Pascal was an outstanding genius who studied geometry as a child. At the age of sixteen he stated and proved Pascal’s Theorem, a fact relating any six points on any conic section. The Theorem is sometimes called the “Cat’s Cradle” or the “Mystic Hexagram.” Pascal followed up this result by showing that each of Apollonius’ famous theorems about conic sections was a corollary of the Mystic Hexagram; along with Gérard Desargues (1591-1661), he was a key pioneer of projective geometry.
He also made important early contributions to calculus; indeed it was his writings that inspired Leibniz. Returning to geometry late in life, Pascal advanced the theory of the cycloid. In addition to his work in geometry and calculus, he founded probability theory, and made contributions to axiomatic theory. His name is associated with the Pascal’s Triangle of combinatorics and Pascal’s Wager in theology.
Like most of the greatest mathematicians, Pascal was interested in physics and mechanics, studying fluids, explaining vacuum, and inventing the syringe and hydraulic press. At the age of eighteen he designed and built the world’s first automatic adding machine. (Although he continued to refine this invention, it was never a commercial success.) He suffered poor health throughout his life, abandoned mathematics for religion at about age 23, wrote the philosophical treatise Pensées (“We arrive at truth, not by reason only, but also by the heart”), and died at an early age. Many think that had he devoted more years to mathematics, Pascal would have been one of the greatest mathematicians ever.