In the foreword to his textbook Algebra, Serge Lang writes (on page vi)

I have frequently committed the crime of lèse-Bourbaki by repeating short arguments or definitions to make certain sections or chapters logically independent of each other.

What does "the crime of lèse-Bourbaki" mean? I do not understand French, so naturally I googled the phrase and what turned up was the Wikipedia page for lèse-majesté.

Lèse-majesté is the crime of violating majesty, an offence against the dignity of the reigning sovereign or against a state.

I am aware that Nicolas Bourbaki is a pseudonym used by a group of influential French mathematicians who wrote a series of textbooks in a terse and formal manner. So, is Lang honoring Bourbaki by equating them with (mathematical) royalty?

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    Well, it looks like a term Lang coined himself. Judging from the quote I'd say that he was asserting that Bourbaki's preferred style would be to put definitions and basic results in one place only, as duplication more or less guarantees distortions (a sentiment very much appreciated by programmers). – lulu Aug 16 at 18:07
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    @lulu Thank you for clarifying! Do you think Lang intends the term lèse-Bourbaki to be related to lèse-majesté? – Brahadeesh Aug 16 at 18:22
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    Well, it's certainly a parallel construction...and since we tend to not to think of lese-majeste as an out-dated concept (encompassing, as it does, any act deemed insulting to the sovereign), one might imagine that Lang means the association to as a subtle rebuke against Bourbaki style didacticism. – lulu Aug 16 at 18:51
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    Possibly the most literary question on Mathematics.SE – smci Aug 16 at 21:14
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    FWIW googling "lèse-Bourbaki" now brings up this question – Conor O'Brien Aug 16 at 22:31
up vote 81 down vote accepted

I don't think it was honoring Bourbaki, but rather gently mocking them.

As stated in the comments and other answers, the Bourbaki group was known for its lack of redundancy : if you read the books, you see they never repeat definitions or arguments, instead they always refer to previously written books with a concise and cold reference (I don't have the format in mind but it'll be something like [Book 5, Ch.6, S.5, §4.3])

Lang is saying he will not do this and he coined the term lèse-Bourbaki. In doing so (if I'm not mistaken, he's a French speaker, and so he's not making a mistake in the use of this image) he's not equating them with royalty, but rather implying that they see themselves as such or that others see them as such: he's gently mocking the status of Bourbaki (which was in a sense the status of royalty, back in the days, at least in France).

I'm saying this because, as a native French speaker, I know how and why French speakers use phrases relating to kings and queens: we use them to disqualify people, rather than honor them. When a child throws a tantrum because s.he is denied something s.he wanted, it's not rare (of course you don't hear it all the time) to hear his/her parents refer to their child as a king or queen, and tell him/her jokingly that they were just victim of a "crime de lèse-majesté".

As a French speaker, this is what I understand from this quote (and again, Lang was himself a French speaker if I'm not mistaken): it's not as bad as a child's tantrum but you can certainly imagine Lang with a wry smile while writing this. So to answer your question in the comments, it's definitely related to "lèse-majesté", but it's very likely not to honor Bourbaki.

(Note that the habit of using phrases and sentences relating to kings/queens mostly as derogative is very common in France and is probably a heritage of our many revolutions and continued failures to attain a democracy)

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    This is the kind of insight I was really hoping to receive. Your point about the typical (or household) usage of the phrase lèse-majesté is really important. Thank you! :) – Brahadeesh Aug 16 at 18:29
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    This is completely on the mark. Lang most certainly was a French speaker, and still had a noticeable accent, even though he had been in the States since his teen years. Somewhere, he apologizes, writing in French, for his “phôtes d’ortograffe”. – Lubin Aug 16 at 18:39
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    To be clear, though, this would be intended as a playful jab at Bourbaki rather than a hostile put-down. Lang himself was a member of the Bourbaki group. – Eric Wofsey Aug 16 at 19:22
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    @EricWofsey : yes perhaps that wasn't clear enough from the beginning; I did write "you can imagine Lang with a wry smile while writing this" hoping the reader would understand that this is not hostile – Max Aug 16 at 19:39
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    References to royalty in English (at least, in America) tend to be mocking as well. "King Bush" would be unlikely to be taken as a compliment. – Acccumulation Aug 16 at 21:53

Bourbaki notoriously references old theorems in a book in order to prove a theorem that might come much later in order to not repeat arguments. Lang is saying that he will try not to do this (he will commit the sin of doing something contrary to what Bourbaki would want.)

This is not really an answer to the stated question, which the other answers address in a quite satisfactory manner, but I would like to point out that Lang somewhat misleadingly describes the Bourbakist principle of economy. Not only should one not repeat definitions or arguments identically, one should more generally not explicitly prove any result (say about vector spaces) if it can be seen as a special case of a result valid in a more general context (say of modules over a not necessarily commutative ring). In that case it should instead just be recalled that the more general result, necessarily appearing at some earlier point due to the "the from general to the specific" ordering of the Bourbaki oeuvre, has a certain implication in the current (more specific) setting.

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