Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavor does: the extent of the negation of man’s corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.

What constitutes its crown may not be cut free from its roots, because it arose not in the course of the three hundred or eight hundred years of civilized history, but through the millennia of linguistic evolution: at the loci of man’s encounter with his environment, from the time of tribes and rivers. Language is wiser than the mind of any one of us, just as the body is wiser than the discernment of any of its units as it moves, self-aware and many-faceted, through the current of the life process. The inheritance of both evolutions, of living matter and of the matter of informational speech, has not yet been exhausted, but already we dream of stepping beyond the boundaries of both. These words of mine may make poor philosophizing, but that cannot be said of my proofs of the linguistic genesis of mathematical concepts, of the fact, in other words, that those concepts arose neither from the enumerability of things nor from the cleverness of reason.

The factors that contributed to my becoming a mathematician are complex, no doubt, but one major factor was talent, without which I could have accomplished in my profession no more than could a hunchback in a championship track-and-field competition. I do not know whether the factors that had to do with my character, rather than with my talent, played a role in the account I intend to give — but I should not rule out the possibility, for the importance of the affair itself is such that neither natural modesty nor pride ought to be considered.