Fifth Abel Conference: Celebrating the Mathematical Impact of John F. Nash Jr. and Louis Nirenberg

The Norwegian Academy of Science and Letters named both John F. Nash Jr. and Louis Nirenberg as the 2015 recipients of the Abel Prize "for striking and seminal contributions to the theory of nonlinear partial differential equations (PDEs) and its applications to geometric analysis."

The Abel Committee's citation weaves together Nash's and Nirenberg's works in a remarkable, almost poetic way, emphasizing the many parallels and connections between their contributions. The most obvious connections are by area; geometric analysis and regularity theory are among the subjects where both made fundamental advances. But the citation also emphasizes a more subtle connection. Beyond solving important problems, each has introduced important methods and tools which have become essential parts of the fabric of the field. As the citation puts it: "Their impact can be felt in all branches of the theory [of nonlinear partial differential equations], from fundamental existence results to the qualitative study of solutions, both in smooth and non­smooth settings."

John Nash's previous honors include INFORMS' John von Neumann Theory Prize in 1978; the Nobel Prize in Economics in 1994 for his work in game theory; election to the National Academy of Sciences in 1996; and the AMS's 1999 Steele Prize for Seminal Contribution to Research (for his 1956 embedding theorem). Most of Nash's mathematical work was done while he was at MIT during the period from 1951 to ­1959. This was followed by a period of mental illness, which subsided by the 1990's. A video interview of Nash is available at the Simons Foundation's Science Lives website. Nash is the subject of a biography, A Beautiful Mind, by Sylvia Nasar. Tragically, John Nash and his wife Alicia were killed in an automobile accident on May 23, 2015, as they returned home from Norway after receiving the Abel Prize.

Louis Nirenberg's previous honors include the AMS's Bôcher Memorial Prize (1959); election to the National Academy of Sciences (1969); the Swedish Academy of Science's inaugural Crafoord Prize (1982); the AMS's Steele Prize for Lifetime Achievement (1994); and the National Medal of Science (1995). In 2010, he received the inaugural Chern Medal, a lifetime ­achievement award from the International Mathematical Union and the Chern Medal Foundation. In 2014, he received the AMS's Steele Prize for Seminal Contribution to Research (for his 1982 paper with Caffarelli and Kohn on the Navier-­Stokes equations). Nirenberg has spent his entire mathematical career at NYU's Courant Institute of Mathematical Sciences. The Mathematics Genealogy website credits him with 46 Ph.D. students and 346 descendants. A video interview of Nirenberg is available at the Simons Foundation's Science Lives website. Other web resources include the site associated with his 2010 Chern Medal and an interview with Allyn Jackson published in the April 2002 Notices of the American Mathematical Society.