Before anyone runs for the exits when I say that I'm going to be writing about a mathematician's book, I'm not going to throw pointy, abstruse theorems at you, and for the most part the author doesn't do so either. Rather, I'm interested in presenting my general thoughts about what drove this man to do what he did well, namely, doing pure mathematics. I should note that I've decided to skip some of what I consider to be the book's peripheral topics (peripheral in the sense of being auxiliary or supplementary). I'm interested in conveying the general character, the sense or tone, of both the author and the book. It's this character which impressed me enough to make it my first guest post. Let's get on with it, then.
G.H. Hardy is the author of the slim book A Mathematician's Apology, first written in 1940. The title, while referring to an apology, isn't exactly one. In fact, Hardy doesn't exactly defend his views as an apologist is expected to do; rather, he presents his views in such a way that: His ideas, he would imply, clearly make sense, and thus need no special, elaborate defense of any kind. Such is the boldness found throughout this book, by one very dedicated mathematician. (Note that He worked in pure mathematics, as opposed to applied mathematics. To put it simply and crudely, he was interested in numbers and theories for the sake of numbers and theories themselves--you know, seriously crazy abstract stuff!)
Why was he dedicated to his chosen field? He gives us these unvarnished answers: Intellectual curiosity, professional pride, and ambition. I suspect that intellectual curiosity was the biggest drive of the three, considering how wonderfully strange pure mathematics can be. However there can be no doubts about it: Professional pride definitely was the second driving force in his professional life. Additionally, Hardy did not clothe his words in warm fuzzy sentiments. That doesn't mean that this is a mean-spirited book--far from it. It just suggests that Hardy's intellectual honesty could be added to that list by us readers. And what this honesty amounts to is an exposition of what drove him to do pure mathematics, a subject for the highest of thinkers. Hardy's concluding note at the end of the book wouldn't disagree with my calling mathematicians as some of the greatest thinkers around.
First and foremost, G.H. Hardy was completely serious about what he did. He was a pure mathematician above all else. Better yet: He was a pure mathematician and nothing else. What this means is that Hardy would have thought it foolish for him to have done anything else apart from mathematics, his calling you might say. And this is a reason why this short book paints a world mixed with both vibrant and sombre colors, an essentially human coloring noted by both its author and its many readers.
Clearly, Hardy would rather have been doing mathematics than writing about it. Right in the opening paragraph, he gives us the impression that, indeed, this is the case. In that paragraph too, we also see two feelings merge or blend into one: heavy-hearted arrogance or pensive self-importance. Even these, I think, aren't adequate descriptions or words. They seem to play too much on the negative, which isn't intended on my or his part. Here's a quote from said paragraph to see what I'm trying to get at: "It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something...." And later on at the end of the same paragraph: "Exposition, criticism, appreciation, is work for second-rate minds." Yes indeed, Mr. Hardy would have rather been doing math than merely writing about it. Unfortunately, at the time of writing the book, Hardy was losing his mathematical gifts, his power to 'see' and sustain original thoughts concerning pure mathematics. In short, he was growing old:
"If then I find myself writing, not mathematics, but 'about' mathematics, it is a confession of weakness, for which I may rightly be scorned or pitied by younger and more vigorous mathematicians. I write about mathematics because, like any other mathematician who has passed sixty, I have no longer the freshness of mind, the energy, or the patience to carry on effectively with my proper job."
So here we have it, a book written by a fastidious mathematician who can no longer carry on doing what he had dedicated his adult life to: doing mathematics.
But that doesn't give this book an encompassing character of self-pity or total gloom. Instead, the book absolutely exudes an air of greatness--rather, Greatness. Yet, for all that, it doesn't come across as entirely egotistical. (OK, it's slightly egotistical, but that's part of what makes it so interesting!) We see Hardy giving us his reasons for doing what he did, showing us the ideas that he held, presenting 'beautiful' theorems anyone can enjoy, and dismissing those who don't take themselves and their studies seriously enough. Here we see his professional pride rising to the surface. Clearly, he had taken great pride in what he had done as a professional mathematician. What he's getting at is clear enough: One ought to care about the quality of work that she or he can produce. You know, don't crank out any old thing and call it 'good enough'. Hardy's pride would have none of that: "Good work is done by no 'humble' men." Perhaps, it was this feeling of self-importance (in a positive sense) that enabled Mr. Hardy to be the ideal mathematician, at least according to his high standards.
Yes, G.H. Hardy was all about being the pure mathematician, a notion he suggests ought to be shared by other pure mathematicians if they are to be seriously called that, and if they are to ever achieve worthy results. Perhaps, this is a notion he felt should be shared by anyone who has exceptional talents. --Do something with them!-- The world of pure ideas, i.e. mathematics, is a world for the most strict and dedicated thinker. No doubts about it. (I deliberately used 'world', since it agrees with his mathematical realism, his philosophy.) And by being such a mathematician with such an outlook, Mr. Hardy was then able to say that at the end of his career he was able to contribute to knowledge, learning, and (I attribute this to him) discovery.
Perhaps after reading this book, someone may take decide to take that difficult, yet rewarding, journey as well.
