- Do you know what he is talking about?
Stefan Zweig, "Die Welt von Gestern"
- For that reason you would expect the arbritrary hypotheses of the
different mathematicians to shoot out in every direction into the
boundless void of arbritrariness. But you do not find any such thing.
On the contrary, what you find is that men working in fields as remote
from one another as the African Fields are from the Klondike, reproduce
the same forms of novel hypotheses. Riemann had apparently never heard
of his contemporary Listing. The latter was a naturalistic Geometer,
occupied with the shapes of leaves and birds' nests, while the former
was working upon analytical functions. And yet that which seems the
most arbitrary in the ideas created by the two men, are one and the
same form. This phenomenon is not an isolated one; it characterizes the
mathematics of our times, as is, indeed, well-known. All this crowd of
creators of forms for which the real world affords no parallel, each
man arbitrarily following his own sweet will, are, as we now begin to
discern, gradually uncovering one great Cosmos of Forms, a world of
potential being. The pure mathematician himself feels that this is so.
He is not indeed in the habit of publishing any of his sentiments nor
even his generalizations. The fashion in mathematics is to print
nothing but demonstrations, and the reader is left to divine the
workings of the man's mind from the sequence of those demonstrations.
But if you enjoy the good fortune of talking with a number of
mathematicians of a high order, you will find that the typical Pure
Mathematician is a sort of Platonist. Only, he is Platonist who
corrects the Heraclitan error that the Eternal is not Continuous. The
Eternal is for him a world, a cosmos, in which the universe of actual
existence is nothing but an arbitrary locus. The end that Pure
Mathematics is pursuing is to discover that real potential world. (pp.
120-1)
-- Charles Pierce, Reasoning and the Logic of Things, (Kenneth
Ketner ed., Harvard University Press, 1992).
Pg. 120-121.
Thanks to David Corfield at the n-category cafe for
pointing out this beautiful piece of writing.