The romantic myth is well-known. Mathematics is a young person's game. If you have not created significant mathematics by age 25 (or 30 or 35), then forget it.
Four examples are well known:
And, we wonder what the first two mathematicians would have accomplished "later," as both died at very young ages.
- Galois produced his notable ideas in group theory by age 20
- Ramanujan produced his notable ideas in number theory by about age 30
- Newton invented his theory of calculus by age 24
- Terence Tao is the modern example!
In contrast, examples to counter the myth are also well-known. Mathematicians with late-in-life accomplishments include Gauss, Euler, Poincare, and Erdos.
In 1978, Nancy Stern investigated this myth, and actually put it to rest, but it refuses to lie down! She investigated possible connections between age and productivity in mathematics. Her conclusion: Mathematicians of ages 35-39 were the most prolific, followed by those of ages 40-44...and both outpacing those of ages 20-35. She adds that these distinctions were based on quantity, but changed little if the measures of quality were used.
Despite it being disproven, Susan Landau adds that "This myth discourages those whose mathematical ability blossoms late, and creates a barrier..."
So, I guess I still have a chance...and many of you as well!
Source: S. Landau's "The Myth of the Young Mathematician," AMS Notices, 11/1997