A Mind at Play: How Claude Shannon Invented the Information Age

by Jimmy Soni

Above all, Doob professed loyalty to the “austere and often abstruse” world of pure mathematics. If applied mathematics concerns itself with concrete questions, pure mathematics exists for its own sake. Its cardinal questions are not “How do we encrypt a telephone conversation?” but rather “Are there infinitely many twin primes?” or “Does every true mathematical statement have a proof?” The divorce between the two schools has ancient origins. Historian Carl Boyer traces it to Plato, who regarded mere computation as suitable for a merchant or a general, who “must learn the art of numbers or he will not know how to array his troops.” But the philosopher must study higher mathematics, “because he has to arise out of the sea of change and lay hold of true being.” Euclid, the father of geometry, was a touch snobbier: “There is a tale told of him that when one of his students asked of what use was the study of geometry, Euclid asked his slave to give the student threepence, ‘since he must make gain of what he learns.’ ”