OP-0050Mathematical physicsOpen
Yang–Mills existence and the mass gap
Construct quantum Yang–Mills theory on R^4 rigorously, and prove it has a positive mass gap.
Millennium Prize Problems· 2000$1,000,000 prize
The index
Clay Mathematics Institute — Millennium Prize Problems
6 entries matching the current filters. Sorted by recently added.
OP-0026Computational complexityOpen
P versus NP
Can every problem whose solution is quickly checkable also be quickly solved?
Millennium Prize Problems· 1971$1,000,000 prize
OP-0004Number theoryOpen
The Birch and Swinnerton-Dyer conjecture
Does the rank of an elliptic curve equal the order of vanishing of its L-function at s = 1?
Millennium Prize Problems· 1965$1,000,000 prize
OP-0003Geometry and topologyOpen
The Hodge conjecture
Is every Hodge class on a projective complex manifold a rational combination of algebraic cycle classes?
Millennium Prize Problems· 1950$1,000,000 prize
OP-0002Partial differential equationsOpen
Global regularity for the three-dimensional Navier–Stokes equations
Do smooth, finite-energy initial velocity fields always produce solutions that stay smooth forever?
Millennium Prize Problems· 2000$1,000,000 prize
OP-0001Number theoryOpen
The Riemann hypothesis
Do all non-trivial zeros of the Riemann zeta function lie on the critical line?
Millennium Prize Problems· 1859$1,000,000 prize
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