Millennium Prize Problems
A set of seven fundamental unsolved mathematical problems established by the Clay Mathematics Institute, each carrying a one-million-dollar prize for a correct solution, representing the foremost open questions in contemporary mathematics.
Core Facts
The Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, comprising seven mathematical problems, each carrying a prize of one million US dollars upon solution.
The existence and smoothness problem of the Navier-Stokes equations is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize.
The Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, comprising seven problems each carrying a prize of $1 million.
Timeline (last 90 days)
克雷数学研究所于 2000 年设立了七个千禧年大奖难题，每个问题的解答者可获得 100 万美元奖金。
According to The New York Times, OpenAI stated that it has made substantial progress on a second Millennium Prize problem, but did not specify which problem or publish any results.
OpenAI claims to have made substantial progress on yet another Millennium Prize Problem.
There is a fundamental gap between solving competition problems and solving Millennium Prize Problems: competition problems have clear solution paths and known answers, whereas Millennium Prize Problems require entirely new mathematical ideas that humanity has yet to discover
The seven Millennium Prize Problems include P vs NP, the Hodge Conjecture, the Poincaré Conjecture, the Riemann Hypothesis, Yang–Mills Existence and Mass Gap, Navier–Stokes Existence and Smoothness, and the BSD Conjecture
IMO problems are closed problems—with definite answers, known solution methods, and clear verification standards—which is fundamentally different from the open-ended nature of the Millennium Prize Problems, which require entirely new mathematical tools.
The Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, comprising seven mathematical problems, each carrying a prize of one million US dollars upon solution.
The existence and smoothness problem of the Navier-Stokes equations is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize.
All Facts (8)
The Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, comprising seven mathematical problems, each carrying a prize of one million US dollars upon solution.
90%VerifiedThe existence and smoothness problem of the Navier-Stokes equations is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize.
90%VerifiedThe Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, comprising seven problems each carrying a prize of $1 million.
80%Unverified克雷数学研究所设立的七个千禧年大奖难题每题奖金百万美元，目前仅黎曼猜想等六题仍未解决
85%UnverifiedThere is a fundamental gap between solving competition problems and solving Millennium Prize Problems: competition problems have clear solution paths and known answers, whereas Millennium Prize Problems require entirely new mathematical ideas that humanity has yet to discover
60%Unverified克雷数学研究所于 2000 年设立了七个千禧年大奖难题，每个问题的解答者可获得 100 万美元奖金。
50%UnverifiedThe seven Millennium Prize Problems include P vs NP, the Hodge Conjecture, the Poincaré Conjecture, the Riemann Hypothesis, Yang–Mills Existence and Mass Gap, Navier–Stokes Existence and Smoothness, and the BSD Conjecture
50%UnverifiedIMO problems are closed problems—with definite answers, known solution methods, and clear verification standards—which is fundamentally different from the open-ended nature of the Millennium Prize Problems, which require entirely new mathematical tools.
50%