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Resolution status records whether a conjecture has actually been settled. Wikipedia notes that "as of 2026, the Poincare conjecture is the only Millennium Prize Problem with a verified solution," making its resolved status genuinely rare among famous open problems. This dimension separates conjectures that have been proven from those still standing open.

Open

112 entries

Branch

Proposed

Posed By

Resolved Year

1/3-2/3 Conjecture

ABC Conjecture

Agoh-Giuga Conjecture

Agrawal's Conjecture

Andre-Oort Conjecture

Andrews-Curtis Conjecture

Andrica's Conjecture

Artin's Conjecture on Primitive Roots

Bass Conjecture

Bass-Quillen Conjecture

Bateman-Horn Conjecture

Beal Conjecture

Beal's Conjecture

Big-Line-Big-Clique Conjecture

Birch and Swinnerton-Dyer Conjecture

Bombieri-Lang Conjecture

Borel Conjecture

Brennan Conjecture

Brocard's Conjecture

Bunyakovsky Conjecture

Carmichael's Totient Function Conjecture

Casas-Alvero Conjecture

Collatz Conjecture

Continuum Hypothesis

Conway's Thrackle Conjecture

Cramer's Conjecture

Dittert Conjecture

Dixmier Conjecture

Eilenberg-Ganea Conjecture

Elliott-Halberstam Conjecture

Erdos Conjecture on Arithmetic Progressions

Erdos-Gyarfas Conjecture

Erdos-Hajnal Conjecture

Erdos-Straus Conjecture

Falconer's Conjecture

Feit-Thompson Conjecture

Fermat-Catalan Conjecture

Filling Area Conjecture

Firoozbakht's Conjecture

Fortune's Conjecture

Four Exponentials Conjecture

Fujita Conjecture

Gauss Circle Problem

Gilbert-Pollak Conjecture

Gilbreath's Conjecture

Goldbach Conjecture

Goormaghtigh Conjecture

Grimm's Conjecture

Grothendieck-Katz p-curvature Conjecture

Hadamard Conjecture

Hall's Conjecture

Hartmanis-Stearns Conjecture

Herzog-Schonheim Conjecture

Hilbert-Smith Conjecture

Hodge Conjecture

Inscribed Square Problem

Invariant Subspace Problem

Jacobson's Conjecture

Kakeya Conjecture

Kalai's 3^d Conjecture

Kummer-Vandiver Conjecture

Legendre's Conjecture

Lehmer's Conjecture

Lemoine's Conjecture

Leopoldt's Conjecture

List Coloring Conjecture

Littlewood Conjecture

Lonely Runner Conjecture

Lovasz Conjecture

Mahler Conjecture

Manin Conjecture

Monomial Conjecture

Montgomery's Pair Correlation Conjecture

N Conjecture

Nagata's Conjecture on Curves

Navier-Stokes Existence and Smoothness

Novikov Conjecture

Oppermann's Conjecture

P versus NP

Parshin's Conjecture