## A Beautiful Mind mathematician wins Abel prize

发布时间：2019-03-15 05:11:01来源：未知点击：

By Jacob Aron (Image: Contrasto/eyevine) John Nash, the mathematician made famous by the film A Beautiful Mind, has been awarded the Abel prize, often called the Nobel prize of maths, by the Norwegian Academy of Sciences and Letters. He shares the $765,000 prize with Louis Nirenberg of New York University for their work linking nonlinear partial differential equations (PDEs), which crop up in all sorts of real-world problems, to the analysis of abstract geometric shapes. Nash previously won the 1994 economics Nobel for his work in game theory, which is used to study how people conflict, cooperate and make decisions, meaning he is the first person to win both prizes. “I must be an honorary Scandinavian,” he joked during a press conference announcing the winners. “I’m overwhelmed,” said Nirenberg. “I was asleep when the phone range yesterday, and I was simply astonished, just flabbergasted.” The pair never authored a paper together but worked informally in the 1950s. They share the prize for linking two seemingly separate areas of mathematics, and providing mathematicians with new tools to analyse problems in both fields. Everyday shapes like triangles and cubes occupy what mathematicians call Euclidean space, after the ancient Greek mathematician Euclid. But there are also other spaces in which familiar geometrical rules, like the internal angles of a triangle adding up to 180 degrees, don’t apply. One important example is called Riemannian space, which was used by Albert Einstein to study the links between curvature and gravity, leading to his theory of general relativity. Translating between different spaces can help mathematicians study them in different ways, but you need rules to do so. That’s where PDEs come into play. PDEs are equations that model changes in systems involving multiple dimensions, which include everything from the flow of heat in a room to the behaviour of financial markets. Curvature can also be thought of as a change across multiple dimensions, meaning PDEs provide the rules to explore complex geometries. Nash and Nirenberg came up with ways to solve PDEs that mathematicians have been benefiting from ever since. “John Nash and Louis Nirenberg have played leading roles in the development of this theory,” said John Rognes, who chairs the Abel committee. In 2012 a team of French mathematicians used their techniques to solve a long-standing mystery of how a square can be transformed into a doughnut, and in 2003 Grigori Perelman used them to prove the Poincaré conjecture, one of the Clay Mathematics Institute’s Millennium Prize Problems. More on these topics: