"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."
He contributed a lot of practical findings in math. The Hardy-Weinberg principle[0] comes to mind...
It's almost frightening to me that the Hardy of the Hardy-Weinberg equilibrium could be writing this. It's part of a healthy understanding of genetics at all!
I very much doubt that Hardy regarded that as a "discovery". From a pure-mathematical point of view it's completely trivial.
(I do not say that to diminish its importance, which is an entirely separate matter. And something can be mathematically trivial but still an important discovery -- the cleverness may e.g. reside in noticing that it's a thing that might be true at all. Be all that as it may, I can't imagine Hardy, given his general dismissive attitude to applications of mathematics, seeing it as a discovery rather than a triviality that happened to be useful to biologists.)
Yes, that is true. He really did not care about it. The paper he wrote is Mendelian Proportions in a Mixed Population (http://science.sciencemag.org/content/28/706/49.full.pdf+htm...). It is brief, barely a page in length, and he introduces the HW equation with the preamble "A little mathematics of the multiplication table type is enough to that in the next generation the numbers will be [equation]".
Math is so huge......I've taken several math classes beyond calculus. Most people I know struggled with algebra, and are confounded and confused by my math skill. My math skill is so far advanced from zero that the average person cannot even conceive what such things mean.....even famous science writers don't understand eigenvalues, but I do.
Despite all that, I consider myself horrible at math. I am aware that I know only a small portion, and even that portion, poorly.
So maybe Hardy spent more time focusing on what he didn't know, and measured his achievements based on that rather than on what he did know.
"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."
He contributed a lot of practical findings in math. The Hardy-Weinberg principle[0] comes to mind...
[0]https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...