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All Conjectures

Claims mathematicians believe are true, or take seriously as live possibilities, that have no accepted proof either way. Belongs here: open conjectures, grouped below by the branch of mathematics the claim belongs to. Does not belong here: settled results, filed as theorems once proved, or the open problems catalogued separately under Open Questions, which record a question's own history and status rather than a specific claim awaiting proof.

Nakai Conjecture

Navier-Stokes Existence and Smoothness

Novikov Conjecture

Oppermann's Conjecture

P versus NP

Parshin's Conjecture

Pierce-Birkhoff Conjecture

Polignac's Conjecture

Reconstruction Conjecture

Riemann Hypothesis

Ringel-Kotzig Conjecture

Rota's Basis Conjecture

Rudin's Conjecture

Ryser's Conjecture

Sato-Tate Conjecture

Schanuel's Conjecture

Schinzel's Hypothesis H

Scholz Conjecture

Second Hardy-Littlewood Conjecture

Section Conjecture

Sendov's Conjecture

Serre's Conjecture II

Serre's Multiplicity Conjectures

Sidorenko's Conjecture

Singmaster's Conjecture

Spectral Gap Conjecture

Standard Conjectures on Algebraic Cycles

Stark Conjectures

Szpiro's Conjecture

Tammes Problem

Tate Conjecture

Torsion Conjecture

Total Coloring Conjecture

Tuza's Conjecture

Twin Prime Conjecture

Ulam's Packing Conjecture

Uniform Boundedness Conjecture for Rational Points

Union-Closed Sets Conjecture

Unique Games Conjecture

Vaught Conjecture

Virasoro Conjecture

Vizing's Conjecture

Vojta's Conjecture

Volume Conjecture

Weibel's Conjecture

Weinstein Conjecture

Whitehead Conjecture

Yang-Mills Existence and Mass Gap

Zeeman Conjecture

Zimmer's Conjecture