# 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).

### "Abel in Barcelona" with lecture by Louis Nirenberg

Institut d'Estudis Catalans will host the Abel in Barcelona-event on Monday the 16th of January. In connection with the final meeting of the Abel committee, whose task it is to select the Abel Prize Laureate for 2017, there will be an afternoon of lectures aimed at a broad mathematical audience. Louis Nirenberg, who shared the Abel Prize 2015 with John Nash, will give the first lecture. There will also be lectures by two of the Abel committee members, Luigi Ambrosio and Ben Green.

(04.01.2017) More### Sir Andrew J. Wiles received the Abel Prize from H.R.H. Crown Prince Haakon

Andrew Wiles received the 2016 Abel Prize from Norway's Crown Prince Haakon at an award ceremony in Oslo today, on 24 May. He receives the prize "for his stunning proof of Fermat's Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory", to quote the Abel Committee. The Abel Prize carries a cash award of 6 million NOK (about EUR 700,000 or USD 750,000) and has been awarded annually since 2003 by the Norwegian Academy of Science and Letters.

(24.05.2016) More### The Abel lectures 2016

Abel Laureate Sir Andrew Wiles will give his prize lecture at the University of Oslo on the 25th of May, followed by two Abel Lectures by Henri Darmon and Manjul Bhargava. Simon Singh will then give the popular lecture *From Fermat's Last Theorem to Homer's Last Theorem.*

### Congratulations from the AMS President

Robert Bryant, President of the American Mathematical Society (AMS), congratulates Sir Andrew Wiles with the 2016 Abel Prize.

(15.03.2016) More### Martin Bridson, Head of the Mathematical Institute, University of Oxford, about Sir Andrew Wiles

“No individual exemplifies the relentless pursuit of mathematical understanding in the service of mankind better than Sir Andrew Wiles. His dedication to solving problems that have defied mankind for centuries, and the stunning beauty of his solutions to these problems, provide a beacon to inspire and sustain everyone who wrestles with the fundamental challenges of mathematics and the world around us. His work will inspire mathematicians and scientists for centuries to come. We are immensely proud to have Andrew as a colleague at the Mathematical Institute in Oxford.

(14.03.2016) More