Bell, Eric Temple. "The Prince of Mathematicians," in The World of Mathematics. James R.

 

Bell, Eric Temple. "The Prince of Mathematicians," in The World of Mathematics. James R.
Newman, editor. New York: Simon and Schuster, 1956, pp. 295-339.

Here is matter of style, a matter of choice: how shall we put forward our ideas? Shall we publish
them in the exciting stage of their origin, in the form of the great and good guess, or shall we
shade our pretty finding until the insightful hypothesis becomes close to scientific law?

Mathematicians tend to publish only after their insights have been rendered almost
unrecognizable as insight and stand unchallengeable, painstakingly proven. Indeed, there is then
no way back to the creative moment save by historical reconstruction. The insight is forever lost.
The proof, but only that, is available to the historians who seek to reconstruct the creative
moment. This is one of the things that makes mathematics so incredibly difficult; the
mathematician seems to be interested only in the formal aspects of his field. This also makes it
difficult for the historian of science who wishes to reconstruct the pathways to the formalisms.

Karl Gauss is chosen as an exemplar of the formalist: "Contemplating as a youth the close,
unbreakable chains of synthetic proofs in which Archimedes and Newton had tamed their
inspirations, Gauss resolved to follow their great example and leave after him only finished
works of art, severely perfect, to which nothing could be added and from which nothing could be
taken away without disfiguring the whole. The work itself must stand forth completed, simple
and convincing, with no trace remaining of the labor by which it has been achieved." (p. 305)