Mathematics lends itself to a unique elegance of rigour. The pursuit of that beauty can also be agonizingly solitary and lonely. John Nash, who died on Sunday in a car accident, epitomized, in his work and in his life, both the beauty of mathematics and the angst-ridden loneliness of a mathematical genius. He was one of the truly great and original mathematicians of the 20th century. Yet, the highest accolade of recognition that he won was the Nobel Prize in Economics in 1994. The Putnam Competition and the Fields Medal, the two highest honours mathematicians can aspire to, did not come to Nash. Many believe that Nash's solving of a problem of differential geometry - derived from the work of G.F.B. Riemann, a 19th century mathematician - when he was only 28 years old should have won for him the two honours that eluded him. Two years later, Nash produced another paper that marked the beginning of the modern theory of differential equations. The Nobel Prize and the book and film on his life, A Beautiful Mind, made him a celebrity, and this, ironically, deflected attention from the fact that Nash was a genius in mathematics.

Within his small peer group, the recognition of his genius came very early. He came to the mathematics department in Princeton as a doctoral student at the age of 20 on the basis of a one-line letter of recommendation: "This man is a genius." In 1950, he produced the paper on the theory of non-cooperative games which, many years later, was to win him the Nobel. The theory of what came to be called the Nash equilibrium was recognized as a robust mathematical tool to understand complex competitive scenarios that could be used on a wide range of problems in the social sciences, in evolutionary biology and even in the field of corporate decision-making. Nash's work in game theory and its wide application radically transformed the subject. His genius, however, could in no way diminish the anguish of his mental world. He suffered from schizophrenia, but refused to completely surrender to his inner demons. The intellectual courage that was manifest in his eagerness to take on intractable mathematical problems was paralleled in the fortitude with which he fought his medical condition. It is one of the ironies of life that a genius who grappled with the rigour and the exactness of mathematics lost his life in a random road accident.