They do not prove to be a monotonous series of contents, involving mere repetition of the same ideas. On the contrary, to know them at all well, is to find in them properties involving the most varied and novel features, as you pass from number to number, or bring into synthesis various selected groups of numbers. Consider, for instance, the prime numbers. Distributed through the number-series in ways that are indeed capable of partial definition through general formulas, they still conform to no single known principle that enables us to determine, a priori, and in merely universal terms, exactly what and where each prime shall be. They have been discovered by an essentially empirical process which has now been extended, by the tabulators of the prime numbers, far into the millions. Yet the process much resembles any other empirical process. Its results are reported by the tabulators as the astronomers catalogue the stars. The primes have, as it were, relatively individual characters,[1] which cannot be reduced to any barren repetition of the same thing over and over. One may call them uninteresting. But one must not judge the truth by one’s private dislike of mathematics, just as, of course, one must not exaggerate the importance of mere forms. Here, then, is one instance of endless novelty within the number-series.
But the real question is, How shall the genuine meaning of all this series of truths be in any way grasped, unless the insight which grasps is adequate to the endless wealth of novel, and relatively individual truth that the various numbers present as one passes on in the series? For the will cannot consciously decide against the further realization of certain types of possibility, unless it clearly knows their value. And this it must know in exhaustive, even if ideal and abstractly universal terms. Nobody can fairly tell what value in life numerical truth may possess, unless he first knows that truth. And the numbers whose ordered rationality is, for us men, the very basis of our exact science, show a wealth of truth
- ↑ Of course they are in no sense true individuals, but taken as members of their series, they have relatively unique features.
