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Zelmanov solves the restricted Burnside problem for groups.
Quidong Wang finds infinite series solutions to the n-body problem (with minor exceptions).
Menasco and Thistlethwaite prove the knot theory conjecture known as "Tait's Second Conjecture", namely that any two reduced alternating diagrams of the same prime knot are related by a sequence of twists.
Wiles proves Fermat's Last Theorem. (See this History Topic.)
Connes publishes a major text on noncommutative geometry.
Lions is awarded a Fields Medal for his work on the theory of nonlinear partial differential equations.
Yoccoz is awarded a Fields Medal for his work on dynamical systems.
Krystyna Kuperberg solves the "Seifert Conjecture" about the topology of dynamical systems.
A large prize is offered by banker Andrew Beal for a solution to the Beal Conjecture: the equation xp + yq = zr has no solutions for p, q, r > 2 and coprime integers x, y, z.
Wiles is awarded the Wolfskehl Prize for solving Fermat's last theorem.
Borcherds is awarded a Fields Medal for his work in automorphic forms and mathematical physics; Gowers receives one for his work in functional analysis and combinatorics; Kontsevich receives one for his work in algebraic geometry, algebraic topology, and mathematical physics; and McMullen receives one for his work on holomorphic dynamics and geometry of 3-dimensional manifolds.
Thomas Hales proves Kepler's problem on sphere packing.
The Great Internet Mersenne Prime Search project finds the 38th Mersenne prime: 26972593 -1.
Conrad and Taylor prove the "Taniyama-Shimura conjecture". Wiles proved a special case in 1993 on his way to giving a proof of Fermat's Last Theorem.
At a meeting of the American Mathematical Society in Los Angeles "Mathematical Challenges of the 21st Century" were proposed. Unlike "Hilbert's problems" from 100 years earlier, these were given by a team of 30 leading mathematicians of whom eight were Fields Medal winners.
A prize of seven million dollars is put up for the solution of seven famous mathematical problems. Called the Millennium Prize Problems they are: P versus NP; The "Hodge Conjecture"; The Poincaré Conjecture; The Riemann Hypothesis; "Yang-Mills Existence and Mass Gap"; "Navier-Stokes Existence and Smoothness"; and The "Birch and Swinnerton-Dyer Conjecture".
List of mathematicians alive in 2000.
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JOC/EFR August 2001
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