# A mathematician’s apology, G.H. Hardy

In between revision, I must admit that I take little five minute breaks every few hours by reading a chapter of some interesting book to hand. Last week, I worked through Hardy’s apologia for his life and work. It is often commended as a defence of pure maths and as a clear articulation of why mathematics is so vital and valuable.

Unfortunately, I found it more effective as an apologetic against Hardy’s life than for it. As he admits (§1), any apology by a mathematician for mathematics inevitably is a defense of oneself, and it is the emptiness of Hardy’s mathematics that is so moving.

Hardy was an odd man, living in an odd era when intellectuals had very few distractions or outside influences. As part of the culture very sadly few of them had wives, and almost all or his contemporaries’ families were totally dysfunctional (see Russell, Littlewood, and so on). His routine was extremely regular and he worked very hard, with cricket forming his main diversion from academic interests. The fellows then were able to amass a large proportion of the current knowledge as a result.

Hardy’s apology then is the fruit of his self-justification of his life and to educate laymen without an academic background, the only people he assumed who would not realise the importance of maths. While many of his points are very valid, and his description of proof and aesthetics is very clear. However, it is the total vacuousness of his world which is shocking.

I have been to plenty of seminars along the lines of ‘how to honour God in your maths’, and always been fairly frustrated by them. There are certainly epistemological insights which change the nature of the maths itself, but it is usually hard to see how those actually change anything in the maths much. There are wonderful apologetics as a deeper appreciation of thought and logic inevitably add up convincingly to some particular applications of general apologetics. The arguments from aesthetics, from communication, and from morality (that is, accepting true statements as a moral requirement) have distinctive mathematical forms which are important. Indeed, real mathematicians cannot understand realism [one of the only varieties of mathematical philosophy which can really claim to avoid man-centredness] without covenant revelation. Finally, the third thing which these seminars usually discuss is working with a Christian attitude.

I have always been cautious about this last point, even though it is generally the predominant emphasis, because it seems so unspecific to maths itself. It is Hardy’s book though that has changed my attitude. Such a lucid explanation of the place maths takes in his life is terrifying, as he genuinely seeks to use it to justify all his activities ultimately done for the self. There is no much quite so gripping to persuade us that living a life of service committed to God makes a real difference.

Hardy’s thinking is strongly humanistic with utilitarian overtones, and he keeps coming back to war. Like many in his set, he was a pacifist shaped by the first World War, but clung doggedly to his hope in his own non-involvement. He had so little hope in society that without commenting on or seemingly realising it, his apologetic is secondly bleak in its lack of hope for society. Hardy’s hate for war leaves him no hope for most of his readers, especially hard given that Hitler had been in power for nearly a decade.

Finally, the book is ghastly because Hardy’s self-justification slightly pitifully stops shorts of explaining his own retirement. Hardy was surrounded by many friends, like C.P. Snow, who were deeply creative and grew up in an environment where good thinking and writing skills were more emphasised than now. He was therefore more able than most mathematicians now to engage with literary ideas (indeed, the loss of this old educated establishment was a major theme of Snow’s later life as his mentors of Hardy’s generation died off). This coloured Hardy’s appreciation of maths as classical ideals led him to emphasise the inherent creativity involved in maths. When he lost his young spark, much of his happiness went with it because he could not contemplate any other sort of mathematical work being meaningful, nor place his self-worth in anything apart from his work. Written when he was sixty-three, the book is therefore very plaintive and retrospective, the apology almost entirely directed back towards his past life.

So, the book is well-written and clear in its account of what maths is, but the work is stark in its depiction of the particular horror of atheism for a mathematician. The inability of Hardy and most of his contemporaries to look outside themselves and their community for value is so sad, and is the overwhelming impression of reading most books from that academic circle. On the other hand, one of his contemporaries was G.K. Chesterton, who knew Bertrand Russell well, though I can find no record of him meeting Hardy. Chesterton’s different approach, though it led him in some directions I do not entirely agree with, shows the transformation in thinking that God can work in anyone, even those surrounded by the same lifeless academics.