Ultimately it all rested on coal; you could hardly forget that, if you lived anywhere near either the river or the coalfields, and Charles Hutton was never likely to forget it either. The sale of coal was so lucrative, contemporaries reckoned, that despite all the goods it imported Newcastle made a net gain every year, and had more money per head than anywhere else in the kingdom.
Mathematically, too, Newcastle and its environs were a rich world. There was William Emerson, a nationally famous mathematician who lived in nearby Hurworth. His studied eccentricity of manner and dress (home-made linen, big floppy hats and shapeless old jackets) earned him a local reputation as a wizard. Hutton corresponded with him and they became acquainted, though unsociable Emerson and ambitious Hutton did not really hit it off. There was John Fryer, who assisted Hutton with his surveying work; he was also Hutton’s teaching assistant at Westgate Street.
The school had its own separate entrance. Advertisements, briefer and more sober now, stated that there ‘Youth are qualified for the Army, Navy, Counting-house’; they could also be ‘compleatly instructed in the Theory and Practice of Land Surveying, with the use of the necessary Instruments’. Newcastle Grammar School took to sending its students to Hutton for specialist mathematics teaching. Not an altogether unusual arrangement – everyone knew that private academies did mathematics and science better than the grammar schools – but a gratifying endorsement of Hutton and his work.
His new-found middle-class status also meant that Hutton could work as a private tutor to the local gentry. As one biographer put it, Hutton’s ‘manners, as well as his talents’, now ‘rendered him acceptable’ in this role. Robert Shaftoe was one such patron, his home at Benwell Hall one of the more impressive local mansions (the Bobby Shaftoe of the popular song was a relative). Hutton’s tuition of his children impressed Shaftoe so much that he took to attending the lessons himself, revising the mathematics he had perhaps learnt at college. And he gave the young man the run of his impressive library. Newcastle had at least a couple of subscription libraries, and no shortage of booksellers, but access to a large, private book collection was a boon for Hutton, who remorselessly continued to improve himself. Over the years he added a reading knowledge of French, Italian and German to his early-acquired Latin. By 1772 he had read enough on geography to offer public lectures in the subject (to ‘gentlemen and ladies’) at half a guinea for the course. How many takers he found is not recorded.
Indeed, Hutton’s school was becoming something of a centre for learning. During the Christmas vacation of 1766–7 Hutton taught mathematics to other schoolteachers there, and at about the same time external lecturers began to use it as a venue. Caleb Rotherham covered geography, astronomy and other scientific subjects; likewise the popular James Ferguson. Ferguson was a house guest, and gave private performances to Hutton’s friends and family in the evenings, though Hutton was shocked when he discovered how little geometry the man knew. Hutton’s school was in a way a forerunner for the Literary and Philosophical Society that would be founded in Newcastle thirty years later, its first paid lecturer the same Caleb Rotherham.
His arrangement with Newcastle Grammar School brought Hutton himself two of his most celebrated pupils, and certainly his most colourful. John Scott was the son of a coal merchant; Bessie Surtees a wealthy banker’s daughter. Both went to Hutton for their mathematics lessons, but it was presumably not under his eye that their youthful romance blossomed. Scott went up to Cambridge in 1772, but the calls of love proved stronger and in November he came back and eloped (ladder, first-floor window) with Bessie. The scandal – or the romantic adventure, depending on your perspective – ran and ran through the nineteenth century, and Bessie Surtees merchandise is still to be had in her Newcastle home town.
A country clergyman, anywhere in England, any time in the eighteenth century. At his desk, in his study. April. Open windows; sunlit air. An open manuscript of mathematical work. Solutions to puzzles from magazines, copied fair.
He copies this year’s set of solutions fairer still, adds a couple of suggestions for problems the magazine could ask this year. Mends his pen and adds a covering letter. Dear Sir. I enclose my mite for this year’s Diary, hoping you will find it worthy of notice. Your humble servant. Dusts the sheets, folds, seals.
A scene repeated many times – many hundreds of times – across Britain every year of the Georgian period. A few months later, in about October, the annual magazines went on sale: The Ladies’ Diary, The Gentleman’s Diary, The Mathematical Repository, and more. Some readers had the thrill of seeing their names, their mathematical work in print – a few won small prizes. Others looked in vain for their names, their work in the magazine, and concluded, humiliated, that their solutions had been wrong.
If Hutton had done no more than succeed as a provincial schoolteacher, his story would be a striking but not a very unusual one. The majority of mathematics teachers in Georgian Britain, indeed, were working-class lads who had made good: self-made men who had themselves attended private academies or bettered themselves by private reading. There were schools right across the United Kingdom that bore witness to their success in attracting students, providing them with high-level instruction and sending them out to work in the burgeoning literate and numerate trades.
Hutton was not satisfied with this. He wanted the wider recognition and the promise of greater rewards that publication would bring. And he approached publication through that remarkable Georgian institution, the mathematical periodical.
Now that they have disappeared, it’s hard even to imagine them, but in their heyday there were a dozen or so monthly or annual magazines whose purpose, or one of whose purposes, was to print mathematical problems and readers’ solutions to them. Construct a triangle given its base, one adjacent angle, and the line bisecting the opposite angle. Find a fraction with the property that, if you subtract its reciprocal, you get a square number. How many ways can you make fifteen from a pack of cards? This was not Sudoku, and it was not elementary arithmetic. The problems could be hard, using