数学上の未解決問題
The einstein problem – does there exist a two-dimensional shape that forms the prototile for an aperiodic tiling, but not for any periodic tiling?
Inscribed square problem – does every Jordan curve have an inscribed square?
Moser's worm problem – 平面内のすべての単位長曲線をカバーできる形状の最小領域は何か?
ソファ問題 – 単位幅のL字型の廊下を通過できる形状の最大領域はどんな形か?
Shephard's problem (a.k.a. Dürer's conjecture) – does every convex polyhedron have a net?
トムソン問題 The Thomson problem - what is the minimum energy configuration of N particles bound to the surface of a unit sphere that repel each other with a 1/r potential (or any potential in general)?
Falconer's conjecture
g-conjecture
Circle packing in an equilateral triangle
Circle packing in an isosceles right triangle
Furstenberg conjecture – Is every invariant and ergodic measure for the action on the circle either Lebesgue or atomic?
Margulis conjecture — Measure classification for diagonalizable actions in higher-rank groups
MLC conjecture – Is the Mandelbrot set locally connected ?
Weinstein conjecture - Does a regular compact contact type level set of a Hamiltonian on a symplectic manifold carry at least one periodic orbit of the Hamiltonian flow?
Is every reversible cellular automaton in three or more dimensions locally reversible?
ケーテ予想 (en:Köthe conjecture)
(en:Birch–Tate conjecture)
セール予想 (Serre's conjecture II)
(en:Bombieri–Lang conjecture)
(en:Farrell–Jones conjecture)
ボスト予想 (Bost conjecture)
(en:Uniformity conjecture)
(en:Kaplansky's conjecture)
(en:Kummer–Vandiver conjecture)
(en:Serre's multiplicity conjectures)
(en:Pierce–Birkhoff conjecture)
(en:Eilenberg–Ganea conjecture)
グリーン予想(英語版)
(en:Grothendieck–Katz p-curvature conjecture)
(en:Sendov's conjecture)
ゴールマハティヒ予想 (en:Goormaghtigh conjecture)