Don Zagier is an American mathematician whose main area of work is number theory. In 1976, aged only 24, he became Germany's youngest professor. Among many other things, he is known for discovering a short and elementary proof of Fermat's theorem on sums of two squares: it consists of a single sentence. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany, and a professor at the Collège de France in Paris, France.
"Partitions:" The number of partitions p(n) of a natural number n is the number of ways of splitting it into positive parts, where the order does not matter. For instance, p(4)=5 because 4 can be written as 1+1+1+1, 1+1+2, 1+3, 2+2 or 4. This function, which was studied by Euler, Ramanujan and many others, has fascinating properties. I will tell some of these and also give a brand-new proof, never yet presented in public, of three famous congruences due to Ramanujan.