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Is there some book or essay which deals with the sociological and economical justification of doing and funding pure mathematics? I'm looking for a modern version of Hardy's A Mathematician's Apology, but if possible from a non-mathematician's point of view. For example, the book should answer the following type of questions:

Why is it (and should it be?) possible in our society to earn a living by calculating, say, K-theory groups of spectra? Why does the society support a subculture of mathematicians who solve abstract problems which "obviously" don't have any connection to the rest of the world?

I'm not asking for personal opinions from math.SE users - this is a reference request.

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In which society? – Did Jul 3 '14 at 10:21
I didn't specify the society because math.SE is an international forum. People around the world may answer this question and specify (if necessary) what is special in their society. I'm German, but didn't want to restrict my question to the role of mathematics in Germany. – Martin Brandenburg Jul 28 '14 at 8:43

2 Answers 2

Not an essay or book, but there is a rather informative and clear video address by Timothy Gowers (a Fields Medalist) in 2000 on the "Importance of Mathematics" for an audience containing non-mathematicians in Paris.

He specifically addresses the issue of the (enormous) benefits that mathematics yields on a (very small) investment, its intrinsic cultural value and the interconnectedness of mathematics that make the "useful" areas inseparable from the "useless" ones.

It is available for download from the Clay Math Institute's website here, you'll have to scroll down to the bottom of that page for the download link.

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Thank you. The text is also available here – Martin Brandenburg Jul 3 '14 at 8:25
Of course, Timothy Gowers is a mathematician, and a very successful mathematician at that. I'm not aware of many people who are very successful in their profession who also actively argue that their profession should not exist, so there's reason not to take this as strong evidence that pure mathematics as a profession is justifiable. – Qiaochu Yuan Jul 3 '14 at 8:27
@QiaochuYuan, Hardy himself fits in the same situation that you describe. Your point well taken by me. :) – J. W. Perry Jul 3 '14 at 8:31
Yes, agreed. ${}$ – Qiaochu Yuan Jul 3 '14 at 8:32
Meanwhile I've read Gowers' text. Needless to say, it is worth reading and contains many interesting examples of mathematical problems which are connected to each other and/or which may be applied to other sciences. Gowers answers my question only in the first pages. The main arguments are: 1) Mathematics is very cheap, and still has an enormous direct or indirect economical benefit. 2) It is impossible to separate the useless from the useful areas. – Martin Brandenburg Jul 6 '14 at 18:20

There doesn’t seem to be published very much:

Mathematics in Society and History: Sociological Inquiries S. Restivo (Springer)

On the Sociology of Mathematics D. J. Struik (Science & Society) (JSTOR) (And other books by same author)

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These are just google results of "mathematics + sociology" or something, right? Without any explanation this answer isn't really informative. For example, from the summary of the first book, I doubt that it answers my question. – Martin Brandenburg Jul 6 '14 at 18:27
well, the books by Reuben Hersh, at least, is a little bit more than google results: I have actually read (one of) them, and it is at least close to getting into your question. But he is no sociologist, I guess your question is so specialized you shoiuld approach some professor of sociology to see if he knows about something. – kjetil b halvorsen Jul 7 '14 at 20:14
The book "What Is Mathematics, Really?" by R. Hersh answers the question what mathematics really is, but rather from a philosophical point of view, right? Of course this is an interesting question, but how is it related to my question? I would like to understand in detail why (and how) pure mathematics in funded by our society. – Martin Brandenburg Jul 28 '14 at 8:47
Maybe you should widen your question to something like "Why do societies fund science without any clear applications? That list is large, study of latin, old greek, large parts of social science, ornithology, etc, etc? Might make it easier to find some answers. – kjetil b halvorsen Jul 28 '14 at 20:29

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