The greatest unsolved problem in mathematics was solved this year – namely, the Poincaré Conjecture. This achievement has now been named by Science magazine as the Breakthrough of the Year. Ars has a nice writeup of the background of the Conjecture and the road to the solution by Russian mathematician Grisha Perelman, including a layman’s description of the proof itself.
What’s intriguing however is the underlying drama. Perelman actually refused the Fields medal for his work – the most prestigious award in mathematics. There have been accusations of ethical lapses and intellectual dishonesty, and even the threat of lawsuits. The sordid details – of the story behind a mathematical proof! – are best outlined in this classic piece at The New Yorker, which features the only interview with Perelman on record.