In 2006, researchers closed a major chapter in mathematics, reaching a consensus that the elusive Poincar Conjecture, which deals with abstract shapes in three-dimensional space, had finally been solved. Science and its publisher AAAS, the nonprofit society, now salute this development as the Breakthrough of the Year and also give props to nine other of the years most significant scientific accomplishments.
Sciences Top Ten list appears in the journals 22 December 2006 issue.
The Poincar Conjecture is part of a branch of mathematics called topology, informally known as "rubber sheet geometry" because it involves surfaces that can undergo arbitrary amounts of stretching. The conjecture, proposed in 1904 by Henri Poincar, describes a test for showing that a space is equivalent to a "hypersphere," the three-dimensional surface of a four-dimensional ball.
A century later, researchers were still trying to prove the conjecture. In 2000, the Clay Mathematics Institute named the Poincar Conjecture as one of its million-dollar "Millennium Prize" problems.
In 2002, Russian mathematician Grigori Perelman, who had been working mostly incommunicado for seven years, posted on the Internet the first of three papers that outlined a proof of Poincars conjecture as part of an even more ambitious result.
The work set experts abuzz. Though there were still many gaps to be filled in, it looked as if Perelman had scored a historic coup. But, after a visit to the United States in 2003, the reclusive mathematician returned to Russia and stopped replying to phone calls and emails. Other mathematicians were left on their own to determine whether Perelman had truly solved the Poincar Conjecture.
By 2006, the others finally caught up. Three separate teams wrote papers that filled in key missing details of Perelmans proof, and there was little doubt among his colleagues that he had solved the famous problem. This summ
Contact: Natasha Pinol
American Association for the Advancement of Science