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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.

Martin Brandenburg
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  • Maybe of interest: http://www.amazon.com/Mathematics-Society-History-Sociological-Inquiries/dp/1402000391/ref=sr_1_11?s=books&ie=UTF8&qid=1404374595&sr=1-11&keywords=pure+mathematics+sociology – kjetil b halvorsen Jul 03 '14 at 09:08
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    In which society? – Did Jul 03 '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 08:43

1 Answers1

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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.

user_of_math
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    Thank you. The text is also available here https://www.dpmms.cam.ac.uk/~wtg10/importance.pdf – Martin Brandenburg Jul 03 '14 at 08:25
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    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 03 '14 at 08:27
  • @QiaochuYuan, Hardy himself fits in the same situation that you describe. Your point well taken by me. :) – J. W. Perry Jul 03 '14 at 08:31
  • Yes, agreed. ${}$ – Qiaochu Yuan Jul 03 '14 at 08:32
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    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 06 '14 at 18:20
  • @QiaochuYuan I think you could strip Gowers' name from the argument and it would still be a good argument. – Austin Mohr Nov 12 '14 at 02:59