A Mathematician's Apology in Mathematics Students

Aug 01, 2020 Mark Hebwood rated it it was amazing

What a wonderful time I had with this book. GH Hardy, one of last century’s towering mathematical figures now known to a wider audience through the film “The Man Who Knew Infinity”, looks back on his life at a time when, by his own testimony, his mathematical genius was fading.

The opening lines establish a sense of melancholy that I was never quite able to banish when reading his memoir:

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The What a wonderful time I had with this book. GH Hardy, one of last century’s towering mathematical figures now known to a wider audience through the film “The Man Who Knew Infinity”, looks back on his life at a time when, by his own testimony, his mathematical genius was fading.

The opening lines establish a sense of melancholy that I was never quite able to banish when reading his memoir:

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 new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.

And yet, throughout the rest of his account, we encounter an intellect as sharp and penetrating as it is possible to meet. Hardy shares his thoughts about the aesthetics and truth value of mathematics, and his thoughts are profound, but they are offered with the charming nonchalance of somebody who does not seem to be truly aware of his own intellectual calibre.

The thought that resonated with me most is the idea that mathematics is, to speak with Hardy’s own diction, ‘useless’, or to put it into less colourful language reserved for somebody who is not a mathematician (me...), free of purpose. I believe what Hardy had in mind was to convey the idea that the study of mathematical objects is itself its purpose, that discovery of new mathematics “pushes back the darkness by a millimetre”, as Greg Chaitin, another genius mathematician, put it, that the purpose of mathematics is not measurable by any practical application that may not have been made without it. In this interpretation, the study of mathematics can be an example of pure thought, of pure intellectual pursuit unencumbered, constrained or possibly diminished, by the demands of the practical world. And that, to me at least, is a beautiful and encouraging thought.

When he wrote his account, Hardy, in the words of Jethro Tull, may have felt “too old to rock and roll, too young to die”, but I want to finish by letting the man himself speak. I started my comment with the first lines of Hardy’s book, allow me to finish it with some of the last:

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. Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating.

The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them. ...more

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Jan 28, 2017 Lthmath rated it really liked it

This was a very interesting read for me. I totally enjoyed the Foreword part written by C. P. Snow, it gave the book more sense and I could understand more subtleties hidden in the actual book. When I started the part by G. H. Hardy, I got stuck by the openness of the book. He was not hiding under the finger and just said what he thought was true. I have to confess that some of his ideas where a little extreme for and I don't agree with them, but the book made me think about how much the politic ...more

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Oct 20, 2014 Angelynn rated it liked it

At first, it took me quite a while for the book to grab my undivided attention---but once it started discussing the actual beauty of mathematics, I could not put the book down. I read the book in one day, which was doable due to the [very] short length of the book. G.H. Hardy is a very very good writer, and the book was formulated in a lucid manner. I believe Hardy did a great job in simply describing the beauty of mathematics as an overall subject, as well as the "utility" in both pure and appl ...more

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Jan 10, 2015 'Asem Ismaiel rated it really liked it

It's good to know I've always had almost the same views as Hardy, although I'm not familiar with any of his work but he did have the pleasure of working with Ramunjan so he rules. :D
I enjoyed most of the book but this line is probably what I liked the most:
"Imaginary universes are so much more beautiful than this stupidly constructed ‘real’ one." ...more

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