The first items in this post were originally in my post on seeing Saltpeter perform Wallace Shawn’s “The Fever” at Brighton in May 2011, but on second thoughts just having a link there is better.
I recommend reading G H Hardy’s short book “A Mathematician’s Apology“, both for what Hardy writes and for the memoir of Hardy by C P Snow which is printed in most editions of the book. The novelist Graham Greene said “I know no writing – except perhaps Henry James’s introductory essays – which conveys so clearly and with such an absence of fuss the excitement of the creative artist.” Yes: creative artist, not mathematician or scientist. (Albeit there must be a lot of creativity in good mathematics and science, and I’ve considered for a long time that mathematics is in some ways more of an art than a science, despite it’s being the most certain science!)
A rather good article in The Hindu on Hardy and “A Mathematician’s Apology“ which quotes lines from the book: “Poetry is more valuable than cricket, but Bradman would be a fool if he sacrificed his cricket in order to write second-rate minor poetry (and I suppose that it is unlikely that he could do better).”
Asides on mathematics and art:
Margaret Dusa McDuff on Israil Gelfand: “Gelfand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which he could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gelfand found hedgehogs lurking in the rows of his spectral sequences!“
Khinchin: “Khinchin was a fascinating figure …, not least because of his early enthusiasms for poetry and acting, and his links with such figures of the revolution as the poet Mayakovsky and members of the Moscow Arts Theatre.”
Christopher Zeeman: “Technical skill is mastery of complexity while creativity is mastery of simplicity.”
Zeeman on whether he regards mathematics as an art or a science: “Both. Sometimes you invent it; sometimes you discover it. You have to invent maths to get a solution to a problem but, in the process, I often discover a whole lot more which I didn’t expect.“
Hardy is an intriguing person. Again quoting from Robert Kanigel’s book “The Man Who Knew Infinity“:
“All his life he was sympathetic to the underdog. Mary Cartwright [who collaborated with Littlewood, so she must have been a very good mathematician] recalled that as a woman mathematician ‘I was a depressed class’ and so enjoyed Hardy’s favour.” Mary Cartwright also said that Hardy was very kind to less able students. In his memoir of Hardy, C P Snow wrote that Hardy preferred the downtrodden of all types “to the people whom he called the large bottomed: the description was more pyschological than physiological … [They] were the confident, booming, imperialist bourgeois English. The designation included most bishops, headmasters, judges, and … politicians.”
Examples of Hardy’s wide range of interests:
* Hardy on examinations: “An examination can do little harm, so long as its standard is low.” (Remember that Hardy knew what he was talking about: he was a world class mathematician in his time. That said, I’d want high standards in some examinations, for example medicine and engineering.)
* Hardy’s not entirely serious resolutions for a new year in the late 1920s:
1. Prove the Riemann hypothesis. [Still – as of 2011 – not proved. Non trivial!]
2. Make 211 not out in the fourth innings of the last test match at the Oval. [A cricket reference. Kanigel comments that this is something like hitting a grand slam home run while behind by three runs in the ninth inning of the final game of a baseball World Series.]
3. Find an argument for the non-existence of God which shall convince the general public.
4. Be the first man at the top of Mount Everest.
5. Be proclaimed the first president of the USSR of Great Britain and Germany.
6. Murder Mussolini.
* Hardy’s letter to the Royal Society advocating electing Ramanujan to be an FRS (Fellow of the Royal Society): “If he [Ramanujan] had not been ill I would have deferred putting him up for a year or so, not that there is any question of the strength of his claim, but merely to let things take their ordinary course. As it is, I felt no time must be lost. I am nervous about trying to rush him [that is Ramanujan’s candidacy], and I am aware that for the time being I am not an ideal supporter. [possibly a reference to Hardy’s views about World War 1] And I realize that the Royal Society has many other things to consider. But there is no doubt that (especially after his disappointment in the Fellowships) any striking recognition now might be a tremendous thing for him. It would make him feel that he was a success, and that it was worth while going on trying. It is this much more than the fear of the Royal Society losing him entirely which seems to me important. I write on the hypothesis that his claims are such as, in the long run in any case, could not be denied. There is an absolute *gulf* between him and all other mathematical candidates.”
I tend to underestimate the positive effect and necessity of appreciation (by those who know) on people, including myself.
Not exactly the same thing, but in the late 1980s or early 1990s the British Indian actor Rita Wolf wrote an article in The Guardian newspaper about her early experience in theatre. She wrote that before she became a professional actor she had gone to see a production of Simon Gray’s “The Rear Column” in a West End theatre, and had only been able to identify with two characters on stage: black slaves, a man and a woman, who had very few lines. She could have added that the woman character had no lines at all.