Garry Kasparov became World Chess Champion in 1985 by defeating Anatoly Karpov. After a glittering career in chess he retired in 2005, turning his energies to writing and politics. An article he wrote in 2010, reviewing a book on artificial intelligence and the human mind, can be found here http://www.nybooks.com/articles/2010/02/11/the-chess-master-and-the-computer/ .
The article is mainly a series of reminiscences about his experience of computer chess, beginning with a simultaneous exhibition in 1985 against 32 of the strongest computers in the world, 8 of them named after him. He won every game, despite being in trouble against one of the Kasparov models. By 1996 chess AI was much stronger and he narrowly won a match against the Deep Blue supercomputer, but was defeated by an upgraded version of Deep Blue the following year. Kasparov explains that although that event shocked many people, chess GMs knew that the AI was improving all the time and suspected that humans would soon be no match for the computers. Apparently many programmers had expected the improvements to result in a machine that could think and play like a human with creativity and intuition, rather than a brute force number-cruncher with no sign of human-like intelligence.
Kasparov believes that chess will never be solved (in the sense of tabulating every move in all possible games), because the number of possible games is 10 followed by 119 zeros. He goes on to discuss how computers have helped today’s best young players to excel and reveals that in a 1999 tournament game against Topalov at Hoogoven, he was able to visualise the winning position a full 15 moves ahead, although he missed a quicker win that a computer would probably have found.