A Mathematician's Apology

Essay

A Mathematician's Apology

G.H. Hardy

'I propose to put forward an apology for mathematics...' says G.H. Hardy, one of the greatest mathematicians of twentieth century as he opens the first chapter in this book. He explains in the chapter what he feels a real mathematician ought to be doing; '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 a new theorem, to add to mathematics, and not to talk about what he or other mathematician have done.' This sadness, this awareness that the powers which were his one source of supreme joy as a creator and which have now abandoned him and the honest admission of the same, pervades the essay like its soul. Another palpable quality is its most measured, pithy but supremely lucid and elegant prose. This is a work of a master craftsman. How I wish Hardy had written more and lengthier books, however against 'writing about mathematics' he may have been!

This book is rather a long essay. Hardy in it justifies the vocation of a professional mathematician. The book speaks for all his co-professionals and is thus not a memoir. But Hardy also says that 'in defending mathematics, I shall be defending myself, and that my apology is bound to be to some extent egotistical. I should not think it worthwhile to apologize for my subject if I regarded myself as one of its failures.' It is this plain candour and unsentimental forthrightness that is one of the main charms of the book. Hardy distinguishes between 'trifle' mathematics as is taught in schools and colleges and one which finds much application in increasing the happiness of the mankind (by providing them with better and more convenient amenities). But he finds this mathematics dull and uninspiring. He is defending here the practice of real mathematics, one that is distinguishable by its beauty, depth and seriousness. He cites two mathematical theorems of captivating beauty and simplicity to illustrate his point. And according to him 'great bulk of higher mathematics is useless'. He has this to say about himself; 'I have never done anything useful. No discovery of mine has made, or is likely to make, direct or indirectly, for good or ill, the least difference to the amenity of the world...I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating and that I have created something is undeniable: the question is about its value.'

This is an outstanding book. It lays bare the heart of an inherently shy genius, at least to an extent he is capable of, and tells us about the process of creation of art, for though the nitty-gritties differ, all creation is a form of art, be it music, painting, poetry, prose or a scientific discovery. There is a subdued lament in the book from an artist who has lived all his life for the ecstasy born of creation but finds that in his old age, his only source of happiness, his creative powers, have deserted him. This grieving over the dwindling creative genius with the passage of time is seen in works of many artists. I can't help quote Ghalib, one of the greatest poets that ever lived, as he bemoans his enfeebled powers:

'Muzmahil¹ ho gaye kuwa² Ghalib         1. Weak 2. Strength 3. Elements 4. Balance

Woh anasir³ mein aitedaal⁴ kahan'

Strengths have all, abandoned Ghalib,

Balance in the elements is thrown out of gear

            There is a long note about Hardy by his friend, the novelist CP Snow as a foreword, in the edition I read. This too is a masterpiece of biographical writing. Snow poignantly and with admirable understated emotions, reveals Hardy's character as he saw it. It's a superb composition and aptly compliments the sublime thoughts of Hardy that follow.