3.1416 And All That

LYTTON STRACHEY tells the following story. In intervals of relaxation from his art, the painter Degas used to try his hand at writing sonnets. One day, while so engaged, he found that his in- spiration had run dry. In desperation he ran to his friend Mallarme, who was a poet. 'My poem won't come out,' he said, 'and yet I'm full of excellent ideas. ' 'My dear Degas,' Mallarme retorted, 'poetry is not written with ideas, it is written with words. ' If we seek an application of Mallarme's words to mathematics we find that we shall want to turn his paradox around. We are led to say that mathematics does not consist of formulas, it consists of ideas. What is platitudinous about this statement is that mathe- matics, of course, consists of ideas. Who but the most unregenerate formalist, asserting that mathematics is a meaningless game played with symbols, would deny it? What is paradoxical about the state- ment is that symbols and formulas dominate the mathematical page, and so one is naturally led to equate mathematics with its formulas.