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The term prophylaxis first entered mainstream chess terminology after the publication of Aron Nimzowitsch's seminal book, My System, in which the principles of hypermodern chess were outlined and analyzed for the first time. Nimzowitsch used the word to describe the action of preventing one's opponent from carrying out their intended plan.
Though this seems like a trivial idea, it was at the heart of Nimzowitsch's system, and his play was a deep example of prophylaxis in action. In simplistic terms, one can interpret prophylaxis as, for example, a single move which in turn prevents one's opponent from playing a single move. For example, if a player sees that his opponent wants to move his knight to a certain square, he might move a pawn forward to attack that square, preventing the move.
However, Nimzowitcsh's idea of prophylaxis runs far deeper than this. He would always attend to the task of preventing his opponent from carrying out their plans before attempting to carry out one of his own, a style of slow strangulation that, when properly carried out, made his opponents feel as if they didn't understand chess at all. The aim was never to allow the other player to gain any significant advantage in any contested area of the board, a highly defensive style of play which lays a lot of emphasis on pawn structure and intricate piece manouevering. The ultimate goal of prophylactic play in chess is therefore to reduce one's opponent to immobility. Possibly the greatest master of prophylaxis in the history of chess was Tigran Petrosian, whose style was built around the slow strangulation of his opponent's activity, "coiling around weaknesses like a python".