3.1416 And All ThatLYTTON 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. |
Contents
The Problem That Saved a Mans Life | 1 |
The Code of the Primes | 7 |
Pompeius Magic Seven | 14 |
Copyright | |
23 other sections not shown
Other editions - View all
Common terms and phrases
A. A. MARKOV abstract algebra angle arithmetic axis bers bylaws called cetera Chutes Chutes and Ladders circle commutative law compass complex numbers Concepts congruent cross-ratios curve decimal digits dimensions distance divided division element equal equation equivalent example factor Fermat Fermat's Last Theorem Figure 1B finite formula four-dimensional frequencies function geodesic graph ideas infinite number intersection Leibniz length limit point located Markov Chains mathe mathematician mathematics matics matrix method motion multiplication neighborhood ordered field pairs of positive path Paul Wolfskehl permutation perpendicular plane Poinsot polygon positive integers Postulate prime numbers problem projective geometry Pythagoras quadrangle map quaternions radius Random House ratio rational numbers real numbers segments sequence set of points simple slide rule solve space spider spin square root statement straight line string subtraction surface tangent tesseract theorem tion translation triangle truth value wall Wolfskehl York zero