# 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).

### Who will be the next Abel Laureate?

The Abel Committee has embarked on the long journey in search of the next Abel Laureate. The committee which consists of five distinguished mathematicians has had its first meeting at the Norwegian Academy of Science and Letters in Oslo the 2nd and 3rd of October. The next meeting will take place in Pittsburgh, Pennsylvania early next year.

(03.10.2018) More### Record turnout for Atiyah’s Abel Lecture at ICM in Rio

1250 mathematicians from all over the world filled the big conference hall in Rio de Janeiro on Monday the 6^{th} of August to listen to Sir Michael Atiyah’s Abel Lecture, “The Future of Mathematical Physics: New ideas in old bottles”.

### Sir Michael Atiyah gives Abel lecture at ICM in Rio

Sir Michael Atiyah who receiced the Abel Prize in 2004, shared with Isadore Singer, will give the Abel Lecture at ICM in Rio on the 6th of August. He has titled the lecture: "The Future of Mathematical Physics: new ideas in old bottles". Atiyah will be introduced by Jacob Palis, former president of the International Mathematical Union and a member of the Abel Committee.

(26.07.2018) More### Robert P. Langlands received the Abel Prize from H.M. King Harald

In the University Aula in Oslo, surrounded by Munch's paintings and a diverse mathematical audience, Robert P. Langlands was today, May 22, awarded the Abel Prize for 2018 by H.M. King Harald. Langlands received the award of 6 million NOK “for his visionary program connecting representation theory to number theory.” The Langlands program is frequently described as a grand unified theory of mathematics.

(22.05.2018) More### The Abel lectures 2018

Abel Laureate Robert Langlands gave his prize lecture titled "*On the geometric theory" *at the University of Oslo on the 23th of May. John Rognes, chair of the Abel committee, introduced Langlands to an almost full auditorium. Langlands' lecture was followed by two others talks, by Jim Arthur and Edward Frenkel. Watch the lectures live