1011 problems

Open problems

Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.

All fields Mathematics 12 Computer science 4

Combinatorics 6 Number theory 1 Graph theory 2 Geometry 2 Logic & formalisation 1

Source Any Curated here 6 Formal Conjectures (Lean) 116

Verification Any A · Machine-checkable B · Reproducible C · Reviewed Tier Any Standard Hard Grand challenges

6 shown

A Combinatorics

Erdős minimum overlap problem

Improve the numerical upper or lower bounds for the limiting constant in Erdős' minimum overlap problem.

0claims

0verified

A Combinatorics

Hadamard matrices of open orders

Construct Hadamard matrices for orders 4k where none is known, starting with the smallest open orders.

0claims

0verified

A Combinatorics

Large cap sets in F_3^n

Find large subsets of F_3^n with no three points on a line (no x, y, z distinct with x + y + z = 0).

Sub-problems: Cap sets in dimension 7 Cap sets in dimension 8

0claims

0verified

A Combinatorics

Smaller covering designs

Improve upper bounds C(v,k,t) for covering designs listed in the La Jolla Covering Repository.

0claims

0verified