Mathematical Developments in 1992

Mathematical research in 1992 revealed a surprising connection between a newly discovered means of checking proofs and the intrinsic difficulty of certain optimization problems. A problem dating to 1910 was finally solved, revealing that there are an infinite number of exceptions to a muchused method of testing whether a number is prime. Two conjectures about higher-dimensional spaces were refuted, leading mathematicians to conclude that our intuition about the familiar spaces of two and three dimensions can lead us astray in higher dimensions. A well-known combinatorial problem, with applications to design of experiments, was solved. A new Mersenne prime was discovered, physics provided a new method of cryptography, a human defeated a computer for the world checkers championship, calculations showed that the solar system is chaotic in the mathematical sense, questions were raised concerning random-number generators, and research suggested that babies may have some numerical understanding. Finally, Fermat's last theorem was verified for larger exponents, but this achievement was overshadowed by a proof in 1993 for all exponents larger than 2.