数学上の未解決問題
Does there exist an o-minimal first order theory with a trans-exponential (rapid growth) function?
Lachlan's decision problem
Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts?
Do the Henson graphs have the finite model property? (e.g. triangle-free graphs)
The universality problem for C-free graphs: For which finite sets C of graphs does the class of C-free countable graphs have a universal member under strong embeddings?
The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?
(MTWO) Is the monadic theory of well-ordering consistently decidable?
The Stable Forking Conjecture for simple theories
For which number fields does Hilbert's tenth problem hold?
Assume K is the class of models of a countable first order theory omitting countably many types. If K has a model of cardinality does it have a model of cardinality continuum?
Shelah's eventual Categority conjecture: For every cardinal \lambda there exists a cardinal \mu(\lambda) such that If an AEC K with LS(K)<= \lambda is categorical in a cardinal above \mu(\lambda) then it is categorical in all cardinals above \mu(\lambda).
アンドレ・オールト予想(英語版)(André–Oort conjecture)
バスの予想(Bass conjecture)
Deligne conjecture
Fröberg conjecture
藤田予想(英語版)
Hartshorne conjectures
Manin conjecture
中井予想
Resolution of singularities in characteristic p
代数的サイクルの標準予想(en:Standard conjectures on algebraic cycles)
Section conjecture
テイト予想 (代数幾何学)(en:Tate conjecture)
Virasoro conjecture
Whitehead conjecture
Zariski multiplicity conjecture
ギルブレース予想(英語版)
完全直方体(英語版)
ヒルベルトの23の問題のうち、第8の問題、第12の問題、第16の問題、第23の問題の4題。
Generalized star height problem
シャヌエル予想(英語版)
ルジャンドル予想
2つのブラックホールが融合する、という現象のモデル化
オイラーの定数 γ は無理数か。
合同数の問題
P = L かどうか。
NL = L かどうか。
フィボナッチ数列の逆数和は超越数かどうか。
ブニャコフスキー予想
コンウェイの問題
バシャドスキー・チェコッティ・大栗・ヴァファ予想
エルデシュ=シュトラウス予想
指数時間仮説
ケーテ予想
単位正方形の有理距離問題(Rational Distance Problem)
素数に関連する未解決の問題
約数の和に関連する未解決の問題
Barnette's conjecture that every cubic bipartite three-connected planar graph has a Hamiltonian cycle
The Erdős–Gyárfás conjecture on cycles with power-of-two lengths in cubic graphs
The Erdős–Hajnal conjecture on finding large homogeneous sets in graphs with a forbidden induced subgraph
The Hadwiger conjecture relating coloring to clique minors
The Erdős–Faber–Lovász conjecture on coloring unions of cliques
Harborth's conjecture that every planar graph can be drawn with integer edge lengths
The total coloring conjecture
The list coloring conjecture