$1 Million:
Honoring Brilliance
Questions of an era. Answers that shape the next.
$1 Million:
Honoring Brilliance
Questions of an era.
Answers that shape the next.
$1 Million:Honoring
Brilliance
Questions of an era.
Answers that shape the next.
Pinnacle Problems
Recognized core difficult problems in the field, designated by the list published by this Prize, with a prize of USD 1 million.
Riemann hypothesis
Riemann hypothesis
Do all nontrivial zeros of the Riemann zeta function have real part one half? This determines how tightly errors in prime distribution can be bounded.
Do all nontrivial zeros of the Riemann zeta function have real part one half? This determines how tightly errors in prime distribution can be bounded.
P versus NP problem
P versus NP problem
If a proposed solution can be verified in polynomial time, can a solution also always be found in polynomial time?
If a proposed solution can be verified in polynomial time, can a solution also always be found in polynomial time?
Birch–Swinnerton-Dyer conjecture (BSD)
Birch–Swinnerton-Dyer conjecture (BSD)
Does the rank of an elliptic curve's rational-point group equal the order of vanishing of its L-function at one? The strong form also predicts the leading coefficient.
Does the rank of an elliptic curve's rational-point group equal the order of vanishing of its L-function at one? The strong form also predicts the leading coefficient.
Hodge conjecture
Hodge conjecture
On a smooth complex projective variety, is every rational Hodge class of equal bidegree a rational linear combination of classes of algebraic subvarieties?
On a smooth complex projective variety, is every rational Hodge class of equal bidegree a rational linear combination of classes of algebraic subvarieties?
Existence and smoothness of the 3D Navier–Stokes equations
Existence and smoothness of the 3D Navier–Stokes equations
For three-dimensional incompressible viscous flow, do smooth initial data always yield globally smooth solutions, or can finite-time singularities be constructed under the official conditions?
For three-dimensional incompressible viscous flow, do smooth initial data always yield globally smooth solutions, or can finite-time singularities be constructed under the official conditions?
Yang–Mills existence and mass gap
Yang–Mills existence and mass gap
Construct a nontrivial quantum Yang–Mills theory rigorously in four dimensions and prove a positive energy gap between the vacuum and the lowest nonzero excitation.
Construct a nontrivial quantum Yang–Mills theory rigorously in four dimensions and prove a positive energy gap between the vacuum and the lowest nonzero excitation.
Poincaré conjecture
Poincaré conjecture
Is every closed simply connected three-manifold homeomorphic to the three-sphere?
Is every closed simply connected three-manifold homeomorphic to the three-sphere?
© 2026 H.E. Justin Sun. All rights reserved.
© 2026 H.E. Justin Sun. All rights reserved.
© 2026 H.E. Justin Sun. All rights reserved.