(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.

(mathematics) A generalization of certain properties of multidimensional spaces.

abc conjecture

(number theory) A conjecture about the distribution of prime numbers in arithmetic progressions, having many applications in sieve theory.

(mathematics) A conjecture in the theory of minimal surfaces, stating that the shape that encloses and separates two given volumes and has the minimum possible surface area is a "standard double bubble": three spherical surfaces meeting at angles of 2π/3 on a common circle.

A conjecture within holography that posits a quantitative relationship between the entanglement entropy of a conformal field theory and the geometry of an associated anti-de Sitter spacetime.