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In 2001, Lékó narrowly defeated Grandmaster Michael Adams in an eight game Fischer Random Chess (Chess960) match played as part of the Mainz Chess Classic. As a result, Lékó was hailed by many as the first Fischer Random Chess world champion. This claim is not universally accepted, since there were no open qualifying matches. Many do accept the claim, however, since this was also true of the first orthodox world chess champion titleholders, and both players were in the top five in the January 2001 world rankings for orthodox chess.
Lékó won the Dortmund Sparkassen Chess Meeting in 2002 and, with Kramnik, the Linares tournament in 2003.
Under the terms of the so-called " Prague Agreement ", masterminded by Yasser Seirawan, and intended to unite the two World Chess Championships, Lékó's 2002 win at Dortmund qualified him to play a match against Vladimir Kramnik. The winner of this match will then play the winner of a match between Garry Kasparov and Rustam KasimdzhanovRustam Kasimdzhanov (born December 5, 1979) is a chess grandmaster from Uzbekistan, and the current FIDE world champion. In the Uzbek language, which officially uses Latin script since 1992, his name is written "Qosimjonov". His best results include first, the 2004 FIDE World ChampionThe FIDE World Chess Championship, 2004 was held at the Almahary Hotel in Tripoli, Libya, from June 18 to July 13. It was won by Rustam Kasimdzhanov, who beat Michael Adams in the final by a score of 4. He takes prize money of around US$100,000 (US$80,000, to decide the undisputed world champion. After several delays, it was announced in January 2004 that his match against Kramnik would be held from September 25-October 18, 2004. The outcome of the match between Lékó and Kramnik was 7-7, which entitled Kramnik to remain the reigning PCA (classical) world championThe Professional Chess Association was created 1993 by Garry Kasparov and Nigel Short for the marketing and organization of its chess world championship. Kasparov and Short accused the FIDE of unprofessionalism and favoritism. Furthermore they refused to.