It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.
I make note of this famous excerpt today because I saw it, again, on a friend’s Facebook status. As I noted in response then, “Hardy says ‘second-rate mind’ like that’s a bad thing. I’d love to have a second-rate mind.” (A response stolen from George Mikes‘ ranking of writers where he says something like “I wish I was at least a fourth-rate writer.”)
But less facetiously, there are two confusions that afflict Hardy’s claim above.
First, Hardy is caught up in the mythology of the lone creator, artist, genius, whose thoughts and works spring ab initio from his or her mind alone, independent of history and context and antecedent work. Such a creature is entirely mythical; there is no fallow ground in the arts and sciences to be worked. All has been worked and tilled before; the creator, the genius, the artist builds on what came before. In one crucial sense, all supposedly ‘creative’ and ‘original’ work is exposition and explication and criticism and appreciation; departures depart from somewhere, they do not find an Archimedean point for themselves. (And can the genius’ work be understood without it being explicated?)
Secondly, a mathematician who writes about mathematical work may be doing philosophy of mathematics or perhaps noting connections between bodies of work that are not visible to those who might have worked on them individually. There is ‘insight’ here to be found, which might be as penetrating in getting to the ‘heart of the matter’ or in affording us a new ‘vision’ as the work of the ‘original creator’–perhaps achieved with flair and style that might lift the work out of the realm of the ordinary. Such might be the case with other kinds of explicatory work. Writing about writing is still writing, and still subject to the critical assessment we direct at the written word; we might find brilliance and innovation and style there too.
Ultimately, Hardy’s view speaks for too many, says too much, and yet manages to convey an impoverished and narrowed vision of the creative mind and its various endeavors. Moreover, it betrays its own trivial concerns in attempting to devise a hierarchy of values for such forays of the intellect: unsurprisingly, we find the work that Hardy saw himself as engaged in placed at the top of this hierarchy. Philosophies are disguised autobiographies indeed. (My defense of the explainer now suddenly becomes comprehensible.)