George Green at the Nottingham windmill

Some discoveries are made by men whose names the institutions already know, and the institutions absorb them without surprise. Others are made in rooms the institutions cannot see, by men with no degree, no chair, no society, no patron; and when such a man writes down a piece of mathematics that ought to be read, the work waits. It waits not for its truth to ripen, which is already done, but for a stranger to walk into a bookshop years later and recognise it.

THE MILLER ON THE SNEINTON RIDGE

He was born on the 14th of July 1793 in the bakery on Sneinton Road, son of George Green the elder, baker turned miller, and Sarah Butler. One year of schooling at Robert Goodacre's Academy on Upper Parliament Street, between his eighth and ninth years, was the whole of his formal instruction. The rest he taught himself, by candle and by lamp, from whatever volumes the Bromley House Subscription Library on Angel Row would lend a tradesman's son. The library kept Lagrange, Laplace, Poisson, the French analysts who were rewriting the calculus in a notation the English universities had spent a century refusing. He read them in their own marks, the Leibniz d's and integral signs, not the Newtonian dots, and learned to think in their language.

His father built the brick tower-mill on the Sneinton ridge in 1807, half a mile east of the Nottingham wall, four storeys with a small writing-room under the cap. By twelve the boy was working the sails. By thirty-four he had ground corn for the town for the better part of twenty years, kept the books, paid the journeymen, married Jane Smith of Nottingham in 1824, and fathered the first of the seven children she would bear him. None of this is the story. The story is what he did with the evenings.

THE UPPER ROOM, SPRING 1828

The room above the millstone floor is reached by a ladder. A dormer takes the western light. There is a small deal table, an inkwell, a sheaf of folio paper, and a shelf with the borrowed Frenchmen on it. The mill turns in the wind outside, and the timbers transmit a low, continuous groan into the boards under his feet; he no longer hears it except as the silence sounds when the sails are reefed. He has been four years at the manuscript. The grinding stops at dusk, the apprentices go down the lane, and he climbs.

On the table this March afternoon lies the finished hand, sixty-two folio pages, fair-copied. He has set the title himself: An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. In Chapter Three he has written down a relation between an integral taken over a closed region and an integral taken around its boundary. He cannot find it in any book on his shelf, nor in any borrowed from Bromley House. In Chapter Five he has built a class of functions which solve the inhomogeneous Laplace equation by working from the conditions at the edge inward. These he cannot find either. The applications, to electricity and to magnetism, follow.

THE SECOND BEFORE THE PRINTER

He sits with the manuscript at his elbow and a sheet of accounts on the other side. Hicklin of Carlton Street will set the sheets for a sum he has calculated to the shilling. Fifty-one names have subscribed at seven and sixpence each, gathered through the Nottingham Subscription Library and through Mr Bromley House's acquaintance, and the seven-and-sixpences will not cover the printing; the balance is his own. The miller's ledger and the mathematician's ledger are the same ledger, kept in the same hand. He has weighed it many evenings. The essay is twenty years of teaching himself on stolen hours, and the question is whether to put those hours into print, and own them, or to keep them folded in the drawer where no one will ever read them and no one will ever know they failed. There is also a third possibility, which is that the gentlemen at Cambridge and at the Royal Society in London will read the pamphlet and write back, and this possibility, by his private judgement, is small. He knows what he is in their eyes: a Nottingham tradesman, no degree, no Latin past what he taught himself, no patron yet, no introducer. He turns the manuscript over once on the table. The work is, by his own working judgement, a small piece of mathematics that ought to be read. That phrase, ought to be read, decides it. He inks the contract with Hicklin in the week following.

THE PAMPHLET GOES OUT

Hicklin sets the type through the spring printing-run and binds the seventy-two pages in plain wrappers. Green carries the copies down from Carlton Street himself and walks them to the subscribers' doors in Nottingham, leaving the rest with the booksellers and posting a small parcel to the address Sir Edward Bromhead has given him in Lincolnshire, for forwarding to the Cambridge fellows of Bromhead's small mathematical acquaintance. He waits through the summer. No letter comes from London. No letter comes from Cambridge. The fifty-one subscribers have his pamphlet on their shelves. The Bromley House copy is shelved at Angel Row, and a generation will pass over it. He climbs the ladder again the next evening and turns to a paper on the equilibrium of fluids.

THE WINDMILL AFTER

Sir Edward Bromhead, who has read the essay and seen what the Cambridge fellows did not, presses him for years to come up to Caius. In 1833, at forty, he goes. He is the oldest undergraduate in the college. He takes the Tripos in 1837 and is placed Fourth Wrangler. He is elected to a fellowship at Caius in 1839. The Fenland winter of 1840 is hard on a man who has spent his life in the dry air of a windmill cap; he contracts a chest illness in the cold rooms of the college, comes home to Sneinton through the spring, and dies in the upper room on the 31st of May 1841, forty-seven years old. Jane and the seven children remain at the mill.

THE BOOKSHOP IN CAMBRIDGE

Four years later, in January 1845, a Peterhouse undergraduate of twenty-one named William Thomson is told by his coach William Hopkins of an obscure Nottingham pamphlet that he might find useful. Thomson hunts a copy through the Cambridge booksellers and at last carries one home. He reads it through the Lent term. He recognises at once that the theorem on the boundary and the region, and the functions built from the boundary inward, are not curiosities but the instruments the new mathematical physics has been reaching for. He carries the pamphlet to Paris that summer, shows it to Liouville and to Sturm, has it reprinted in Crelle's Journal in three parts between 1850 and 1854, and writes it into the foundations of his own work and Stokes's and, through them, Maxwell's. By 1860 the theorem is in every lecture room in Europe under the name of a miller who never set foot in a lecture room.

THE RETURN

The opportunity that comes to an unknown man in a small upper room comes without ceremony and without witness. It can be taken or refused in privacy, and the refusal will leave no record, because there was no record to begin with. What is decided in such a room is whether a thing is to exist in the world at all. Green decided, and paid the printer, and the pamphlet existed, and waited; and because it existed, it could be found. The brick tower on the Sneinton ridge was derelict by the middle of the next century, restored by the Nottingham City Council in 1986, and stands today as Green's Windmill and Science Centre, the sails turning again above the city, grinding flour on weekdays as it did in 1828, with the small dormered writing-room kept under the cap.