Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
There are two reasons why I propose to make myself thoroughly and unashamedly happy by talking about myself. The first is that on several occasions, both in England and America, I have been told that I am a legendary character.
When I was at Manchester, where there was a modern swimming pool, I was looked on as a great man, not for so trivial a reason as being an FRS, but because I used to dive off a five-metre board.
In 1912 I attended an international mathematical congress held in Cambridge. I went into the buffet room where all the distinguished mathematicians were gathered and I thought to myself, "What an odd looking lot they are."
All I remember about the examination is that there was a question on Sturm's theorem about equations, which I could not do then and cannot do now.
[said at age 80]
I am the world's worst good bridge player.
Mathematical study and research are very suggestive of mountaineering. Whymper made several efforts before he climbed the Matterhorn in the 1860's and even then it cost the life of four of his party. Now, however, any tourist can be hauled up for a small cost, and perhaps does not appreciate the difficulty of the original ascent. So in mathematics, it may be found hard to realise the great initial difficulty of making a little step which now seems so natural and obvious, and it may not be suprising if such a step has been found and lost again.