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Grothendieck (if it was him) said somewhere :

This XXX, at least, is an idea that will not be used in physics.

Q1 : Is XXX an n-groupoid? a stack? Can someone supply the precise quote, either in French or in English?

Q2: Predecessors of this quote in the same vein would also be of interest. Thank you.

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1. I've edited the title and the question. 2. Are you sure you aren't thinking of Hardy and number theory (factorization)? – Victor Protsak Sep 7 '10 at 1:22
"Very little of mathematics is useful practically, and that that little is comparatively dull. The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects." --GHH – Steve Huntsman Sep 7 '10 at 1:43
"...the theory of numbers is, because of its supreme uselessness, the queen of mathematics...The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as ‘useless’ as the theory of numbers...No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the ‘highbrow’ applied mathematics will become ‘useful’ in as unexpected a way; is what is commonplace and dull that counts for practical life." --GHH – Steve Huntsman Sep 7 '10 at 1:47
XXX is "sane notation." :) – Cam McLeman Sep 7 '10 at 2:07
@Victor: the XXX in the arXiv precursor is the XXX of the Heisenberg model. Paul Ginsparg initially ran the arXiv from one of the computers in his research group and indeed there were also other computers called XXZ and XYZ, IIRC. The change of name didn't come soon enough, since URLs containing xxx were being increasingly blocked in many places :) – José Figueroa-O'Farrill Sep 7 '10 at 11:26
up vote 13 down vote accepted

Dear Jérôme, I doubt that Grothendieck ever said that.

However, in an analogous vein, Jean Leray, a brilliant French mathematician, was taken prisoner by the Germans in 1940 and sent to Oflag XVIIA ("Offizierslager", officers' prison camp) in Edelsbach (Austria), where he remained for five years till the end of WW2.

He managed to hide from his captors that he was an expert in fluid dynamics and mechanics, lest they would force him to contribute to their war effort (submarines, planes). Instead, he organized a course, attended by his fellow prisoners, on the foundations of Algebraic Topology, a harmless subject for applications in his eyes. It is in these courses that he introduced sheaves, cohomology of sheaves and spectral sequences.

His strategy worked out fine since these discoveries didn't play any role in the construction of weapons by the German enemy, who never cared about Leray's courses and findings. On the other hand, these theoretical tools have had a non entirely negligible role in pure mathematics since.

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"a non entirely negligible role" : quelle litote! – Chandan Singh Dalawat Sep 7 '10 at 10:13
Cher Chandan, félicitations pour votre peu commune érudition: I am amazed at your command of French since I would guess that not so many native French speakers know the meaning of litote! (For interested readers: litote is a sort of understatement where you convey an idea by essentially doubly negating it.) – Georges Elencwajg Sep 7 '10 at 10:53
As "litotes", it's an English word, too. – Aaron Bergman Sep 7 '10 at 12:08
Doug Piranha was the most feared man in the London underworld. This was largely due to his merciless use of sarcasm, dramatic irony, metaphor, bathos, puns, parody, litotes and satire. – Gerry Myerson Sep 7 '10 at 12:39
The question was put to me by someone else yet when he asked it I felt I had heard it before. You might be right that It is a Hardy quote . Do you remember if it is in his Number theory book. A META QUESTION : ( I do not known where to ask it ? - this is a meta-meta question- ) How do I click the check mark to accept an answer ???? . I would be glad to give points – Jérôme JEAN-CHARLES Sep 9 '10 at 23:34

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