernels having irrational dimension|journal=Proceedings of the London Mathematical Society|volume=107|issue=6|pages=1424–1448|arxiv=0909.2360|bibcode=2009arXiv0909.2360A|doi=10.1112/plms/pdt029|s2cid=115160094}}</ref>
* [[Hipotesis kobordisme]] ([[Jacob Lurie]], 2008)<ref>{{cite journal|last1=Lurie|first1=Jacob|year=2009|title=On the classification of topological field theories|journal=Current Developments in Mathematics|volume=2008|pages=129–280|arxiv=0905.0465|bibcode=2009arXiv0905.0465L|doi=10.4310/cdm.2008.v2008.n1.a3|s2cid=115162503}}</ref>
* [[Konjektur bentuk ruang bola]] ([[Grigori Perelman]], 2006)
* [[Konjektur Poincaré]] ([[Grigori Perelman]], 2002)<ref name="auto">{{cite press release|publisher=[[Clay Mathematics Institute]]|date=March 18, 2010|title=Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman|url=http://www.claymath.org/sites/default/files/millenniumprizefull.pdf|access-date=November 13, 2015|quote=The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.|archive-url=https://web.archive.org/web/20100322192115/http://www.claymath.org/poincare/|archive-date=March 22, 2010|url-status=live}}</ref>
* [[Konjektur geometrisasi]], dibuktikan oleh [[Grigori Perelman]] dalam serangkaian pracetak tahun 2002–2003
* Bantahan [[konjektur Ganea]] (Iwase, 1997)<ref>{{cite web|author=Norio Iwase|date=1 November 1998|title=Ganea's Conjecture on Lusternik-Schnirelmann Category|url=https://www.researchgate.net/publication/220032558|work=ResearchGate}}</ref>

=== Masalah yanag belum dikategorisasikan ===

==== Abad ke-20 ====

===== 2010an =====

* [[Masalah ketakcocokan Erdős]] ([[Terence Tao]], 2015)
* Konjektur [[Sinar bulan umbral|sinar bulan ''umbral'']] (John F. R. Duncan, Michael J. Griffin, Ken Ono, 2015)
* Konjektur Anderson tentang bilangan kelas difeomorfisme hingga dari kumpulan 4-manifold yang memenhi sifat-sifat tertentu ([[Jeff Cheeger]], Aaron Naber, 2014)<ref>{{cite journal|last1=Cheeger|first1=Jeff|last2=Naber|first2=Aaron|date=2015|title=Regularity of Einstein Manifolds and the Codimension 4 Conjecture|url=https://archive.org/details/sim_annals-of-mathematics_2015-11_182_3/page/1093|journal=Annals of Mathematics|volume=182|issue=3|pages=1093–1165|arxiv=1406.6534|doi=10.4007/annals.2015.182.3.5|doi-access=free}}</ref>
* [[Pertidaksamaan korelasi Gauss]] ([[Thomas Royen]], 2014)<ref>{{Cite magazine|date=March 28, 2017|title=A Long-Sought Proof, Found and Almost Lost|url=https://www.quantamagazine.org/20170328-statistician-proves-gaussian-correlation-inequality/|publisher=Natalie Wolchover|access-date=May 2, 2017|magazine=[[Quanta Magazine]]|archive-url=https://web.archive.org/web/20170424133433/https://www.quantamagazine.org/20170328-statistician-proves-gaussian-correlation-inequality/|archive-date=April 24, 2017|url-status=live}}</ref>
* Konjektur Beck tentang ketakcocokan sistem himpunan yang dibentuk dari tiga permutasi (Alantha Newman, [[Aleksandar Nikolov (computer scientist)|Aleksandar Nikolov]], 2011)<ref>{{Cite arXiv|eprint=1104.2922|last1=Newman|first1=Alantha|last2=Nikolov|first2=Aleksandar|title=A counterexample to Beck's conjecture on the discrepancy of three permutations|class=cs.DM|year=2011}}</ref>
* [[Konjektur Bloch–Kato]] (Voevodsky, 2011) ([[konjektur Quillen–Lichtenbaum]] dan [[Teorema isomorfisme residu bernorma|konjektur Beilinson–Lichtenbaum]] dipecahkan oleh [[Thomas Geisser (matematikawan)|Thomas Geisser]] dan [[Marc Levine (matematikawan)|Marc Levine]] (2001))
* [[Barisan Sidon|Masalah himpunan Sidon]] (Javier Cilleruelo, [[Imre Z. Ruzsa]], dan Carlos Vinuesa, 2010)<ref>{{cite journal|last1=Cilleruelo|first1=Javier|year=2010|title=Generalized Sidon sets|journal=[[Advances in Mathematics]]|volume=225|issue=5|pages=2786–2807|doi=10.1016/j.aim.2010.05.010|hdl=10261/31032|s2cid=7385280|doi-access=free|hdl-access=free}}</ref>

===== 2000an =====

* [[Konjektur Kauffman–Harary]] (Thomas Mattman, Pablo Solis, 2009)<ref>{{Cite journal|last1=Mattman|first1=Thomas W.|last2=Solis|first2=Pablo|year=2009|title=A proof of the Kauffman-Harary Conjecture|journal=Algebraic & Geometric Topology|volume=9|issue=4|pages=2027–2039|arxiv=0906.1612|bibcode=2009arXiv0906.1612M|doi=10.2140/agt.2009.9.2027|s2cid=8447495}}</ref>
* [[Konjektur subgrup permukaan]] ([[Jeremy Kahn]], [[Vladimir Markovic]], 2009)<ref>{{cite journal|last1=Kahn|first1=Jeremy|last2=Markovic|first2=Vladimir|year=2012|title=Immersing almost geodesic surfaces in a closed hyperbolic three manifold|url=https://archive.org/details/sim_annals-of-mathematics_2012-05_175_3/page/1127|journal=Annals of Mathematics|volume=175|issue=3|pages=1127–1190|arxiv=0910.5501|doi=10.4007/annals.2012.175.3.4|doi-access=free}}</ref>
* [[Konjektur kelengkungan skalar Norman]] dan [[konjektur Böttcher–Wenzel]] (Zhiqin Lu, 2007)<ref>{{cite journal|last=Lu|first=Zhiqin|date=September 2011|orig-year=2007|title=Normal Scalar Curvature Conjecture and its applications|journal=Journal of Functional Analysis|volume=261|issue=5|pages=1284–1308|arxiv=0711.3510|doi=10.1016/j.jfa.2011.05.002|doi-access=free}}</ref>
* [[Konjektur Nirenberg–Treves]] ([[Nils Dencker]], 2005)<ref>{{citation|last=Dencker|first=Nils|author-link=Nils Dencker|title=The resolution of the Nirenberg–Treves conjecture|journal=[[Annals of Mathematics]]|volume=163|issue=2|year=2006|pages=405–444|url=https://annals.math.princeton.edu/wp-content/uploads/annals-v163-n2-p02.pdf|doi=10.4007/annals.2006.163.405|s2cid=16630732|access-date=2019-04-07|archive-url=https://web.archive.org/web/20180720145723/http://annals.math.princeton.edu/wp-content/uploads/annals-v163-n2-p02.pdf|archive-date=2018-07-20|url-status=live}}</ref><ref>{{citation|url=https://www.claymath.org/research|title=Research Awards|website=[[Clay Mathematics Institute]]|access-date=2019-04-07|archive-url=https://web.archive.org/web/20190407160116/https://www.claymath.org/research|archive-date=2019-04-07|url-status=live}}</ref>
* [[Peter Lax|Konjektur Lax]] ([[Adrian Lewis (mathematician)|Adrian Lewis]], [[Pablo Parrilo]], Motakuri Ramana, 2005)<ref>{{Cite web|title=Archived copy|url=https://www.ams.org/journals/proc/2005-133-09/S0002-9939-05-07752-X/S0002-9939-05-07752-X.pdf|archive-url=https://web.archive.org/web/20160406184603/http://www.ams.org/journals/proc/2005-133-09/S0002-9939-05-07752-X/S0002-9939-05-07752-X.pdf|archive-date=2016-04-06|access-date=2016-03-22|url-status=live}}</ref>
* [[Lema dasar Langlands–Shelstad]] ([[Ngô Bảo Châu]] dan [[Gérard Laumon]], 2004)<ref>{{cite web|author=<!--Staff writer(s); no by-line.-->|date=19 August 2010|title=Fields Medal – Ngô Bảo Châu|url=http://www.icm2010.in/prize-winners-2010/fields-medal-ngo-bao-chau|website=International Congress of Mathematicians 2010|publisher=ICM|archive-url=https://web.archive.org/web/20150924032610/http://www.icm2010.in/prize-winners-2010/fields-medal-ngo-bao-chau|archive-date=24 September 2015|access-date=2015-11-12|quote=Ngô Bảo Châu is being awarded the 2010 Fields Medal for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.|url-status=live}}</ref>
* [[Teorema Green–Tao]] ([[Ben J. Green]] dan [[Terence Tao]], 2004)<ref>{{cite journal|author=<!--Staff writer(s); no by-line.-->|date=May 2010|title=Bombieri and Tao Receive King Faisal Prize|url=https://www.ams.org/notices/201005/rtx100500642p.pdf|journal=[[Notices of the AMS]]|volume=57|issue=5|pages=642–643|issn=1088-9477|oclc=34550461|archive-url=https://web.archive.org/web/20160304063504/http://www.ams.org/notices/201005/rtx100500642p.pdf|archive-date=2016-03-04|access-date=2016-03-18|quote=Working with Ben Green, he proved there are arbitrarily long arithmetic progressions of prime numbers—a result now known as the Green–Tao theorem.|url-status=live}}</ref>
* [[Konjektur Cameron–Erdős]] ([[Ben J. Green]], 2003, Alexander Sapozhenko, 2003)<ref>{{citation|last=Green|first=Ben|author-link=Ben J. Green|arxiv=math.NT/0304058|doi=10.1112/S0024609304003650|issue=6|journal=The Bulletin of the London Mathematical Society|mr=2083752|pages=769–778|title=The Cameron–Erdős conjecture|volume=36|year=2004|s2cid=119615076}}</ref><ref>{{cite web|author=<!--Staff writer(s); no by-line.-->|date=31 December 2007|title=News from 2007|url=https://www.ams.org/news?news_id=155|website=American Mathematical Society|publisher=AMS|archive-url=https://web.archive.org/web/20151117030726/http://www.ams.org/news?news_id=155|archive-date=17 November 2015|access-date=2015-11-13|quote=The 2007 prize also recognizes Green for "his many outstanding results including his resolution of the Cameron-Erdős conjecture..."|url-status=live}}</ref>
* [[Konjektur Milnor]] ([[Vladimir Voevodsky]], 2003)<ref>{{cite journal|last1=Voevodsky|first1=Vladimir|year=2003|title=Reduced power operations in motivic cohomology|url=http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_2003__98_/PMIHES_2003__98__1_0/PMIHES_2003__98__1_0.pdf|journal=Publications Mathématiques de l'IHÉS|volume=98|pages=1–57|arxiv=math/0107109|doi=10.1007/s10240-003-0009-z|archive-url=https://web.archive.org/web/20170728114725/http://archive.numdam.org/item/PMIHES_2003__98__1_0|archive-date=2017-07-28|access-date=2016-03-18|citeseerx=10.1.1.170.4427|url-status=live|s2cid=8172797}}</ref>
* [[Konjektur Kirillov]] (Ehud Baruch, 2003)<ref>{{Cite web|title=Archived copy|url=https://annals.math.princeton.edu/wp-content/uploads/annals-v158-n1-p04.pdf|archive-url=https://web.archive.org/web/20160403094319/http://annals.math.princeton.edu/wp-content/uploads/annals-v158-n1-p04.pdf|archive-date=2016-04-03|access-date=2016-03-20|url-status=live}}</ref>
* [[Konjektur Kouchnirenko]] (Bertrand Haas, 2002)<ref>{{Cite web|last=Haas|first=Bertrand|title=A Simple Counterexample to Kouchnirenko's Conjecture|url=https://www.emis.de/journals/BAG/vol.43/no.1/b43h1haa.pdf|archive-url=https://web.archive.org/web/20161007091417/http://www.emis.de/journals/BAG/vol.43/no.1/b43h1haa.pdf|archive-date=2016-10-07|access-date=2016-03-18|url-status=live}}</ref>
* [[Konjektur n!|Konjektur ''n''!]] ([[Mark Haiman]], 2001)<ref>{{Cite web|title=Archived copy|url=https://www.ams.org/journals/jams/2001-14-04/S0894-0347-01-00373-3/S0894-0347-01-00373-3.pdf|archive-url=https://web.archive.org/web/20161007102814/http://www.ams.org/journals/jams/2001-14-04/S0894-0347-01-00373-3/S0894-0347-01-00373-3.pdf|archive-date=2016-10-07|access-date=2016-03-18|url-status=live}}</ref> (dan juga [[Polinomial Macdonald#Konjektur kepositifan Macdonald|konjektur kepositifan Macdonald]])
* [[Konjektur Kato]] ([[Pascal Auscher]], [[Steve Hofmann]], [[Michael Lacey (mathematician)|Michael Lacey]], [[Alan Gaius Ramsay McIntosh|Alan McIntosh]], dan Philipp Tchamitchian, 2001)<ref>{{Cite web|title=Archived copy|url=http://junon.u-3mrs.fr/monniaux/AHLMT02.pdf|archive-url=https://web.archive.org/web/20150908215443/http://junon.u-3mrs.fr/monniaux/AHLMT02.pdf|archive-date=2015-09-08|access-date=2016-03-18|url-status=dead}}</ref>
* [[Konjektur Deligne 1-motif]] (Luca Barbieri-Viale, Andreas Rosenschon, [[Morihiko Saito]], 2001)<ref>{{cite journal|last1=Barbieri-Viale|first1=Luca|last2=Rosenschon|first2=Andreas|last3=Saito|first3=Morihiko|date=2003|title=Deligne's Conjecture on 1-Motives|url=https://archive.org/details/sim_annals-of-mathematics_2003-09_158_2/page/593|journal=Annals of Mathematics|volume=158|issue=2|pages=593–633|arxiv=math/0102150|doi=10.4007/annals.2003.158.593|doi-access=free}}</ref>
* [[Teorema modularitas]] ([[Christophe Breuil]], [[Brian Conrad]], [[Fred Diamond]], dan [[Richard Taylor (mathematician)|Richard Taylor]], 2001)<ref>{{Citation|last1=Breuil|mr=1839918|pages=843–939|issue=4|volume=14|issn=0894-0347|journal=[[Journal of the American Mathematical Society]]|year=2001|doi=10.1090/S0894-0347-01-00370-8|first1=Christophe|title=On the modularity of elliptic curves over '''Q''': wild 3-adic exercises|first4=Richard|last4=Taylor|first3=Fred|last3=Diamond|first2=Brian|last2=Conrad|doi-access=free}}</ref>
* [[Konjektur Erdős–Stewart]] ([[Florian Luca]], 2001)<ref>{{Cite journal|last1=Luca|first1=Florian|year=2000|title=On a conjecture of Erdős and Stewart|url=https://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01178-9/S0025-5718-00-01178-9.pdf|journal=Mathematics of Computation|volume=70|issue=234|pages=893–897|bibcode=2001MaCom..70..893L|doi=10.1090/s0025-5718-00-01178-9|archive-url=https://web.archive.org/web/20160402030443/http://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01178-9/S0025-5718-00-01178-9.pdf|archive-date=2016-04-02|access-date=2016-03-18|url-status=live}}</ref>
* [[Masalah Berry–Robbins]] ([[Michael Atiyah]], 2000)<ref>{{Cite web|title=Archived copy|url=http://intlpress.com/site/pub/files/_fulltext/journals/sdg/2002/0007/0001/SDG-2002-0007-0001-a001.pdf|archive-url=https://web.archive.org/web/20160402010819/http://intlpress.com/site/pub/files/_fulltext/journals/sdg/2002/0007/0001/SDG-2002-0007-0001-a001.pdf|archive-date=2016-04-02|access-date=2016-03-20|url-status=live}}</ref>
* [[Masalah Erdős–Graham]] ([[Ernest S. Croot III]], 2000)<ref>{{citation|last=Croot|first=Ernest S., III|author-link=Ernest S. Croot III|publisher=[[University of Georgia]], Athens|series=Ph.D. thesis|title=Unit Fractions|year=2000}}. {{citation|last=Croot|first=Ernest S., III|author-link=Ernest S. Croot III|arxiv=math.NT/0311421|doi=10.4007/annals.2003.157.545|issue=2|journal=[[Annals of Mathematics]]|pages=545–556|title=On a coloring conjecture about unit fractions|volume=157|year=2003|bibcode=2003math.....11421C|s2cid=13514070}}</ref>

==== Abad ke-20 ====
* Konjektur Harary tentang jumlah integral dari graf lengkap (Zhibo Chen, 1996)<ref>{{Cite journal|last1=Chen|first1=Zhibo|year=1996|title=Harary's conjectures on integral sum graphs|url=https://www.researchgate.net/publication/220188021|journal=[[Discrete Mathematics (journal)|Discrete Mathematics]]|volume=160|issue=1–3|pages=241–244|doi=10.1016/0012-365X(95)00163-Q|doi-access=free}}</ref>

== Lihat pula ==
*[[Masalah terbuka]]
*[[Daftar persoalan yang belum terpecahkan]]

== Referensi ==
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[[Kategori:Masalah matematika yang belum terpecahkan| ]]