# John F. Nash, Jr. and Louis Nirenberg share the Abel Prize

The Norwegian Academy of Sciences and Letters has decided to award the Abel Prize for 2015 to the American mathematicians John F. Nash, Jr. and Louis Nirenberg “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” The President of the Academy, Kirsti Strøm Bull, announced the new laureates today 25 March. They will receive the Abel Prize from His Majesty King Harald at a ceremony in Oslo on 19 May.

John F. Nash, Jr., aged 86, spent his career at Princeton University and the Massachusetts Institute of Technology. Louis Nirenberg, aged 90, worked at New York University’s Courant Institute of Mathematical Sciences. Even though they did not formally collaborate on any papers, they influenced each other greatly during the 1950s. The results of their work are felt more strongly today than ever before.

### Mathematical giants

Nash and Nirenberg are two mathematical giants of the twentieth century. They are being recognized for their contributions to the field of partial differential equations (PDEs), which are equations involving rates of change that originally arose to describe physical phenomena but, as they showed, are also helpful in analyzing abstract geometrical objects. The Abel committee writes: “Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory.”

In the 1950s Nash proved important theorems about PDEs, which are considered by his peers to be his deepest work. Outside mathematics, however, Nash is best known for a paper he wrote about game theory, the mathematics of decision-making, which ultimately won him the 1994 Nobel Prize for economics, and which features strongly in the 2001 film about him, A Beautiful Mind.

### Long career

Nirenberg, who was born in Canada, has had one of the longest and most feted careers in mathematics, having produced important results right up until his 70s. Unlike Nash, who wrote papers alone, Nirenberg preferred to work in collaboration with others, with more than 90 per cent of his papers written jointly. Many results in the world of elliptic PDEs are named after him and his collaborators, such as the Gagliardo–Nirenberg inequalities, the John–Nirenberg inequality and the Kohn–Nirenberg theory of pseudo-differential operators.

“Far from being confined to the solutions of the problems for which they were devised, the results proven by Nash and Nirenberg have become very useful tools and have found tremendous applications in further contexts,” the Abel committee says.

### Many awards

Both men have received many distinguished awards. As well as winning the prize in economic sciences in memory of Alfred Nobel, Nash has won the John von Neumann Theory Prize (1978) and the American Mathematical Society’s Steele Prize for a Seminal Contribution to Research (1999). Nirenberg has won the American Mathematical Society’s Bôcher Memorial Prize (1959) the inaugural Crafoord Prize awarded by the Royal Swedish Academy of Science (1982), the Steele Prize for Lifetime Achievement from the American Mathematical Society (1994) and the first Chern Medal for lifetime achievement from the International Mathematical Union and the Chern Medal Foundation (2010).

### Karen Uhlenbeck first woman to win the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, USA “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.”

His Majesty King Harald V will present the Abel Prize to the laureate at the award ceremony in Oslo on the 21^{st} of May.

### Congratulations to Karen Uhlenbeck from University of Texas at Austin

"At the University of Texas at Austin and the Department of Mathematics, we are delighted and tremendously proud of Karen Uhlenbeck, recipient of the 2019 Abel Prize" - Thomas Chen, Chair of the University of Texas at Austin Math Department

(19.03.2019) More### Congratulations to Karen Uhlenbeck from AMS President

"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Karen Uhlenbeck, recipient of the 2019 Abel Prize. Professor Uhlenbeck has made legendary advances in several fields of mathematics. Her early groundbreaking work on harmonic maps gave rise to a new field, geometric analysis. Her analysis via gauge theory of solutions of Yang-Mills equations, had and will continue to have a profound influence on all future work in this field. She transformed the fields of geometry and analysis, crossing boundaries and making deep discoveries at the interfaces." AMS President Jill Pipher

(19.03.2019) More### President of the Academy announces Abel Prize winner

The President of the Norwegian Academy of Science and Letters, Hans Petter Graver (photo), will announce the winner of the 2019 Abel Prize at the Academy on March 19. The Academy's choice of laureate is based on the Abel Committee's recommendation. The chair of the Abel Committee, Hans Munthe-Kaas, will give the reasons for the awarding of the prize. The popular science presentation of the prize winner's work will be given by Jim Al-Khalili - a British physicist, author and broadcaster. He will also talk to the prize winner to get his/her immediate response to the news of being awarded the Abel Prize.

(08.03.2019) More### Sir Michael Atiyah, Abel Prize laureate, dies at 89

Atiyah was the recipient together with Isadore Singer of the Abel Prize in 2004, and he also received the Fields Medal, the American Philosophical Society’s Benjamin Franklin Medal, among many other honors. He was the former President of the Royal Society and of the Royal Society of Edinburgh. Atiyah was most recently an Honorary Professor in the School of Mathematics at the University of Edinburgh. Sir Michael, working at Cambridge University before he retired, made outstanding contributions to geometry and topology.

(14.01.2019) More