Notice the early mental development of some of the great mathematicians.
Blaise pascal, at age 16, wrote a treatise on conics, considered one of the foundations of modern geometry. Pascal contributed decisively to the creation of two new branches of mathematics: Projective Geometry and Probability Theory.
Évariste Galois, at age 15, discussed and commented on the works of Legendre and Lagrange, which later culminated in the perception of the impossibility of finding an expression for roots of algebraic equations greater than 4.
Alexis Clairaut, at 10, read and understood the works of the Marquis de L'Hôpital on calculus. And it ended up being the precursor of Differential Geometry.
Joseph Bertrandat age 11, started the course at the Polytechnic school, and at 17 received the degree of doctor. At the age of 23, he conjectured that there is always at least 1 prime number between n and 2n-2 for every n greater than 3.
Nicolas Henri Abel, at the age of 16, was investigating the problem of solving the fifth degree equation, which later triggered the first complete proof of the absence of an algebraic formula for these roots. He died at age 26 of tuberculosis.
Johann Carl Friedrich Gauss, at age 7, summed the whole numbers from 1 to 100 quickly using the reasoning that demonstrates to this day the summation formula of an arithmetic progression.