March 02, 2005

Speaking of Borges ...

Posted by Henry

there’s something a little Borgesian about this mathematical anecdote from ‘Mind of Winter’ (found via Chad Orzel).

… Zygmund posed Calderón a question and the puzzled Calderón replied that the answer was contained in Zygmund’s own book Trigonometric Series. Zygmund disagreed: what transpired was that Calderón only ever read the statements of the results, preferring to give his own reasoning and proofs… . One of these proofs gave a highly original answer to Zygmund’s question. This originality was to be the hallmark of Calderón’s work in the years to follow.

Posted on March 2, 2005 02:22 PM UTC
Comments

I always like to build my own ladder.

Posted by John Isbell · March 2, 2005 05:00 PM

Lucky Calderón: not only was he a great mathematician, he married Alexandra Bellow!

Posted by pedro · March 2, 2005 06:18 PM

Historians of philosophy will recognize the story of the Stoic Chrysippus telling his teacher Cleanthes “just tell me the theorems, and I’ll work out the proofs myself!” (DL 7.179).

And sure enough, the Chrysippean system that emerged was far more powerful than Cleanthes’ had been.

Posted by tad brennan · March 2, 2005 09:45 PM

Tad B.: Oddly enough, once one knows something is a theorem, it becomes much easier to prove the thing, even if one hasn’t seen the proof. I call it the “oracle effect”.

Posted by pedro · March 3, 2005 01:28 AM

There is a similar story about J.J. Sylvester:
“I remember once submitting to Sylvester some investigations that I had been engaged on, and he immediately denied my first statement, saying that such a proposition had never been heard of, let alone proved. To his astonishment, I showed him a paper of his own in which he had proved the proposition; in fact, I believe the object of his paper had been the very proof which was so strange to him.”
—W.P. Durfee

Posted by Jack · March 3, 2005 10:30 AM
Followups

This discussion has been closed. Thanks to everyone who contributed.