数学上の未解決問題（すうがくじょうのみかいけつもんだい、英: unsolved problems in mathematics）とは、未だ解決されていない数学上の問題のことで、未解決問題の定義を「未だ証明が得られていない命題」という立場を取るのであれば、そういった問題は数学界に果てしなく存在する。ここでは、リーマン予想のようにその証明結果が数学全域と関わりを持つような命題、P≠NP予想のようにその結論が現代科学、技術のあり方に甚大な影響を及ぼす可能性があるような命題、問いかけのシンプルさ故に数多くの数学者や数学愛好家たちが証明を試みてきたような有名な命題を列挙する。
(Wild Problem（英語版）): Classification of pairs of n×n matrices under simultaneous conjugation and problems containing it such as a lot of classification problems
Finding a formula for the probability that two elements chosen at random generate the symmetric group
en:Union-closed sets conjecture: for any family of sets closed under sums there exists an element (of the underlying space) belonging to half or more of the sets
en:Lonely runner conjecture: if runners with pairwise distinct speeds run round a track of unit length, will every runner be "lonely" (that is, be at least a distance from each other runner) at some time?
en:1/3–2/3 conjecture : does every finite partially ordered set that is not totally ordered contain two elements x and y such that the probability that x appears before y in a random linear extension is between 1/3 and 2/3?
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?
The Ringel–Kotzig conjecture on graceful labeling of trees
How many unit distances can be determined by a set of n points? (see Counting unit distances)
The Hadwiger–Nelson problem on the chromatic number of unit distance graphs
Lovász conjecture
Deriving a closed-form expression for the percolation threshold values, especially (square site)
Tutte's conjectures that every bridgeless graph has a nowhere-zero 5-flow and every bridgeless graph without the Petersen graph as a minor has a nowhere-zero 4-flow
Petersen coloring conjecture
The reconstruction conjecture and new digraph reconstruction conjecture concerning whether or not a graph is recognizable by the vertex deleted subgraphs.
The cycle double cover conjecture that every bridgeless graph has a family of cycles that includes each edge twice.
Does a Moore graph with girth 5 and degree 57 exist?
The Cherlin–Zilber conjecture: A simple group whose first-order theory is stable in is a simple algebraic group over an algebraically closed field.
The Main Gap conjecture, e.g. for uncountable first order theories, for AECs, and for -saturated models of a countable theory.[22]
Determine the structure of Keisler's order[23][24]
The stable field conjecture: every infinite field with a stable first-order theory is separably closed.
Is the theory of the field of Laurent series over decidable? of the field of polynomials over ?
(BMTO) Is the Borel monadic theory of the real order decidable? (MTWO) Is the monadic theory of well-ordering consistently decidable?[25]
The Stable Forking Conjecture for simple theories[26]
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?[27]
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).[22][28]
Shelah's categoricity conjecture for L_{\omega_1,\omega}: If a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number.[22]
Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property?[29]
If the class of atomic models of a complete first order theory is categorical in the , is it categorical in every cardinal?[30][31]
Is every infinite, minimal field of characteristic zero algebraically closed? (minimal = no proper elementary substructure)
Kueker's conjecture[32]
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?[33]
The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?[34]
