Over the course of time, several lists of unsolved mathematical problems have appeared. The computation of singular solutions in elliptic problems and elasticity PDF problem, the Poincaré conjecture, has been solved.
2e, ee, Catalan’s constant, or Khinchin’s constant rational, algebraic irrational, or transcendental? Singmaster’s conjecture: is there a finite upper bound on the multiplicities of the entries greater than 1 in Pascal’s triangle? Finding a function to model n-step self-avoiding walks. Give a combinatorial interpretation of the Kronecker coefficients.
Jordan curve have an inscribed square? Is the Mandelbrot set locally connected? Is every reversible cellular automaton in three or more dimensions locally reversible? Many problems concerning an outer billiard, for example show that outer billiards relative to almost every convex polygon has unbounded orbits. Sudoku: What is the maximum number of givens for a minimal puzzle? How many puzzles have exactly one solution? How many minimal puzzles have exactly one solution?
Tic-tac-toe variants: Given a width of tic-tac-toe board, what is the smallest dimension such that X is guaranteed a winning strategy? The Oberwolfach problem on which 2-regular graphs have the property that a complete graph on the same number of vertices can be decomposed into edge-disjoint copies of the given graph. Is there a drawing of any complete bipartite graph with fewer crossings than the number given by Zarankiewicz? Does a Moore graph with girth 5 and degree 57 exist? The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted subgraphs. The second neighborhood problem: does every oriented graph contain a vertex for which there are at least as many other vertices at distance two as at distance one?
Is every finitely presented periodic group finite? The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals? Are there an infinite number of Leinster Groups? The stable field conjecture: every infinite field with a stable first-order theory is separably closed.
Is the Borel monadic theory of the real order decidable? Is the monadic theory of well-ordering consistently decidable? 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 a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number. Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property?
Is every infinite, minimal field of characteristic zero algebraically closed? Here, « minimal » means that every definable subset of the structure is finite or co-finite. Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts? Do the Henson graphs have the finite model property? 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? Proof claimed in 2012, currently under review. Do any odd perfect numbers exist? Are there infinitely many perfect numbers?
Do any odd weird numbers exist? Are there infinitely many amicable numbers? Are there any pairs of amicable numbers which have opposite parity? Are there any pairs of relatively prime amicable numbers? Are there infinitely many betrothed numbers?