George Green(1793–1841)

George Green was born at Sneinton, then a village on the eastern edge of Nottingham, on the fourteenth of July 1793, the only son of George Green the elder, a master baker who in 1807 built the brick-tower windmill on Belvoir Hill that still stands today as Green's Windmill. The boy was sent for a year and a half between the ages of eight and nine to Robert Goodacre's Academy in Upper Parliament Street, the best school in Nottingham; that was the whole of his formal education before Cambridge. He worked from boyhood in the bakery and from his early teens in the mill, and what mathematics he learned beyond the academy he taught himself from books borrowed from the Bromley House Subscription Library, where he was admitted as a member in 1823 at the age of thirty.

The intellectual world of Sneinton in the 1820s was small, but Bromley House had on its shelves the leading French mathematical literature of the day, the work of Lagrange, Laplace, Lacroix, Poisson and Cauchy. From this self-taught reading Green produced in March 1828, working in a small room at the top of the mill, a treatise titled An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. He published it by private subscription in Nottingham, printed by T. Wheelhouse of Bridlesmith Gate, with fifty-one subscribers found by his patron the local squire Sir Edward Bromhead. He was thirty-five years old. The press run was small and the work effectively unknown to the wider scientific community for almost twenty years.

The Essay was, nevertheless, one of the most original pieces of mathematics produced in nineteenth-century England. It introduced the concept of what Green called the potential function, the term he gave to the scalar function whose gradient is the force; it stated and proved the integral identity now universally called Green's theorem, relating an integral over a region to an integral over its boundary; and it set out the integral representation now called the Green's function, the response of a linear system to a point source, from which the response to any distribution of sources can be built by superposition. The Green's function is one of the central computational devices of every mathematical physics that came after, from electrostatics to acoustics to quantum field theory.

Bromhead, who recognised what his miller had done, persuaded Green to read for a degree at Cambridge. He went up to Gonville and Caius College in October 1833 at the age of forty, took his Bachelor of Arts as Fourth Wrangler in the mathematical tripos of January 1837, and was elected a fellow of Caius in October 1839. He produced in the four years between his degree and his death six further mathematical papers, on the reflection and refraction of light, on the equilibrium of fluids, on wave motion in canals, and on the propagation of sound in tubes; each is a permanent contribution to its field.

He fell ill in the winter of 1840 and went home to Sneinton, where he died on the thirty-first of May 1841, in his forty-eighth year, and was buried in the churchyard of St Stephen at Sneinton, fifty yards from the mill. The Essay was rediscovered in 1845 by William Thomson, the future Lord Kelvin, then a twenty-one-year-old Cambridge undergraduate who came upon a copy in the library of his coach William Hopkins, and reissued it through the Journal für die reine und angewandte Mathematik. From that moment Green's work entered the mainstream of European mathematical physics, where it has remained the daily working apparatus of the field. The Green name in modern science carries the weight of an essay written above a Nottingham windmill by a self-taught miller, and through which the next two centuries of physical theory have flowed.