[…] A Mathematician’s Apology is, if read with the textual attention it deserves, a book of haunting sadness. Yes, it is witty and sharp with intellectual high spirits: yes, the crystalline clarity and candour are still there: yes, it is the testament of a creative artist. But it is also, in an understated stoical fashion, a passionate lament for creative powers that used to be and that will never come again. I know nothing like it in the language: partly because most people with the literary gift to express such a lament don’t come to feel it: it is very rare for a writer to realise, with the finality of truth, that he is absolutely finished. – Foreword to A.M.A, by Dr. C. P. Snow.
It is a testament to Hardy’s great powers as a writer that, even in the throes of despair at having lost his powers, his apology for mathematics retains an austere, crystalline beauty. I recently finished my second reading of this short autobiographical essay, combined with Dr. C. P. Snow‘s excellent foreword which is about as long as the apology itself. In a mere 90 pages, one gets a very sharp picture of a most interesting mathematician who is at once cognizant of his strengths and brutally frank about his shortcomings, who revels in a game of cricket and has a comical life-long feud with God.
Hardy reached his creative zenith during his collaborations with Littlewood and Ramanujan. Hardy notes that, in terms of natural mathematical talent, Ramanujan was in the league of Euler and Gauss. He had no formal training whatsoever and did not initially understand the concept of a proof. He had even failed to matriculate in English. Yet, in the foreword, when Hardy visited the dying Ramanujan and lamented about the dullness of his taxicab’s number (1729), Ramanujan burst out:
No Hardy! No Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.*
Hardy talks at length about his view that a mathematician must do his/her best work at a young age, and can hope to accomplish little thereafter, citing examples of Newton and Laplace. (Bertrand Russell has also made the same observation about himself.) It made me think about the issue of burnout, applied particularly to the faculty of doing productive research. If Hardy and Russell are to be believed, then mathematics is very much like many professional sports: One cannot reasonably hope to play professional tennis or one-day international cricket beyond the age of 35. The raw talent still remains but the physical and/or mental strength to harness it leeches away with time.
This is altogether horrible. Just the other day, I was talking with a friend about research burnout, a condition dreaded by students in my position. There we were, nearing the end of our Ph.D. fearing the prospect of new research and wondering whether we would ever be so productive again. It has happened to me a couple of times before (and I think it happens to most people) that after a productive period of research and publications, there is a lull in which one wonders if the tank is empty. Every time, like most people, I discovered that the tank was not empty after all, but this time it is more difficult for us to see the light, partly because of the stress of finishing a never-ending dissertation and partly because of the realization that after we finish, we have to start all over again.
* 1729 = 93 + 103 = 13 + 123 😉