LITMIR.BIZ

      The tree of mathematical knowledge.

      It all seems premature, precocious, absurdly risky. Hutton was just four years out of the coal pits; he was quite unknown, his fees were twice those asked by his rivals and his list of subjects promised an impossible range of expertise, including any number of practical subjects in which the twenty-two-year-old had no practical experience. He was aiming very high, hoping to become a different class of teacher: a specialist in mathematical training, no longer bound to the drudgery of teaching the very young to read and write. Friends advised him to promise less, and ask for less money. He didn’t listen, and the result was a struggle, the high prices keeping some away during years when Hutton’s family was growing.

      But there was real demand for this sort of thing: specialist mathematics teaching for boys up to fourteen or even older. In a period when a quarter of the country was unable to read, northern parents had a reputation for being keen to educate their children, for sending able, well-educated boys to London to work in counting houses and trade. Trade was increasing during the eighteenth century, and the demand for those boys multiplied; they became bookkeepers, accountants, land stewards, surveyors, navigators (think of James Cook, who would sail round the world on a Whitby coal-ship; while he was still in the coal trade he learned all the mathematics he could at Newcastle schools between voyages). Schools proliferated, and Newcastle became England’s best-educated city after London: four charity schools and the prestigious Trinity House School were founded in the first half of the century, and its well-regarded grammar school flourished. A few landowners maintained schoolmasters for the benefit of their employees, and it wasn’t unknown for the employees themselves to club together to fund a school, as they did at the Newcastle ironworks. Hutton had picked a growing market.

      Teaching mathematics at this level meant teaching to add, subtract, multiply and divide, to find square roots and cube roots (Hutton had his own special method for this). It meant fractions both natural and decimal: how to read and write them and how to do arithmetic with them. It meant handling England’s enormously complicated systems of units: grains, scruples and drams for drugs; yards, poles and furlongs for length; firkins, kilderkins and barrels for beer; and many, many more. It meant converting between currencies, which brought similar difficulties: how many Flemish guilders will I buy with one hundred and seventy-three pounds, fourteen shillings and twopence, if one pound is worth thirty-five stuivers three and a half penning?

      Above all, it meant reasoning with proportions: or rather, for the less able who were the majority, applying a series of rote-learned rules that would tell you the right answer in certain situations to do with linked ratios. If eight yards of cloth cost twenty-four shillings, what will ninety-six yards cost? In how many days will eight men finish a piece of work that five could do in twenty-four days? In a school career a child might do hundreds, if not thousands of these problems.

      It was dry stuff; but Hutton made it work, and over time the numbers at his school grew. By 1764 he moved downhill to the more fashionable, though somewhat unfortunately named ‘Back-Row’, where he, his school and his family shared premises with a dancing master named Stewart. Hutton got involved with selling tickets for the man’s public balls. Stewart’s prices (half a guinea at entrance and a guinea a quarter for six days’ teaching each week) would have limited his students to the well-to-do, but still the presence of a dance school in the house can only have been disruptive, both to Hutton’s own teaching and to his domestic life.

      We have few glimpses of that life. In one of his books Hutton, searching for a memorable image, remarked that a triangular prism ‘is something like a hat box’. Indeed it is: but hats in hat boxes were not a picture that would have sprung to Hutton’s mind a few years before. An admirer remarked much later that Hutton ‘was soon conscious of his great abilities, and claimed that rank in society to which they entitled him’. That was a polite gloss on the fact that material success gave him the means to act, dress, and for all practical purposes be middle-class. He was now indisputably the butterfly, not the caterpillar.

      Still, he could not altogether avoid criticism. Some remembered ‘a very modest, shy man’ at this period; but we also hear of him knocking a boy down in the street while he was surveying Newcastle. In this or another incident someone taxed him with being only a pit boy, and Hutton retorted that if he – the critic – had been a pit boy he would be there still. Memories of the cap and gown lingered; two different witnesses, seventy years later, independently recalled the red cap.

      There were three more children: Isabella, Camilla and Eleanor (known to her family as Ellen). They were baptised in the nonconformist chapel at Hanover Square.

      At the time of writing Hanover Square

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