Princeton University mathematician John Nash was awarded the 2015 Abel Prize by the Norwegian Academy of Science and Letters March 25 for his seminal work on partial differential equations, which are used to describe the basic laws of scientific phenomena. Established in 2003, the award is one of the most prestigious in the field of mathematics and includes an $800,000 prize.
Nash, a Princeton senior research mathematician, will share the prize with longtime colleague Louis Nirenberg, a professor emeritus at New York University's Courant Institute of Mathematical Sciences. Nash is the second consecutive Princeton researcher to receive the honor; Yakov Sinai, a Princeton University professor of mathematics, was awarded the 2014 Abel Prize for his influential 50-year career in mathematics. Several past winners have been University alumni.
Nash is a 1994 Nobel Prize laureate in economics publicly known for his work in game theory as dramatized in the 2001 film "A Beautiful Mind" in which he was portrayed by actor Russell Crowe.
It is Nash's work in geometry and partial differential equations that "the mathematical community regards as his most important and deepest work," according to the academy. The prize citation recognized Nash and Nirenberg for "striking and seminal contributions? to the theory of nonlinear partial differential equations and its applications? to geometric analysis."
The academy went on to say: "Their breakthroughs have developed into versatile and robust techniques, which have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory .... [T]he widespread impact of both Nash and Nirenberg on the modern toolbox of nonlinear partial differential equations cannot be fully covered here."
David Gabai, the Hughes-Rogers Professor of Mathematics and department chair, said that Nash's approach to a mathematical problem was so innovative that his methods, such as the Nash embedding theorems, became just as important as the solution.
Nash's name is attached to a range of influential work in mathematics, including the Nash-Moser inverse function theorem, the Nash-De Giorgi theorem (which stemmed from a problem Nash undertook at the suggestion of Nirenberg), and the Nash embedding theorems, which the academy described as "among the most original results in geometric analysis of the twentieth century."
"The Nash embedding/immersion theorems are absolutely incredible results that any mathematician can appreciate," Gabai said. "Nash's work in game theory and geometry are absolutely fundamental, yet there is no comparison between the depth of the latter and that of the former. His embedding theorems required not only unusual insight but also tremendous technical expertise."
While a Princeton graduate student in the 1970s, Gabai, like other students, was encouraged by Nash's work and presence at the University, he said. "We all knew about his amazing and hard-to-believe work. That strongly contributed to an atmosphere that encouraged us to be ambitious and to ask bold and crazy questions," Gabai said.
Peter Sarnak, Princeton's Eugene Higgins Professor of Mathematics, said that the Abel Prize is the latest and most prestigious of the many honors that Nash began receiving later in his career starting with the Nobel Prize.
"While his publication list is shorter than many mathematicians, the novelty and impact of each of his papers is unique," Sarnak said. "I have discussed mathematics with him over the years and he thinks very differently to most of us."
Nash joined the Princeton mathematics department as a senior research mathematician in 1995. His honors include the American Mathematical Society's 1999 Leroy P. Steele Prize for Seminal Contribution to Research and the 1978 John von Neumann Theory Prize. Nash holds membership in the National Academy of Sciences and in 2012 was an inaugural fellow of the American Mathematical Society.
A native of Bluefield, West Virginia, Nash received his doctorate in mathematics from Princeton in 1950 and his graduate and bachelor's degrees from Carnegie Institute of Technology (now Carnegie Mellon University) in 1948.
Nash and Nirenberg were announced as the 2015 Abel Prize recipients in Oslo on March 25 by the president of the Norwegian Academy of Science. They will accept the prize from His Majesty King Harald V of Norway during a May 19 ceremony in Oslo.