To the general public, he was the subject of the award-winning movie "A Beautiful Mind". But to mathematicians, John Nash was a multidisciplinary genius whose creative approach to mathematics led to advances in game theory and pure mathematics. His death Saturday, 23 May 2015, in a car crash has shocked everyone.
Nash attended ICTP's 40th anniversary celebrations in 2004, closing the two-day event with a lecture titled "An Interesting Equation". His achievements continue to inspire research at the Centre. Matteo Marsili, a researcher in ICTP's Quantitative Life Sciences section who applies game theory to a number of different scenarios, pointed to the concept of the Nash equilibrium--a situation where each individual makes choices of strategy that are optimal, given the choices made by others--as one of the mathematician's most important contributions to game theory. "This concept not only offers a framework for predicting the outcomes of strategic interactions, but also provides a scheme to understand the social norms that prevail in different societies, and the nature of the incentives that sustain them," he explained.
Marsili added, "The Nash equilibrium expanded significantly the application of game theory to virtually any strategic interaction, providing a general mathematical framework that paved the way for the growth of game theory into one of the most active branches of mathematical economics."
ICTP mathematician Claudio Arezzo points to another of Nash's achievements: his great contributions to pure mathematics. Indeed, Nash and Louis Nirenberg shared the 2015 Abel Prize for their work in partial differential equations (equations involving rates of change). "In just a few years during the 1950s, Nash proved three grounbreaking results in the theory of partial differential equations with applications to real and complex geometry. His results opened lines of research that are still active and are considered milestones in the field," said Arezzo.