useful theory


I have never done anything ‘useful.’  No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.

That is a quote from Oxford/Cambridge mathematician (number theorist) G.H. Hardy’s entertaining 1940 book titled A Mathematician’s Apology (free online pdf copy). 

Hardy discusses (and logically illustrates) his twin criteria of beauty and “seriousness” in evaluating mathematical theory, contrasts basic versus applied/’useful’ science, discusses the role of science in war, etc.  He also throws in many biographical diversions for good measure.   A fun, quick read. 

Written by teppo

January 5, 2008 at 8:01 am

5 Responses

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  1. I always thought Hardy’s sentiment was interesting. His specialty – number theory – is now highly important for cryptography and computer security. Hardy was also important in early population genetics – which we all know is completely useless!!


    Fabio Rojas

    January 5, 2008 at 8:42 pm

  2. I love the purist disdain toward “usefulness,” true scholars — eventually however many of these theories end up being tremendously useful.



    January 5, 2008 at 8:48 pm

  3. Perhaps one of the greatest lessons I have learned in life about intellectual work is that the pure/applied division is extremely bogus. I think it is totally reasonable for an academic to work on topics for abstract aesthetic reasons, but in the long run, a lot “pure” ideas have big impacts on applied areas. Also, applied areas also motivate a lot of “pure” theoretical work. In short, intellectual life is really one giant mixed equilibrium where we switch from pure to applied.


    Fabio Rojas

    January 5, 2008 at 9:15 pm

  4. There’s a big relevance-usefulness-rigor discussion going on around b-schools these days, with the AACSB etc involved. The same pressures don’t exist in sociology – no one asks: “what are the mgrl implications?”- though I guess there is the whole pub sociology issue.

    In my mind directing research toward more practical implications does not make sense. As it is, there’s a division of labor of sorts: you have folks who do work with more practical implications, and often that work is the downstream result of good, basic science and social theory done by others. (And, you’re right, the applied-basic distinction is not dichotomous.)



    January 5, 2008 at 9:23 pm

  5. […] Fish (not one of my favorites) channels G. H. Hardy: To the question “of what use are the humanities?”, the only honest answer is none whatsoever. […]


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