Date: Feb 15, 2013 7:14 PM
Subject: Attitudes to mathematics among successful research mathematicians
Hardy wrote this in A mathematician's apology
"I do not remember having felt, as a boy, any passion for mathematics, and such notions as I may have had of the career of a mathematician were far from noble. I thought of mathematics in terms of examinations and scholarships: I wanted to beat other boys, and this seemed to be the way in which I could do so most decisively."
I wonder if this type of attitude is prevalent among successful research mathematicians, even among the world's elite. Do all renowned mathematicians have a strong aesthetic sense of the beauty of mathematics or is the main motivation often that doing well at it allows people to believe that they're more intelligent than others?
I suspect that many renowned mathematicians don't really have a strong aesthetic appreciation of maths at all, but the motivation is often a competitive motivation, and the desire to be thought to be intelligent.
This becomes obvious when elegant and remarkable concepts get discovered, and the vast majority of mathematicians are completely indifferent unless they can use these concepts or results in their research.
For example, how many mathematicians have any motivation to find out about surreal numbers? Few, I would think. If someone is in PDEs for example and doesn't use algebra, and has forgotten undergrad Galois theory, how many of such people can be bothered to open an undergrad textbook and relearn it?