When Einstein Walked with Gödel: Excursions to the Edge of Thought

by Jim Holt

Bertrand Russell penned a gushing tribute to the glories of mathematics. “Rightly viewed,” Russell wrote, mathematics “possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” These lines, which play up the transcendent image of mathematics, are often quoted in mathematical popularizations. What one seldom encounters in such books, however, is the rather different view that Russell expressed in his late eighties, when he dismissed his (relatively) youthful rhapsodizing as “largely nonsense.” Mathematics, the aged Russell wrote, “has ceased to seem to me non-human in its subject-matter. I have come to believe, though very reluctantly, that it consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal.” So, in the course of his life, Russell underwent an evolution in his thinking about mathematics. I think our civilization will have undergone a similar evolution by the Year Million.