Until relatively recently, I possessed a commonplace view of mathematics as being a subject that is simply a tool for other subjects. It saddens me now, that for all the comparison to creative arts that pure maths can be, we very often just focus on its applications rather than the existence of patterns and I daresay beauty of this subject. It took G.H Hardy’s ‘A Mathematician’s Apology’ to alter my previously misguided views on mathematics.
I don’t mean for this post to be a review of the book as such; I just want to get this weird frustration out of my system. I would not want to fall into the category of a ‘critic’, as according to Hardy, “exposition, criticism, appreciation, is work for second-rate minds”. In some ways, this I agree with. By criticising someone else’s work, you are in no way contributing anything to the greater knowledge of the world. You are not creating; merely stating an opinion on somebody else’s creation. And opinions there are as many as there are people in the world – precisely, some 7 billion-odd minds, each of them holding a view on something. If all these views were to be made public… what would the world have gained? Absolutely nothing.
Whereas if you are the one creating, exploring, proving – then you are benefiting not only yourself but the rest of the world in the process. Provided that your ‘creations’ aren’t used in the wrong ways – warfare, for example. But I’ll talk about that later. For now though, I can’t help but feel belittled. No matter how much I would like to be the one to prove the Riemann Hypothesis or Goldbach’s Postulate, the sad truth is that I probably won’t be. Another sad truth is that I will also be unlikely to discover a new, significant curiosity myself. Does that make me a lesser mathematician? Worse still – does that make me a lesser person? “Most people can do nothing at all well”, Hardy claims. Does this mean that, because you don’t rank in the top few in a specific subject – be it maths, sprinting, horse-racing, I don’t know – then you can’t do it ‘well’? This point of view depresses me slightly. Surely, if you enjoy what you do, that’s all that matters? I enjoy my degree course so far, yet I can truthfully say that it is a struggle. Nonetheless, a struggle which I enjoy – regardless of how disappointing my grade was at the end of year 1. I enjoy playing the piano – hell, I’m not particularly good at it, but it’s something I enjoy. Therefore making myself enjoy my time is something I do well. Does this not contradict Hardy’s view that most people can’t really excel at anything in particular?
But this has turned into a somewhat frustrated digression. From another standpoint, Hardy’s claim that “mathematics is, if an unprofitable, a perfectly harmless and innocent occupation” is something I do agree with. Pursuing the study of Number Theory, for instance, may seem the most useless occupation in the world. But will it lead to further bombing of Gaza? Oil spillages? Rape? Banking frauds? Unlikely. So whilst they may seem completely unapplied, the greatest minds can revel in proving this or that conjecture and enjoy the satisfaction, the beauty, of the subject.
I honestly don’t know where I’m going with this, just like I often don’t know where I’m going with life. Like many undergrads, I don’t yet know what I would like to do in the future – although I know I would (perhaps naively) like to have a positive impact on the world. Even if it is only one person. So would pursuing a beautiful subject like the seemingly useless study of numbers not allow me to have a positive influence on the rest of the world? Surely, I would then be ‘creating’ something, thus backing the point I made at the beginning of this post. At the same time though, active research in new methods of energy production or the search for a cancer cure or something else viewed as “useful” – wouldn’t that have more of a practical, positive conclusion? But my cancer cure could save the life of the next Hitler. Or my new method of energy production could make the next atomic bomb and destroy the lives of thousands.
Hardy’s defence of mathematics in “A Mathematician’s Apology” as a “pointless” subject is definitely worth a read. Just… don’t let it make you contemplate on the morality of life too much. Like it made me.