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JS Milne has a page about common errors in mathematical papers, and one of them is the usage of "verify" to mean "satisfy".

Improper usage: "The set $A$ verifies the condition."

Proper usage: "The set $A$ satisfies the condition."

Proper usage: "We verify that $A$ satisfies the condition."

Strangely enough, I've only seen this once or twice in a paper or book written in English, but I've seen it in nearly every paper or book written in French that I've read. That is, we have:

L'ensemble $A$ vérifie la condition.

Now, there's another error on Milne's page that he notes, the "associated to" and "associated with" error. If one is attempting to use proper English, "associated with" is the only correct choice. It turns out that this error comes from a mistranslation of the French, "associé à", which means "associated with".

My question then: Is the French usage of "vérifier" to mean "satisfy" acceptable in French, like the usage of "associé à", but not in English, or is it just an error that has propagated to both languages (possibly from a third language where the word for "verify" is the same as the word for "satisfy")?

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Harry -- "v\'erifier une condition" is perfectly acceptable in French (one can also say "satisfaire `a une condition") and so is "associe\'e `a...". But none of this has much to do with mathematics, I'm afraid. –  algori Jun 4 '10 at 0:16
that is, associ\'e(e) `a. –  algori Jun 4 '10 at 0:26
It has to do with mathematical writing. Anyway, add your answer as an answer! –  Harry Gindi Jun 4 '10 at 0:33
Your question practically answers itself: as algori says, the usage of "vérifier" in this way is fine in French but not in English. And, I have always suspected, this is the source of the error: French mathematicians writing in English and/or anglophone mathematicians reading French and carrying over the usage. –  Pete L. Clark Jun 4 '10 at 0:41
Sadly, the mixup is way too frequent in Spanish, and not correct. –  Mariano Suárez-Alvarez Jun 4 '10 at 1:13

2 Answers 2

up vote 2 down vote accepted

Dear Harry, in Serre's collected papers, vol.1, page 183 [or Annals of Math.58(1953) page 270] you'll find (line -5)

"Soit $\mathcal C$ une classe vérifiant (II_A)..."

and many such examples on the same page, corroborating your testimony on papers and books you read in French. I recoil in horror at the thought that some heretic might not consider this a sufficient proof that the usage of "vérifie" in the sense "satisfies" is more than acceptable in French. Another quote: Bourbaki, in Topologie Générale, Chapitre 1, §6, page 61 (line -15)[Quatrième édition] writes

"Pour qu'un ensemble de parties satisfaisant à (F_1) vérifie aussi..."

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Great! I would have taken your word for it, but this is proof! –  Harry Gindi Jun 4 '10 at 0:46
This is just a proof that Serre has terrible style inherited from at least one of his teachers and that he is not alone among the Bourbaki team whose influence on mathematical writing tradition in France and elsewhere is significant. This is clearly a minor "abus de langage" and its frequency and diffusion does not reduce the absurdity of using an active verb implying consciousness with a mathematical object as a subject. –  ogerard Jun 5 at 21:16
@ogerard "This is just a proof that Serre has terrible style" As we French say: better to hear that than be deaf. You might add to your hilarious comment that he is a dreadful mathematician, for good measure. –  Georges Elencwajg Jun 5 at 21:39
@GeorgesElencwajg : I really dislike his way of writing and talking about mathematics, the architecture of most of his books, his choice of emphasis, even if he is one very important mathematician of the 20th century with deep contributions to many fields, great and even devastating insight, etc. In the particular case we are discussing I do not think he originated this way of using "verifier" but I hold it to a higher standard than most and I regret that he employs it. –  ogerard Jun 7 at 21:27

This is probably not what you were talking about, but if "the condition" is " there exists a set such that ..." and $A$ is such a set, then I would find it perfectly correct to say "The set $A$ verifies the condition."

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