A Mathematician's Apology

Hardy believed that the great discoveries of math are made by mathematicians in their twenties and thirties. Think of another field in which young adults seem to have a distinct advantage, and examine how that field resembles and differs from math. What is it about each field that gives younger participants an advantage?

Pick an example of a profession in which older people seem to have a career advantage, and explain why this is so. Compare the requirements of this profession to the requirements for a mathematician.

Hardy believed that success in top-level math necessitates a great competitive spirit and the willingness to do hard, sustained work. Why did he consider these characteristics vital? Why might someone who’s lazy and noncompetitive fail specifically in the field of mathematics?