Rewarding Mathematics

John F. Nash Jr. and Louis Nirenberg, two mathematical giants of the twentieth century, have been awarded the Abel Prize by the Norwegian Academy of Sciences and Letters.  

The two were cited for their “striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” Partial differential equations (PDEs) 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.

Both mathematicians have connections to ICTP. Nash participated in ICTP's 40th anniversary celebrations in 2004, closing the two-day event with a lecture titled "An Interesting Equation". Nirenberg came to the Centre several times during the 1990s as a course lecturer and a visiting mathematician.

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.

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.

Nirenberg 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.

The Abel Prize, which has been awarded annually since 2003, recognizes contributions of extraordinary depth and influence to the mathematical sciences and comes with a cash award of NOK 6,000,000 (about EUR 700,000). For more details, visit the Abel Prize website.