The 2006 recipients of the Fields Medal—considered by mathematicians around the world to be equivalent to the Nobel Prize—were named in August at the International Congress of Mathematicians during a ceremony in Madrid. The International Mathematical Union awards the honors every four years to mathematicians under 40.

For the first time in the prestigious prize’s 40-year history, one of this year’s recipients turned down the medal and $9500 purse and declined to attend the August ceremony. Grigori Perelman, whose work may have resolved two outstanding problems in topology, the Poincaré conjecture and the Thurston geometrization conjecture, refused the prize after receiving a personal visit and invitation to the ceremony from Sir John Ball, IMU president. Perelman, who last December left his job of some years as a researcher at the Steklov Institute of Mathematics in St. Petersburg, Russia, had been named as a recipient of the medal “for his...

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