Review of A Mathematician’s Apology (G.H. Hardy)
It is a melancholy experience for a professional mathematician to find himself writing about mathematics.
So starts Hardy in this essay that I admire slightly more for its prose than for its intent. Hardy is an excellent writer, who holds some firm convictions that I ask the reader to forgive me for disagreeing with.
There is no doubt that, save for the peripheries, his ideas are still relevant in the modern age. The reader will also agree, even without any background on the man G.H. Hardy, that he was a mathematician who was attached to his work, and believed in it even when doubting the very reason he did it for. Here was a considerably talented man in his youth, thinking of mathematics not in terms of its aesthetics or beauty, but rather in terms of scholarships, examinations, and ‘beating other boys’. This recalls questions expressed early in the book about why someone should decide to do mathematics. His answer is immortality. Mathematical immortality in particular, which according to him, perseveres through time more stoutly than that of other disciplines because of the abstractness of its machinery. I guess then it is not fair to think Hardy of consistently having a purely competitive spirit; clearly it grew into nobler intentions at his peak, but subsequently deteriorated as his age pulled down on it.
But is mathematics a practical profession? What uses are there for it? Hardy splits the realm into a two: pure and applied. Mathematics used to describe a physical reality is certainly useful, after all, we get useful information from study of the system. But Hardy wasn’t a mathematical physicist. He was a pure mathematician, who could render any reality he wanted, not being limited by the nature of physical law. Certainly this isn’t useful for the real world. What good could knowing the irrationality of the square root of 2 possibly do to society? It doesn’t help us generate power more efficiently. It doesn’t cure cancer. It does, however, provide delight to the few who appreciate the beauty of its proof. Hardy acknowledges this humbly, “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.” This says little about his capabilities as a mathematician; after all, he was a brilliant specimen, but instead expresses his thoughts on the view of a pragmatic outsider looking down on pure mathematics as an ascetic would look upon a gilded ornament. How meretricious it would seem!
Hardy tells us a few times that like the case for most other subjects, creativity for mathematics dies down with age. Abel (27), Galois (21), and Ramanujan (33), he claims, all died young but contributed magnificently. Newton was done with mathematics by the age of fifty and as the Master of the Mint, only dabbled in it occasionally as he did with the brachistochrone. By his tone, one feels as if Hardy’s passion is all but extinguished. Throughout this essay, he brings together ‘pure’ mathematics with art, allowing us glimpses of the subject, sharing with us what he believed to be beautiful. At the end of the essay we see him plainly, a tired, old artist, his best behind him, but still possessing the innate appreciation for his trade that has so enriched his life.
I recommend this book to anyone. It truly is great in my opinion, mainly because we find so much to disagree with in it. If nothing else, we will recognize that pure mathematics is a very joyful endeavor; he presents a few theorems and their proofs (the infinitude of prime numbers and the irrationality of the square root of 2) which will hopefully encourage you to pick up a book on the theory of numbers (I did), even if you abhorred mathematics before reading the essay. I also consider this essay a worthwhile read because of how well it’s crafted. Hardy, in his advanced aged, may have considered himself a lesser mathematician than he used to be, but even then he was an elegant wordsmith.
Happy Reading!
Originally published at http://purehistoryjuice.com on February 23, 2017.
