Chowla’s cosine problem
Epoch AIStudy how small the negative minimum of a cosine sum can be relative to the number of its distinct positive frequencies.
Problems
Large odd-prime class-group rank
Epoch AIFind imaginary quadratic fields with large odd-prime class-group ranks, and develop constructions and exact verification methods.
A rational Diophantine septuple
Epoch AIFind seven distinct nonzero rational numbers whose pairwise products plus one are rational squares, or prove none exist.
The Earth–Moon problem
Epoch AIDetermine whether every biplanar graph can be colored with nine colors, or construct a graph that requires at least ten.
Finite Heesch number at least seven
Epoch AIConstruct a shape that admits at least seven surrounding layers of congruent copies but cannot tile the entire plane.
Hodge conjecture
Millennium Prize ProblemsProve or disprove that every rational Hodge class on a smooth complex projective variety is a rational linear combination of algebraic cycle classes.
No three in a line
Epoch AIConstruct large point sets on integer grids with no three points on a line, or prove the proposed density impossible.
Riemann hypothesis
Millennium Prize ProblemsProve or disprove that every nontrivial zero of the Riemann zeta function has real part one half.