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2025 Clay Research Conference and Workshops
The 2025 Clay Research Conference was held on Wednesday and Thursday, 1-2 October, with associated workshops held Monday, Tuesday, and Friday during the week of the conference. Videos of the plenary talks can be found in the Video Library in Online Resources.
Call for Proposals
CMI invites proposals under the Enhancement and Partnership Program for fiscal year 2026 (1 October 2025-30 September 2026) and later. The principal aim of the program is to enhance activities that are already planned and financially viable.
CMI-HIMR Summer School
CMI and the Heilbronn Institute announce the 2026 CMI-HIMR Summer School on Random Geometries and Random Matrices.
The Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.
The Millennium problems
See allBirch and Swinnerton-Dyer Conjecture
Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.
Navier-Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Hodge Conjecture
The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.
Upcoming events
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Trends in Differential and Complex Geometry: a celebration of Nigel Hitchin’s 80th birthday
University of Oxford
NZMRI 2026
Napier, NZ
CMI-HIMR Summer School on Random Geometries and Random Matrices
University of Bristol
New Methods in Evolution Partial Differential Equations
Princeton University
