So the king is dead, the game over. Bobby Fischer - perhaps the greatest player in the history of chess, certainly the most charismatic and controversial - has died of kidney failure in his adoptive home, Iceland.

Fischer the chess genius died more than 30 years ago. He hadn't played top-level chess since he sensationally beat Boris Spassky in their world championship match in the Icelandic capital, Reykjavik, in 1972. This was not just the highest profile chess event ever, but the only time the game has made primetime TV. Fischer was always headline news.

Tragically, after 1972, Fischer became a recluse, rootless, increasingly deranged, popping up occasionally on unlikely radio stations (especially in the Philippines) to rail against the US and the Jews, and - the final straw for his native America which had once adored him - to applaud the attacks of September 11. "This is all wonderful news. I want to see the US wiped out," he declared to a Philippines radio station in the high-pitched Brooklyn accent he never lost despite three decades being blown around the world, the Flying Dutchman of chess.

The former British chess champion Bill Hartston once said: "Chess doesn't drive people mad, it keeps mad people sane." Fischer embodied the truth of his remark. While he was playing chess as a teenage prodigy in New York, then as a twentysomething single-handedly taking on the might of the Soviet Union, he inhabited a world he understood; the 64 squares were his home, fulfilling and comforting; the rules were comprehensible, the goal easily understood. "Chess is better than sex," he was once reported to have said.

When Fischer found refuge in Iceland in 2005 - he had been in prison in Japan awaiting extradition to the US - I went to Reykjavik to join the welcoming committee. The Icelanders still revered him; he, after all, had put them on the map. Chess made a change from cod. During my stay in Reykjavik I met Gudmundur Thorarinsson, the organiser of the 1972 world title match. He had originally met Fischer when the prodigy visited Iceland as a teenager. "I pointed out Alaska Road to him," Thorarinsson told me. " 'Gee', Fischer had said. 'I always wondered where Alaska was.' "

The naivety and unworldliness summed up Fischer. While he had chess and was feted as the west's great hope of unlocking the Soviet stranglehold, he was OK - a young man in a sharp suit whose brilliance overwhelmed opponents. Without chess, once he had voluntarily abandoned the world title in 1975, he was anchorless and raged against a world, at times coming close to madness.

I witnessed this at first hand on that trip to Iceland. He gave a press conference the day after he arrived to a small group of journalists. They were mostly polite Icelanders, asking the great man whether he liked herring, but the US sports channel ESPN had sent along a young journalist called Jeremy Schaap, whose father had been a friend of the up-and-coming Fischer in New York in the 1950s. When Schaap asked a question and mentioned his father, Fischer, a big, burly man with a buzz-saw voice, suddenly turned. "I hate to rap people personally, but his father many years ago befriended me, took me to see Knicks games, acted kind of like a father figure, and then later, like a typical Jewish snake, he had the most vicious things to say about me."

The room froze, Fischer pressed on, his mania growing. He had talked sensibly, even at times wittily, for half an hour, but suddenly it was nothing but paranoia and the Jewish conspiracy. "It's all on the internet," he kept saying. "Why don't you look it up?" The obsessionalism that had made him a great chess player made him an impossible human being.

Fischer was born in Chicago in 1943 - how appropriate that the master of the 64 squares should die at 64 - to a German father and a mother of Jewish extraction (though there are suggestions that his biological father was a Hungarian-Jewish physicist with whom his mother had had an affair). He was thus half-Jewish and possibly fully Jewish, making his tirades against Jews a bizarre form of self-hatred.

His parents divorced while he was an infant and his mother, an immensely strong-willed woman, moved to Brooklyn with her son and daughter Joan, who was five years older than Bobby and bought him his first chess set. The young Bobby buried himself in the game he first learned at six. By 13 he became the youngest player to win the US junior championship. A year later, he was US chess champion, and by the age of 15 was the youngest person ever to hold the title of grandmaster - at a time when it was much harder than now to gain the title.

He climbed steadily up the world chess ladder in the 1960s, but in 1967 dropped out of a tournament halfway through after an argument with the organiser. He played little chess for the next two years, and was already exhibiting signs of the paranoia and reclusiveness that would eventually engulf him.

In 1970, however, he roared back, becoming the number one player in the first ever official Fide ratings and winning 20 games in a row against the best grandmasters in the world - one of the great winning streaks not just in chess but in all sporting history. It would be unthinkable today, when three-quarters of grandmaster games end in draws. It shows the supremacy Fischer had established and his sheer will to win. Easy draws were spurned; opponents were ground into the dust. To beat the Soviet machine, he had turned himself into a machine.

Fischer played before the age of the computer. Grandmasters now use computer programs in their opening theory and to analyse games. Fischer had to work it out for himself, plot his own path. Nonetheless, his games have a computer-like clarity: he played deeply logical moves that make sense to the novice, yet overwhelmed his grandmaster opponents. His chess had a glorious certainty that he could never find in life.

It was the 1972 match in Reykjavik that sealed Fischer's fame. Initially, he didn't want to play, complaining about everything - the hall, the board, the chairs, the chess pieces, the audience, the cameras, the noise. The match was so important to the US that Henry Kissinger, the secretary of state, phoned Fischer to beg him to play. US honour was at stake against the commies, who had held the chess world title since the second world war. Fischer eventually agreed to play.

He lost the first game to the suave Spassky, who many thought would defeat the eccentric and volatile Fischer, and forfeited the second. Surely, most people thought, it was all over. He only agreed to play the third game if it was away from the gaze of the audience. It was played behind a curtain in a small room at the side of the sports hall in which the event was being held. Fischer triumphed brilliantly, the first game he had ever won against Spassky.

He dominated the next few games, establishing a healthy lead, but seemed to waver as the finishing post loomed. Nevertheless, the winning margin, 12.5 to 8.5, was comfortable enough. The boy from Brooklyn had beaten the might of the Soviet Union, in the process sparking a chess boom across the western world and inspiring a generation of players, not least in the UK, which was to enjoy two golden decades in the wake of Fischer's heroics.

It should have been the beginning of a wonderful reign. In fact, it was the end. Fischer didn't play in any of the great tournaments after 1972; promoters wanted him to play exhibitions, but he demanded exorbitant fees and they never took place; and then, due to defend his world title against the new Soviet hero, Anatoly Karpov, in 1975, he made even more outrageous demands, wanting an open-ended match in which the winner would have win 10 games, with draws not counting - a match that would have taken many months to complete. Fide tried to accommodate him, but negotiations broke down and Fischer forfeited his crown.

Thorarinsson has a theory. "Fischer was scared of losing," he told me. "Chess and the world title meant so much to him that he couldn't bear the prospect of being beaten." He had come close to perfection, to finding the objective truth for which chess players strive, and feared a falling off, a loss of certainty. Chess players rarely get better after their 20s; perhaps he realised the peak had been climbed and the only way was down.

After 1972, Fischer's wanderings became ever more self-defeating. He moved to the west coast and had a spell with a Californian religious cult, which, as so often with Fischer, ended in acrimony. The US sued him for unpaid taxes and impounded some of his belongings. He was even falsely accused of taking part in a bank robbery and questioned by police - an episode that prompted his brilliantly titled philippic "I Was Tortured in a Pasadena Jailhouse."

He returned to the board in 1992 to play an exhibition match against his old foe, Spassky, in Yugoslavia. This at the height of the civil war in the Balkans. The US added sanctions-busting to tax evasion. The first game in that 1992 match was reckoned a brilliant one - Fischer, after a 20-year absence, could clearly still play. But, thereafter, he and Spassky played uneven chess (by grandmaster standards, of course): like two old, flabby boxers trading blows, this was strictly for money (the purse was said to amount to $5m).

After this match, he knew he was in danger of being arrested if he returned to the US and never went back. He spent much of the 1990s in Budapest, a shambling, bushy-bearded figure spotted from time to time at public baths. He was said to be besotted with a 17-year-old Hungarian chess player; she eventually married someone else. He moved to the Philippines, where in 2000 he married and had a daughter with a young Filipino woman, but the relationship foundered.

Then came 2001, when Fischer noisily sided with al-Qaida and the charge sheet was complete. Tax evasion and sanctions-busting may have been the official reasons the US wanted its prodigal son back, but revenge was now the true motive. The home-grown monster had to be tamed. He was held in prison in Japan, which claimed his passport was invalid, and there was a strong chance he would have to return to the US to face trial. But Iceland intervened with an offer of instant citizenship and he fled to safety in March 2005, receiving something close to a state reception when his private aircraft touched down close to midnight in driving rain.

He was to end his life among well-wishers, worshippers even, but he remained a recluse and was reluctant to play chess. At the press conference I attended in Reykjavik, he admitted to having played against a Burmese guard while he was in prison in Japan. The young man had even managed a draw in one game. Might this unknown be the last person to have played chess against Fischer?

Ever the iconoclast, he had invented his own form of chess, Fischerandom, in which at the beginning of the game the pieces are randomly distributed. Conventional chess, Fischer said, was played out - killed by computers and over-analysis. Psychologically, he had to believe that chess died with him, the last, undefeated champion. In a way, perhaps it did.

· This article was amended on Tuesday January 22 2008 to restore elements edited out for the print edition.