Amateur Mathematicians

Pierre de Fermat is the best known amateur mathematician, but the story of Grassman is much sadder. Something of a mathematical Van Gogh, he created the subject of linear algebra single-handedly, devised the first axiomatisation of arithmetic, and much else besides. His work was rejected by almost all professional mathematicians of the day, including Möbius and Kummer. Unlike Van Gogh, he didn't end up killing himself, but became a noted philologist instead!

Another case of a neglected mathematician is Kurt Heegner who solved Gauss' class number problem for imaginary quadratic fields (finding all nine such fields of class number 1). His proof was dismissed by the mathematical community until 1967 when Harold Stark developed a proof and showed it to be equivalent to Heegner's. Unfortunately, Heegner had died two years earlier.