Charles Hermite (1822-1901) France

Hermite studied the works of Lagrange and Gauss from an early age and soon developed an alternate proof of Abel's famous quintic impossibility result. He attended the same college as Galois and also had trouble passing their examinations, but soon became highly respected by Europe's greatest mathematicians for his successes in number theory and elliptic functions. Along with Cayley and Sylvester, he founded the important theory of invariants. He was a kindly modest man and an inspirational teacher. Among his students was Poincaré, who said of Hermite, "He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures."

Although he and Abel had proved that the general quintic lacked algebraic solutions, Hermite introduced an elliptic analog to the circular trigonometric functions and used these to provide a general solution for the quintic equation. He developed novel ways to apply analysis to number theory. He developed the concept of complex conjugate which is now ubiquitous in mathematical physics and matrix theory. He was first to prove that the Stirling and Euler generalizations of the factorial function are equivalent. Hermite's most famous result was his ingenious proof that e (along with a broad class of related numbers) is transcendental.