"Mathematics is what we want to keep for ourselves. When playing games, we stick to the rules (or we are changing the game...), but when doing serious mathematics (not executing algorithms) we make up the rules—definitions, axioms... even logics. ...[I]n arithmetic we find s, which are a whole new 'game'... [T]o identify mathematics with games would be one of those part-for-whole mistakes (like 'all geometry is projective geometry' or 'arithmetic is just logic' from the nineteenth century)... [M]y separation of game analysis from playing games tells... against the analogy of mathematics to the expert play of the game itself."
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Algorithms
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