there’s something a little Borgesian about this “mathematical anecdote”:http://mindofwinter.blogspot.com/2005/03/viva-la-revolucion.html from ‘Mind of Winter’ (found via “Chad Orzel”:http://www.steelypips.org/principles/2005_02_27_principlearchive.php#110977081518935637).

bq. … Zygmund posed CalderÃ³n a question and the puzzled CalderÃ³n replied that the answer was contained in Zygmund’s own book Trigonometric Series. Zygmund disagreed: what transpired was that CalderÃ³n 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 CalderÃ³n’s work in the years to follow.

{ 5 comments }

John Isbell 03.02.05 at 5:00 pm

I always like to build my own ladder.

pedro 03.02.05 at 6:18 pm

Lucky CalderÃ³n: not only was he a great mathematician, he married Alexandra Bellow!

tad brennan 03.02.05 at 9:45 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.

pedro 03.03.05 at 1:28 am

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”.

Jack 03.03.05 at 10:30 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

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