Written: June 20, 2023
I enjoyed your most recent one and I am most grateful that you scanned Trefethen's book. Of course, I will order a couple of copies for myself and others.
A couple of points occurred to me whilst skimming the scan. While Hardy was a superb stylist, Trefethen's book is far more useful and productive than Hardy's apology. Indeed one can say his idiotic remark about "mathematics being a young man's game", did the profession considerable damage.
The second is that some of Hardy's finest work arose in collaboration with a computational mathematician par excellence,Ramanujan, with Ramanujan providing the results and Hardy the proofs. If you read the first chapter of Hardy's book Ramanujan, there are some intriguing comments on Ramanujan's working style. In particular, there is the following passage from Hardy's obituary of Ramanujan. (See the top of page 14 of Ramanujan.)
"... He worked far more than the majority of modern mathematicians, by induction from numerical examples; all of his congruence properties of partitions, for example, were discovered in this way. But with his memory, his patience, and his power of calculation he combined a power of generalisation, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling,..."
Maybe, instead of Ramanujan being mentored by Hardy, it would have been more productive if Ramanujan had mentored Hardy!