It is often said that mathematicians hit their prime in their twenties, and some even say that no great mathematics is created after that age, or that older mathematicians have their best days behind them. Many mathematicians explain the phenomenon in terms common to any academic field: With increasing seniority and age comes a heavy load of responsibilities that can distract mathematicians from their research.
However, I don’t think this is exactly true. Thus, historically speaking the greatest mathematical discoveries were made between ages 25 and 45 (average of 35-37). As just as a small example of that, Gauss discovered his Theorema Egregium, a central result in differential geometry, in his fifties. Andrew Wiles proved Fermat’s Last Theorem in his late thirties. Newton’s universal law of gravitation (Newton age 44). Euler’s formula for polyhedra (Euler age 43). The Fourier transform (Fourier age 43). And The Schrödinger equation (Schrodinger age 40).
Never mind that Freeman Dyson recently published an important contribution to the iterated prisoner’s dilemma at age 89. Weierstrass proved his famous Approximation Theorem at age 70. And Tibor Rado introduced “Busy Beaver” functions at age 67.
So… Are we too old to study Mathematics? Well, I don´t think so!
Sources of Information:
Lila Guterman. Math StackExchange.