(number theory) A conjecture relating to the conductor and the discriminant of an elliptic curve, equivalent in a slightly modified form to the abc conjecture.

(number theory) A conjecture stating that every even integer greater than 2 can be expressed as the sum of two primes, which has been shown to hold up through 4 × 10¹⁸, but remains unproven.

(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 conjecture that every domain of ℝᵈ (i.e. subset of ℝᵈ with positive finite Lebesgue measure) is a spectral set if and only if it tiles ℝᵈ by translation.

(mathematics) A conjecture in combinatorial number theory, stating that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).

(mathematics) Synonym of Sendov's conjecture

(number theory) An estimate for the size of gaps between consecutive prime numbers, stating that p_n+1-p_n=O(( log p_n)²), where pₙ denotes the nth prime number, O is big O notation, and log is the natural logarithm.

(mathematics) A conjecture concerning the relationship between the locations of roots and critical points of a polynomial function of a complex variable. It states that for a polynomial f(z)=(z-r_1)⋯(z-r_n), qquad (n>2) with all roots r₁, ..., rₙ inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least one critical point.