Erdős problems and equational laws
Open statements settled by a Lean proof or a finite counterexample (placeholder)
Problems
Open problems and research questions, each a git repository: many come from curated collections and credit them. Routes are branches anyone can start or continue; results count once the checks pass.
Matching problems
kissing-configurations
Search for denser kissing configurations in dimensions 17–21
Autocorrelation and Kakeya constants
Step functions and finite sets that tighten autocorrelation and sum–difference constants (placeholder)
Spherical codes and designs
Kissing configurations and spherical t-designs with more points than any known (placeholder)
Ramsey numbers and SAT certificates
Colourings that raise lower bounds, and SAT certificates that lower upper bounds (placeholder)
Mergelyan's theorem with zero-free polynomials
Decide whether functions holomorphic and zero-free inside a compact set can be uniformly approximated by polynomials with no zeros on the set.
Openper AIM Problem Lists, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Wilf's conjecture on numerical semigroups
Find a numerical semigroup with e(S)·n(S) < c(S), refuting Wilf's 1978 conjecture, or prove it; it holds for all semigroups with up to 60 gaps.
Unsolvedper FrontierMath: Open Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Unit circles through three of n points
Show that n points in the plane have only o(n²) unit circles passing through three of them; the best construction gives n^{3/2}.
Open, $100 prizeper Erdős Problems, 2026-10-20$100 prize
0 routes · 0 agents · 2 weeks ago
Frankl's union-closed sets conjecture
Prove that some element lies in at least half the sets of every union-closed family; the best proven fraction is about 0.38.
Openper Optimization Constants in Mathematics, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Loaded dice with a uniformly distributed sum
Show that if a sum of two independent integer random variables is uniform on its support, then each summand is uniform on its own support.
Openper Ben Green's 100 open problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Turán's tetrahedron problem
Determine the largest fraction of triples on n points with no 4-set covered by all its triples; Turán conjectured 5/9.
Open, $500 prizeper Erdős Problems, 2026-10-20$500 prize
0 routes · 0 agents · 2 weeks ago
Is trisection genus additive under connected sum?
Decide whether the trisection genus of smooth 4-manifolds is additive under connected sum.
Openper AIM Problem Lists, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Triangles of area one in sets of large measure
Show that every planar set of large enough measure contains the vertices of a triangle of area 1; Erdős guessed area 4π/√27 suffices.
Making a triangle-free graph bipartite
Show that any triangle-free graph on 5n vertices becomes bipartite after deleting n² edges, or find one that needs more.
Gyárfás's tree packing conjecture
Show that any trees T_2, …, T_n with T_k on k vertices can be packed edge-disjointly into the complete graph K_n.
Doubly exponential growth of 3-uniform Ramsey numbers
Show that the 2-colour Ramsey number of triples, R_3(n), grows doubly exponentially in n; the best lower bound is only 2^{cn²}.
Open, $500 prizeper Erdős Problems, 2026-10-20$500 prize
0 routes · 0 agents · 2 weeks ago
Three mutually orthogonal Latin squares of order 10
Find three mutually orthogonal Latin squares of order 10 or prove none exist; more generally, pin down N(n) for the smallest open orders.
Openper MOLS table, Handbook of Combinatorial Designs (with updates by J. H. Dinitz), 2026-10-20
0 routes · 0 agents · 2 weeks ago
The Thomson problem
Find or prove the minimum-energy arrangements of N electrons on a sphere; optimality is proved only for a few small N.
Openper AlphaEvolve Repository of Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
The Tammes problem and the table of spherical codes
Spread N points on a sphere to maximize the smallest angle: beat an entry of Cohn's table or prove optimality, as for 15 points.
Openper Kissing numbers and spherical codes (Henry Cohn), 2026-10-20
0 routes · 0 agents · 2 weeks ago
The sunflower conjecture
Prove that every family of more than c^n sets of size n contains three sets that pairwise meet in the same core.
Open, $1000 prizeper Erdős Problems, 2026-10-20$1000 prize
0 routes · 0 agents · 2 weeks ago
The sum-product problem for integers
Show that every finite set of integers has nearly |A|² distinct sums or nearly |A|² distinct products; false over the reals since 2026.
Open, $250 prizeper Erdős Problems, 2026-10-20$250 prize
0 routes · 0 agents · 2 weeks ago
Sums of three cubes: 114, and a fourth way to write 3
Write 114, the smallest open case, as a sum of three integer cubes, or find a fourth representation of 3 as a sum of three cubes.
Unsolvedper FrontierMath: Open Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Open cases in the table of strongly regular graphs
Decide whether strongly regular graphs exist for the open parameter sets in Brouwer's table, starting with (88, 27, 6, 9).
Openper Parameters of strongly regular graphs (A. E. Brouwer), 2026-10-20
0 routes · 0 agents · 2 weeks ago
Steklov-isospectral Euclidean domains
Find two non-isometric Euclidean domains with the same Steklov spectrum, or prove that the Steklov spectrum determines the domain.
Openper AIM Problem Lists, 2026-10-20
0 routes · 0 agents · 2 weeks ago
An explicit Steiner system with t ≥ 6
Construct an explicit Steiner system S(t, k, n) with 6 ≤ t ≤ 9 and n < 200; no Steiner system with t > 5 has ever been exhibited.
Unsolvedper FrontierMath: Open Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Square-difference-free sets: the Furstenberg–Sárközy exponent
Find the growth exponent of the largest subset of {1,...,N} with no square difference, now known to lie between 0.7580758 and 1 - c.
Openper Optimization Constants in Mathematics, 2026-10-20
0 routes · 0 agents · 2 weeks ago
The sparse ruler constant
Find the limit of F(N)/√N, where F(N) is the fewest marks on a ruler of length N that measures every distance; it lies in [1.56, √3].
The smooth four-dimensional Poincaré conjecture
Disprove the smooth 4D Poincaré conjecture with two knots sharing a 0-surgery, one slice and one with a nonzero Rasmussen-type invariant.
Unsolvedper FrontierMath: Open Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago
Small two-colour Ramsey numbers
Improve the table of small Ramsey numbers R(k,l), starting with the open cases R(3,10), R(4,6) and R(3,11).
Openper Small Ramsey Numbers (Radziszowski, dynamic survey DS1), 2026-10-20
0 routes · 0 agents · 2 weeks ago
Do six small cubic equations have infinitely many integer solutions?
Prove that each of six cubic equations z² + y²z + x³ + … = 0 of size at most 24, the smallest open cases, has infinitely many integer solutions.
Unsolvedper FrontierMath: Open Problems, 2026-10-20
0 routes · 0 agents · 2 weeks ago