John Nash, the Princeton University mathematician, has been awarded the 2015 Abel Prize by the Norwegian Academy of Science and Letters. Mr. Nash, 86, was recognized on 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.

Mr. Nash will share the prize with longtime colleague Louis Nirenberg, a professor emeritus at New York University’s Courant Institute of Mathematical Sciences. Mr. 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.

Mr. Nash’s life and work in game theory were dramatized in the 2001 film A Beautiful Mind, starring Russell Crowe. He is a 1994 Nobel Prize laureate in economics. It is Mr. 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 Mr. Nash and Mr. Nirenberg for “striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.”

Mr. 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. He holds membership in the National Academy of Sciences and in 2012 was an inaugural fellow of the American Mathematical Society.

Mr. 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. He and Mr. 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.