Drawing of Charles Hutton

Mathematician Charles Hutton.Credit: Sheila Terry/SPL

Gunpowder and Geometry: The Life of Charles Hutton, Pit Boy, Mathematician and Scientific Rebel Benjamin Wardhaugh William Collins (2019)

Until the 1990s, eighteenth-century science received comparatively little attention. Historians of British science would leap from what they called the scientific revolution — culminating in the foundation of the Royal Society and Isaac Newton’s achievements in the seventeenth century — to a ‘second scientific revolution’ in the early nineteenth. This saw the founding of a host of specialist societies (astronomical, geological, geographical, zoological). That narrative suggests that, by the eighteenth century, the Royal Society was dominated by trivial pursuits and aristocratic dilettantes rather than disciplinary experts.

Although that has since been revised, the mathematician Charles Hutton (1737–1823) would certainly have agreed, as his role in the 1780s ‘Dissensions’ at the Royal Society attests. Hutton saw himself as continuing Newton’s legacy, applying mathematics to natural philosophy and to real-world problems, such as navigation, cartography and engineering. In Gunpowder and Geometry, historian of mathematics Benjamin Wardhaugh gives us the man and his method.

As Wardhaugh shows, during the Dissensions, Hutton was dismissed from his post as the society’s foreign secretary. That provoked those claiming to be the real, scientific members to attack the autocratic presidency of botanist Joseph Banks, and the “train of feeble Amateurs” (as they put it) surrounding him. The rebels included mathematicians and astronomers, and a majority of active members. Banks, however, rallied his own supporters to pack the meetings and thereby defeat a series of votes aimed at limiting his power. Hutton did not return to the society until after Banks’s death, in 1820.

Whereas Banks saw mathematics as little more than a tool “with which other sciences are hewd into form”, Hutton championed its significance. And, as Wardhaugh puts it, Hutton “carefully, deliberately, made himself the leading voice speaking for mathematics in English”. Hutton’s world was chiefly the classroom and print rather than the observatory or field. He was remarkably prolific, producing mathematical tables, textbooks, dictionaries, compendia and periodicals. These works, which ranged from elementary arithmetic to the mathematics of bridge building, leisure puzzles and historical discourses, cemented his reputation. It also gave him readers and networks, both before his election to the Royal Society and after he was excluded.

He overcame considerable obstacles, as Wardhaugh reveals. Newcastle-born, Hutton was a “pit boy turned professor” who avoided life at the coalface, eventually becoming a figure worthy of a bust (copies were produced to allow at-home “veneration” by admirers). His success began at school, where his intellectual talents were recognized. He was an unproductive coal hewer, but convinced his schoolmaster that he could command a classroom.

In this, Hutton was fortunate. Schooling in general, and mathematical education in particular, were in demand. By the age of 22, he was advertising an ambitious curriculum to cater to a range of pupils looking for specialist training in Newcastle. Wardhaugh shows why, and what sort of, mathematics was important in Georgian Britain. An education emphasizing basic principles, theory and applications in architecture, navigation, trade and engineering was promoted as both useful and a means of refining minds.

Hutton’s ability as mathematician and teacher landed him one of the few available state-funded scientific positions. A public examination, private recommendations and a remorseless campaign of self-improvement led to a professorship at the Royal Military Academy at Woolwich, near London. He taught there for more than 30 years. He also became a neighbour, collaborator and friend of the astronomer royal, Nevil Maskelyne.

Through Maskelyne, Hutton contributed to key projects, including efforts to improve navigation by means of astronomy (H. Lewis-Jones Nature 564, 340–342; 2018). To measure Earth’s density, Maskelyne made observations of the gravitational pull of a mountain’s mass; his assistant surveyed the site; and Hutton undertook arduous calculations. Yet Hutton’s most original project was an experimental and mathematical investigation of ballistics, including the weight and shape of gun and projectile, the quality of gunpowder and the effects of air pressure. One of his papers on this won the Royal Society’s Copley Medal in 1778.

Wardhaugh draws on sources from local, social, religious and military histories to histories of science and mathematics. Few of Hutton’s personal papers have survived, so we have lost much of his voice. That does raise questions about the choice of writing a full biography, especially because Wardhaugh is commendably cautious in his claims for Hutton’s significance. This is no ‘the man who changed X’ romp, but an informed, referenced and contextualized history. It might have made sense to place Hutton in a group biography, or in a broader treatment of Georgian mathematical culture, in the style of Jenny Uglow’s 2002 book Lunar Men. Although revealing, the life-trajectory approach leaves little space to explore, say, key institutions such as the Spitalfields Mathematical Society or Royal Mathematical School.

The approach does, however, ensure that the women in Hutton’s life are given due attention. As was typical, the family business — mathematics, computation, transcription, editing — was a cottage industry in which wife, son and daughters were involved, if officially obscured. We follow, as far as possible, their lives and the dramas of bereavement, including the loss of Hutton’s favourite daughter, Charlotte, marital breakdown (Hutton left his first wife, Isabella, and lived with Margaret Ord for many years before they married) and a surprising number of elopements.

There are tantalizing clues that might have brought the domestic element further to life. A portrait of his daughters Isabella and Camilla is included but not explored; a poem by Margaret, attacking Banks and lauding mathematician Samuel Horsley, Hutton’s thundering defender at the Royal Society, is reproduced but not interpreted.

Nevertheless, Gunpowder and Geometry is engaging and skilfully handled. Hutton’s rise reveals how technical and intellectual ability, with luck and opportunity, could propel a few individuals up the social ladder. In Georgian Britain, mathematics was appreciated, not only for the utility that Hutton championed but also for its rich literary culture. Here, especially because of The Ladies’ Diary, a hugely successful miscellany that he edited for more than 40 years, Hutton reigned supreme.