The numerology, conspiracies and supernatural beings arrived in John Nash's mind with the same sparkling clarity as his insights into the isometric embeddability of abstract Riemannian manifolds in Euclidean spaces. Those thoughts had made him one of America's most promising young mathematicians. So he took the other ones seriously, too.
His gift was insight, not theory -- he solved problems first, finding out how he had done so later. His work on manifolds (crudely: proving that a line drawn on a multidimensional idealised piece of paper remains the same length no matter how tightly it is crumpled) could have won him the greatest mathematical prize, the Fields Medal, had an unknown rival not reached the same conclusion. But in a profession where ability often peaks by 30, his genius seemed not quite great or early enough. Arrogance and oddness (notable even by academic standards) did not help either. Favourite insults included "burble", "trivial" and "hack". The outside world added stress to setbacks. His wife was pregnant. The abandoned mother of another child was hassling him. It all helped trigger schizophrenia, "the cancer of the mind".
On New Year's Eve 1959 he was (by his standards; and it was a fancy dress party) normal enough, wearing a nappy and sash, mutely sitting on his wife Alicia's lap and alternately sucking a dummy and swigging a bottle of milk. Only days later he declined a longed-for plum position, saying he was about to become "Emperor of Antarctica". What actually awaited him was psychiatric incarceration, with torturous insulin comas to burn "excess sugars" from the brain.
He felt "captured like a chessman", but the brief, fragile remissions were unwelcome too. "I was forced to accept normal thinking. But when I returned to delusional thinking I felt I was escaping from the thought police." Friends' attempts to help brought more bizarre jaunts and upsets. Even the besotted Alicia divorced him.
Recovery from schizophrenia is rare, but calm, friendly surroundings can help -- which is what Alicia provided when, homeless after his mother died, he begged her to take him in. "Being taken care of and not too much pressure", she said, was what he needed. It worked. Gradually, he recalled later, he "began to intellectually reject some of the delusionally influenced lines of thinking" as a "hopeless waste of intellectual effort."
During his illness, his groundbreaking work on game theory, largely neglected when he published it in 1950, had become one of the most important ideas of the century. The idea of equilibrium in the behaviour of firms and individuals is central to economics. Adam Smith's idea of the invisible hand had stoked the belief that rational, competitive interaction necessarily brings the best outcome. But Mr Nash's mathematics, in what was then the arcane sub-discipline of game theory, showed something else, more useful in practice. In a "non zero-sum" game (ie, in which mutual benefit is possible), he worked out what happens when players compete not in isolation, but in anticipation of and in response to others. Such a game, he proved, ends in a result where no player can gain by changing his strategy.
The implications, once fully understood, were stunning. In the real world of less-than-perfect competition, a "Nash equilibrium" may well be stable, but not optimal. Avoiding that outcome requires careful intervention -- for example, to encourage co-operation. This framework now influences rules about markets, mergers and auctions (notably of the radio spectrum), and offers insights in fields from evolutionary biology to nuclear strategy and politics. Yet outside his old stamping-grounds of Princeton and MIT, its author was forgotten, even presumed dead.
The Swedish Royal Academy of Sciences (which awards an economics prize cheekily named after, but not endorsed by, Alfred Nobel) hesitated before it awarded Mr Nash, and two other game theorists, the honour in 1994. He was too mad, too obscure, too risky. In the event, he epitomised courtesy and convention, and thereafter relished his sanity, solvency and further acclaimed mathematical work. He treated the media, saccharine and prurient by terms, with studied politeness. The Oscar-nominated Hollywood version of his life, "A Beautiful Mind", was, he said, "helpful in changing attitudes towards mental illness, albeit inaccurate: he had auditory, not visual hallucinations."
He and Alicia remarried in 2001 (they died in the same car crash, returning from yet another honours ceremony). Lately he advocated an index-linked "ideal money", to be as unchanging as a metre or kilogram. That was unorthodox. But nobody dared dismiss it as mad.