Green · 1828
George Green at the Nottingham windmill
In the spring of 1828 the Nottingham miller George Green, thirty-four years old, with only one year of formal school under his belt and twenty-five years of running the family windmill at Sneinton outside the city behind him, published at his own expense a pamphlet of seventy-two pages titled *An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism*. The essay introduced what is now called Green's Theorem, the formal mathematical relationship between an integral over a closed region and an integral around its boundary, and Green's Functions, the technique for solving inhomogeneous differential equations from boundary conditions, that became the foundational mathematical tools of nineteenth-century mathematical physics. The pamphlet had been written in the upper room of the windmill on the Sneinton ridge above Nottingham, on stolen evenings from the day's grinding work. Fifty-one subscribers paid seven and sixpence each to put it into print. They were the only readers. Green's name was unknown to the English mathematical establishment of the period and remained unknown until William Thomson (the future Lord Kelvin), then a twenty-one-year-old Cambridge undergraduate, came across a second-hand copy in a Cambridge bookshop in 1845, four years after Green's death, recognised what the country had missed, and put the essay back into the literature.
It is mid-afternoon on an unrecorded day in March 1828, in the upper-storey small writing-room of the Green family windmill at the Sneinton ridge half a mile east of the Nottingham city wall, in the spring light through the dormer-window above the millstone-floor. He is thirty-four years old. He is George Green, born in the Sneinton Road bakery on 14 July 1793, son of the baker (and later miller) George Green the elder and Sarah Butler. He had one year of formal school at the Robert Goodacre Academy on Upper Parliament Street, Nottingham (1801-02), aged eight to nine. He has run the windmill since his father's death in 1829-30 (the year date conflict in the standard biographical sources reflects an uncertain Green-family-record dating that the post-1976 Mary Cannell biography substantially resolved on a 1829 reading).
On the desk in front of him is the finished manuscript of the essay he has been working on through the spring evenings of the past four years. The manuscript is sixty-two folio pages in his own hand, the differential-equation notation laid out in the Leibniz form he has taken from the French analytical-mathematical tradition (Lagrange, Laplace, Poisson) rather than the Newtonian dot-notation that the Cambridge English mathematical establishment was still using through the post-1812 Analytical Society reforms of the period. He has paid the Nottingham printer J. S. Hicklin & Co. of Carlton Street to set the essay at his own expense across the spring 1828 printing-run.
He thinks: the essay is twenty years of teaching myself the mathematics on the evenings of the millwright's day. The essay is what I have done with the thirty-four years.
He thinks: the English mathematicians at Cambridge and Edinburgh will not read it. They do not know my name. They will not know my name because I have no university degree, no academic post, no small mathematical-society membership, no small ecclesiastical-or-academic patron. The essay will sell its fifty-one subscriber copies and be put in the Bromley House Library at Nottingham and at the Bromley House Reading Room at Sneinton and the Bromley House library copy will be unread for forty years.
He thinks: the theorem I have put in Chapter Three connects the integral over a region to the integral around its boundary. The small theorem is, as far as I have been able to read, new. The small functions I have put in Chapter Five solve the inhomogeneous Laplace equation from the boundary conditions. The small functions are, as far as I have been able to read, also new. The small essay is the proof of the theorem and the functions and the applications to electricity and magnetism. The small essay is, by my private working judgement, a small piece of mathematics that ought to be read.
He takes the small printed pamphlet down from the Hicklin printing-house at Carlton Street the following week, distributes the fifty-one subscriber copies to the Nottingham subscribers and to a London-and-Cambridge mathematical-establishment list at the five Cambridge fellows of Sir Edward Bromhead's small Lincolnshire-mathematical-circle, and resumes the Sneinton-windmill working life. He never receives a reply from any of the London-or-Cambridge mathematical recipients of the pamphlet. He marries Jane Smith of Nottingham in 1824 and has seven children with her across the Sneinton-windmill-and-Nottingham-property period. He enters Caius College Cambridge in 1833 at forty (the Sir Edward Bromhead recommendation having made the Cambridge admission possible), takes the Cambridge mathematical-tripos Fourth-Wrangler ranking in 1837 at forty-four, is elected to a Caius fellowship in 1839 at forty-six, contracts a respiratory illness on the Cambridge-Fenland working winter of 1840-41, returns home to Nottingham, and dies at the Sneinton windmill on 31 May 1841, forty-seven years old.
William Thomson, the twenty-one-year-old Cambridge undergraduate of Peterhouse, comes across a second-hand copy of the 1828 essay in a Cambridge bookshop in January 1845. He reads it through the Cambridge term, recognises what the mathematical establishment has missed, and across the post-1845 period puts the essay into the Cambridge-and-Edinburgh mathematical-physics-research literature. Green's Theorem and Green's Functions become, by 1860, the standard small reference-techniques of the Maxwell-Stokes-Kelvin Victorian mathematical-physics generation. The small Sneinton windmill was restored by the Nottingham City Council in 1986 and is now the Green's Windmill and Science Centre, open continuously since 1986 as the foundational small commemorative-museum of the self-taught-Nottingham-miller mathematical achievement.