(mathematics, physics) An attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics.

(algebra) The conjecture that any endomorphism of a Weyl algebra is an automorphism.

(mathematics) A famous problem on polynomials in several variables.

plural of Jacobian conjecture

(mathematics) The proven conjecture that a regular hexagonal grid, or honeycomb, is the best way to divide a surface into regions of equal area with the smallest total perimeter.

(mathematics) The conjecture that the process of taking a number n and, if n is even, dividing it by 2, or if n is odd, multiplying it by 3 and adding 1, then repeating this process, will eventually yield 1.

(graph theory) A conjecture concerning the connection between graph coloring and the tensor product of graphs. A counterexample was found in 2019.

(number theory) The conjecture (disproved in 1958) that at least half of the natural numbers smaller than any given number have an odd number of prime factors.

(geometry) The conjecture that, in any tiling of n-dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire (n − 1)-dimensional face with each other.

(number theory) The conjecture that there are at least four prime numbers between (pₙ)² and (pₙ₊₁)², where pₙ is the nth prime number, for every n ≥ 2.