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Can anyone point me towards some good work on the semantics of ordinary language mathematical claims? Any tips would be greatly appreciated.

For example, when a geometer says of Euclidean geometry "Euclidean points have no extension" he is saying something that goes beyond the axioms. Has there been any linguistic study of this "informal" element of mathematical discourse?

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  • Are you referring to sentences involving comparatives, "at least one," "more than five," "every man," etc.? These fall under the general field of degree semantics. Schwarzschild (2008) is a survey article, and there are two MIT course archives on the topic: (1), (2).
    – Aerlinthe
    Commented Oct 20, 2012 at 23:49
  • No, I'm not referring to the semantics of quantification or any similar topic. I'm asking about the semantics of what you might call "informal" mathematics. The natural language counterpart of model theory for axiomatic mathematical theories.
    – Dennis
    Commented Oct 21, 2012 at 4:04
  • You should clarify your question with examples, then, because I don't have a prototypical example of "informal mathematics."
    – Aerlinthe
    Commented Oct 21, 2012 at 4:43
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    The scope of the question is not clear enough. Perhaps you have something like this paper in mind?
    – prash ♦
    Commented Oct 21, 2012 at 12:54
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    @Dennis: It would have been clearer to me if you had mentioned that the informal discourse is part of a larger work with formal and informal parts. The larger work would help "ground" the context of both these parts. (If you append an @ followed by my name in your comments, I get notified of it.)
    – prash ♦
    Commented Oct 21, 2012 at 15:57

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A standard dictionary or encyclopaedia of mathematics should have these types of historical usages your talking about. You might find The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English if you can find a copy. You might also search works on history of mathematical notation, you should find historical key terms and usages alongside notation compendiums. Otherwise start browsing indices of books like Dictionary of Mathematics. The book Mathematical Methods in Linguistics Chapter 7.7 "Informal Style in Mathematical Proofs" but it's not something like a discourse analysis. It's more like an explanation of notation and common omissions in proofs.

Another thing you might find useful are books on the history of mathematics. Such as Boyer's A History of Mathematics. These types of books should explain the contemporaneous concepts, key terms, and notation of mathematical science.

I think the only way to find serious academic material on linguistic analysis of mathematical discourse is to approach it as mathematics being a domain of discourse. So, study discourse, then take as your domain "mathematical works" just as you would any other domain like "cooking" or "legal statutes". Then do as you would, eg extract collocations, classify documents, whatever.

All this should really should be more than you asked for, but a less related subject is MathML and LaTex typesettings for mathematical documents. Reading about these would not be directly related to what you want, but it is the current and future course of mathematical publication, and if your seriously studying mathematical discourse you would be remiss to neglect this pertinent aspect.

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