Mathematics as a Game

Mathematics can be considered analogous to a board game such as chess.

To make the analogy clearer first consider a branch of mathematics such as algebra: any such branch starts out with definitions or axioms, these axioms are akin to the board layout and initial setting of the pieces on the chessboard.

Next we have the idea of proof and theorems in mathematics. A theorem is simply something which can be derived by applying logical rules to the axioms. In our chessboard example a true theorem is any configuration of the chess board that is possible with valid moves. The valid moves are analogous to a the logical rules.

Next is the concept of interesting theorems, in our chessboard example only few configurations are interesting, for example those which lead the rival to checkmate. similarly in mathematics infinite theorems can be proven but few are interesting and insightful.

It is said that grandmasters can view positions that are 20 moves ahead. A mathematician builds upon existing theorems and aims to prove new ones. A gifted mathematician can view moves that are far ahead thus being able to collapse several steps of logic into one, which allows him to explore more in a short time. Some of this collapsing is taught to students as well.

This analogy is clearly evident while reading a book on mathematics. A book of mathematics is typically full of proofs. If you try to read them as fast as a novel you are bound to be frustrated by the lack of understanding. Rather one has to read it as if reading an endgame position in chess and understand the gameplay step by step. Further one must retain some of the tricks used in this game for future reference.