hardy (adjective): : able to live through difficult conditions (such as a cold winter or a drought) : strong and able to accept difficult or unpleasant conditions (Merriam-Webster)
In this extended essay he argues among other points that mathematics has a deep intrinsic beauty, and it is worthy to be pursued for its own sake.
I tried very hard to like this essay, but failed miserably on every occasion. It would be too easy to mock from our 21st century perspective Hardy’s mistake when he uses number theory as an example branch of mathematics with absolutely no practical applications (which by the way Hardy views as a huge positive). However, I also find the main point about mathematical beauty (mentioned before) not very convincingly presented, even if you agree with him before opening the book.
But what I disliked most were Hardy’s strong opinions such as “there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds”, and in another paragraph “it is a tiny minority who can do something really well, and the number of men who can do two things well is negligible” and finally the notorious “mathematics is a young man’s game”.
To express my dislike of this essay, I am making the modest proposal of a Hardy prize in mathematics, to be awarded to people who achieve significant mathematical results in ways contrary to the letter and the spirit of Hardy’s book (we can never know of course, whether Hardy himself would consider the results of any significance, although we can guess with good confidence.)
More positively, the fictional Hardy prize recognizes:
- pure mathematical work deeply influenced by practice and applications or by teaching and other expository work
- mathematicians (men or women) who started their mathematical career or achieved their most significant result at a relatively late age
- mathematicians who went about their mathematical career in a less than straightforward way, possibly having strong interests or accomplishments outside mathematics, possibly doing mathematics as a hobby
Ignoring historical examples (some of which Hardy must have known), as a small (and quite random) initial sample from our times I would suggest as first recipients: Persi Diaconis, Marjorie Rice, Preda Mihăilescu, Yitang Zhang, Raymond Smullyan.
This post is of course only half-serious and half-ironic (unless someone takes a serious initiative in this direction). Would such a prize make sense? This post benefited from discussions with colleagues, who would probably prefer to stay unnamed. I was also informed by this post.