The Poincaré conjecture has been in the news lately. Russian mathematician Grigori Perelman submitted a proof 3 years ago claiming that he had proved the famous conjecture. In August, he won a prestigious Fields medal for his achievement.
But what is the Poincaré conjecture? Here’s how geometer Jeff Weeks describes it: “Basically, it’s a conjecture about what the simplest possible space is in each dimension.”