George Green (1793–1841) is one of the great underdog stories in mathematics. He was a miller's son from Nottingham who worked in the family windmill, had only about one year of formal schooling as a child, and taught himself advanced mathematics from library books in his spare time. At 35, entirely self-taught, he published a booklet that quietly changed physics forever.
In 1828 Green privately printed An Essay on the Mathematical Analysis of
Electricity and Magnetism and sold it to just 51 subscribers, most of whom
probably couldn't read it. Hidden inside were the ideas we now call the
Green's function and the theorem that ties a loop integral around a boundary
to a double integral over the region inside it —
He also coined the word potential for the quantity whose gradient is a force field — a word physicists still use every single day.
Green's essay was so obscure that it was nearly lost. Only after a wealthy patron encouraged him did he finally go to Cambridge as an undergraduate — at the age of 40, older than some of his professors. He died just a few years later, still largely unknown. The rescue came from a young William Thomson (later Lord Kelvin), who stumbled on a copy, realised its brilliance, and championed it across Europe. Today "Green's function" is a phrase every physicist knows, and his restored windmill still stands in Nottingham as a museum.