Quotations XXV: Math is a Game

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

David Hilbert
quoted by Nicholas Rose, Mathematical Maxims and Minims

It’s like asking why Beethoven’s Ninth symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.

Paul Erdös

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Godfrey H. Hardy
A Mathematician’s Apology

How then shall mathematical concepts be judged? They shall not be judged. Mathematics is the supreme arbiter. From its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.

David van Dantzig

I love mathematics … principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game — the encompassing of the infinite.

Rózsa Péter
quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul’s quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment.

Rudy Rucker


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