In 1999, the Frenchman Laurent Lafforgue solved a 33-year-old mathematical problem: The English Robert Langlands proposed that the algebra of mathematics (representation of Galois) and analysis (automorphic forms) have much to do. Fermat's last theorem can be considered a particular case in this area. Lafforgue clarified the relationship between the two, taking a great step towards unifying the theory of mathematics. He has now been awarded the Fields Prize awarded every four years.
The second winner, American Vladimir Voevodsky, has also developed a theory that combines two fields of mathematics. He has 'united' algebraic geometry and algebraic topology, so he has received this year's Fields award.