In an article I'm writing I want to quote (with attribution) the original version of an aphorism that says that one can often find mathematical gold in the waste-baskets of physicists. Would someone provide a reference to that original version?

Note added after awarding bounty: For the time being, I'm going to assume that the quote is actually due to me! (I came up with it a few weeks ago, but it leaped into my mind with such rapidity that I suspected I wasn't inventing it so much as remembering it.) If anyone finds the quote in the next few months (before I include it in my own published work without attribution), please let me know! I'll be glad to make private arrangements to transfer 50 of my reputation points to you.

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    $\begingroup$ I don't suppose I could interest you in a joke about wastebaskets and philosophers? $\endgroup$ – Tom Goodwillie May 28 '14 at 13:10
  • $\begingroup$ Not what I need (though it's a good one). $\endgroup$ – James Propp May 29 '14 at 14:29
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    $\begingroup$ "The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation." Excerpt from Ex-Prodigy: My Childhood and Youth by Norbert Wiener, p. 21 $\endgroup$ – Ian Agol May 30 '14 at 16:20
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    $\begingroup$ The only (alleged) quotation I recall about a mathematician and a trash can: mathoverflow.net/a/7207/22971 $\endgroup$ – Benjamin Dickman Jun 1 '14 at 16:25
  • $\begingroup$ @TomGoodwillie: And what would be the source of the quote about waste-baskets and philosophers? $\endgroup$ – José Hdz. Stgo. Oct 14 '14 at 22:06

Here's one scientist (not quite a mathematician) who found gold in wastebaskets:

I started looking in the trash cans of science for such phenomena [fractal scaling], because I suspected that what I was observing was not an exception but perhaps very widespread.

Benoit Mandelbrot

It seems he meant this literally, and at least one paper [1] was inspired by a scrap he grabbed from a wastebasket.

[1] B. Mandelbrot, Information theory and psycholinguistics: a theory of words frequencies, in: P. Lazafeld, N. Henry (Eds.), Readings in Mathematical Social Science, MIT Press, Cambridge, MA, 1966.

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    $\begingroup$ Apparently he used both "the trash cans of science" and "a pure mathematician's wastebasket". A resourceful man. $\endgroup$ – Matt F. May 30 '14 at 15:18
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    $\begingroup$ I consider Mandelbrot to be quite a mathematician. $\endgroup$ – Robert Israel May 30 '14 at 15:35
  • $\begingroup$ I like this answer, and will award it the bounty, since it comes the closest (in meaning) to the quote whose attribution I was seeking. $\endgroup$ – James Propp Jun 4 '14 at 14:54
  • $\begingroup$ Well to have been more accurately (R.I.P.) $\endgroup$ – stankewicz Jun 4 '14 at 16:37

A somewhat similar quote of Alain Connes "The mathematical concepts that arise naturally in physics often turn out to be fundamental, as Hadamard pointed out" can be found in "The Princeton Companion to Mathematics" http://press.princeton.edu/titles/8350.html page 1006 (Article VIII-6).

I searched in the Hadamard's "An Essay on the Psychology of Invention in the Mathematical Field" https://archive.org/details/eassayonthepsych006281mbp for the mathematical gold in the waste-baskets of physicists but have found nothing.

P.S. Dyson's "Missed opportunities" can be found here http://projecteuclid.org/euclid.bams/1183533964 However it does not contain your quote.

Note added: I just found a remotеly similar quote "On the fringes of physics it contains such recent mathematical gems as Virasoro algebra representations on the moduli spaces of curves" in Yuri Мanin's essay "Interrelations between Mathematics and Physics" http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_157-168.pdf His other essays can be found in the book http://www.ams.org/bookstore-getitem/item=cworks-20 I have not checked it for the searched quote (I doubt it can be found there).


A somewhat different quote has been attributed to Einstein: http://izquotes.com/quote/226612

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    $\begingroup$ That sounds a little different to me. $\endgroup$ – Dan Ramras May 30 '14 at 5:09
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    $\begingroup$ ... and also reminiscent of the un-snarky half of the joke that Tom Goodwillie was reminded of. $\endgroup$ – Noam D. Elkies May 30 '14 at 13:25
  • $\begingroup$ this is Einsteins's quote in context: Einstein came to Princeton University in 1935 and was asked what he would require for his study. He replied: "A desk, some pads and a pencil, and a large wastebasket to hold all of my mistakes." $\endgroup$ – Carlo Beenakker May 30 '14 at 13:37
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    $\begingroup$ Something tells me there wasn't a lot of mathematical gold in Einstein's wastebasket. $\endgroup$ – Todd Trimble May 30 '14 at 14:23
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    $\begingroup$ The quote as cited by @CarloBeenakker is not to be trusted: Einstein mostly wrote in ink. I wouldn't trust the quote in the answer either. See some images of his writing, the references to ink in his letters, and his gift to Ehrenfest of a pen that he used. lorentz.leidenuniv.nl/history/Einstein_archive, google.com/search?q=ink+site%3Aalberteinstein.info, musingsonmath.com/2011/03/14/has-anyone-seen-einsteins-pen $\endgroup$ – Matt F. May 30 '14 at 15:15

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