# John Nash: What a Beautiful Mind

John Forbes Nash was born on June 13, 1928 at Bluefield, a flourishing railway town in Appalachia. His father worked as an electrical engineer and mother was an English school teacher. Nash had the eccentric qualities of genius getting over him during his childhood when he conversed little with other children and used to carry out scientific experiments in his home earning him the title 'Big Brains'. Right from the school days Nash developed a great interest in the inquisitive realms and the intrinsic patterns that embodied the universe while being less attentive to the formalistic procedures

At the ripe age of 14 he entered Bluefield College and evinced a great keenness in mathematical thinking while leafing through E.T Bell's classic Men of Mathematics succeeded in proving classic Fermat theorem. The similar epiphanies of revelatory experiences were recounted by other geniuses like Einstein and Bertrand Russell in their early adolescence with Einstein reminiscing of the 'wonder' episode during his first encounter with Euclid at 12. The solving of the same Fermat Theorem helped Carl Friedrich Gauss, the renowned German Mathematician in choosing Mathematics instead of philology. After winning a scholarship at Carnegie Institute of Technology Nash for a brief time studied chemistry until he said 'I reacted negatively of the regimentation' and then acknowledged for his mathematical talents by his teachers (calling him young Gauss), he did his masters in mathematics in 1948. When applying for Princeton's doctoral program in math, one of his professors wrote for him the one line recommendation as: "This man is a genius." He chose Princeton for his doctorate instead of Harvard as he knew Einstein and Neumann were there and also on the grounds of the offer he received of the most prestigious John S Kennedy Fellowship there. After arriving, Nash quickly became one of the brilliant young minds showcasing the braininess of cerebral pyrotechnics and also inventing a clever game played with markers on tessellated bathroom tiles. This game as name named Nash or John became very popular as after couple of years Parker Brothers brought out a new version of it called 'Hex'.

John Nash shared the 1994 Nobel Prize in Economics for what he considered was his "most trivial work" – a 27-page dissertation, "Non‑Cooperative Games" (1950), when he was just 21. Roger Myerson who won Nobel Prize for economics in 2007 in his 1999 paper termed Nash's work as "one of the great breakthroughs in the history of social science" and also as compared it to that of the "discovery of the DNA double helix in the biological sciences". John von Neumann and economist Oskar Morgenstern had pioneered the Game theory in the 1940s. The duo explored the "zero-sum" games – the kind where winner takes all behaviour pervaded and a loser gets nothing. Enmeshed with mathematical elegance, Nash studied more complex 'competitions' and found ways to strike a perfect chord – the Nash equilibrium – wherein each player gets the best fit situation in his favour under given conditions. Significantly, though, the Nash equilibrium presented something truly new and epoch-making – the predictability to analyse states of 'conflict and co-operation' and prognosticating about how people will behave. These game scenarios are prevalent everywhere in the current times from having the best possible decisions in the fields diverse form the geopolitical border 'disputes' and in economic behaviours upto their relevance in evolutionary biology and in artificial intelligence . Generally very less has been said about Nash's other mathematical achievements. Nash through his unconventional ideas and methods made him the symbol of 'new spirit' in Mathematics. Many mathematicians who understand Nash's work would agree that although his work in game theory had the most impact on other fields, Nash made other breakthroughs which were even more striking. Besides game theory, Nash prospered in fields as diverse as partial differential equations, cryptography, algebraic topology, geometry etc. Nash proved of 'embedding' in a Riemannian manifolds into space of some dimension, sans distorting its geometry. With this historic result, he solved the isometric embedding problem which had been lingering on from Gauss to Bernhard Riemann. Nash and Louis Nirenberg being the giants of the twentieth century's mathematics were conferred with Abel Prize (considered Nobel Prize of Mathematics) by the Norwegian Academy of Arts and Sciences in 2015. The academy commented on Nash's embedding theorems, and describing them as "among the most original results in geometric analysis of the twentieth century." Nash revolutionised economics, Sylvia Nasar (Nash's biographer) writes just as "Mendel's ideas of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day." Fortune Magazine in 1958 called him one of the America's brilliant young mathematicians for his achievements in algebraic geometry, game theory, and non-linear theory. His ground-breaking contributions in the domain of differential equations made him the frontrunner for yet another prestigious Fields Medal but his contemporary de Giorgi of Pisa proved the same result before Nash by using different methods. His honors included the 1978 John von Neumann Theory Prize and the American Mathematical Society's 1999 Leroy P. Steele Prize for Seminal Contribution to Research. Nash held membership in the National Academy of Sciences and in 2012 was an inaugural fellow of the American Mathematical Society.

Nash became famous in the public as the subject of an Oscar nominated biopic 'A Beautiful Mind (1998)', the adaptation of his biography by Sylvia Nasar, starring Russell Crowe, in 2002. This riveting biography and equally spellbinding movie revealed the Nash's brilliance as a 'mathematician' wrestling with the silhouettes of a paranoid schizophrenia was rendered incapacitated by this disabling condition for more than two decades. He used to roam barefooted in Princeton's math building for years mumbling to himself. He was also called as 'Phantom of Fine Hall' as he scribbled mysterious revelations and strange equations in the empty classrooms of Princeton's Fine Hall. Mostly a solitary figure, he frequently wandered into the bouts of strange delusions. He once rejected a faculty position at the University of Chicago, replying that he was about to be crowned as the Emperor of Antarctica.

**Tailpiece**

John Nash is the only person to be awarded both Abel as well as Nobel Prize on account of his intellectual prowess and his 'beautiful mind'. One fateful day while returning to their Princeton home from the Abel award ceremony in Oslo, Nash and his wife Alicia had a fatal car crash. Sergiu Klainerman who was close associate of the couple remarked "Their deaths at the same time after such a long life together of highs and lows seemed literary in its tragedy and romance", further adding that "It was a tragic end to a very tragic life. Tragic, but at the same time a meaningful life," Nash had the signature marker of being the legendary Mathematician who was 'pathologically logical' and his graceful symmetry both flashing on his face and the geometric refinement in his expressions makes him one of the immortalized minds in the mathematical world.

*Mir Sajad is a Researcher, Department of Geography and Regional Development University of Kashmir*