# 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 Oxford" with lecture by Sir Andrew Wiles

It has become a tradition that the Abel Committee after its final meeting hosts an Abel seminar. This year the committee meeting at London Mathematical Society was followed by "Abel in Oxford" with Abel Laureate Andrew Wiles as the main speaker. Martin Bridson, head of the Mathematical Institute, University of Oxford and Camilla Serck-Hanssen, Vice President of the Norwegian Academy of Science and Letters gave introductory talks.

(02.02.2018) More### Yves Meyer received the Abel Prize from H.M. King Harald

H.M. King Harald presented the Abel Prize to Yves Meyer of the École normale supérieure Paris-Saclay, France at an award ceremony in Oslo on 23 May. He receives the prize for his pivotal role in the development of the mathematical theory of wavelets, says John Rognes, chair of the Abel committee. Among the prominent guests attending the award ceremony was the French ambassador to Norway, Jean-François Dobelle and the Norwegian Minister of Education and Research, Torbjørn Røe Isaksen.

(26.05.2017) More### Three days of celebration for Abel Laureate Yves Meyer

His Majesty King Harald will present the Abel Prize to Yves Meyer at an award ceremony in Oslo on 23 May. He receives the prize "for his pivotal role in the development of the mathematical theory of wavelets", to quote the Abel committee. Yves Meyer, of the École normale supérieure Paris-Saclay, was the visionary leader in the modern development of this theory, at the intersection of mathematics, information technology and computational science.

(12.05.2017) More### The Abel lectures 2017

Abel Laureate Yves Meyer gave his prize lecture at the University of Oslo on the 24th of May, with following Abel lectures by Stéphane Mallat, Ingrid Daubechies og Emmanuel Jean Candès. Watch the lectures here.

(08.05.2017) More### Congratulations from AMS President

"On behalf of the American Mathematical Society, it is my great pleasure to congratulate Professor Yves Meyer, recipient of the 2017 Abel Prize. Professor Meyer has been a visionary in a broad range of fields, including number theory and differential equations. His fundamental work in the theory of wavelets has transformed the world of signal processing and has led to a myriad of practical applications." -- AMS President Kenneth A. Ribet (University of California, Berkeley)

Photo: Jim Brook

(02.04.2017) More