Gunpowder and Geometry is a well-written biography of Charles Hutton (1737–1823), mathematician, educator and author, by Benjamin Wardhaugh of the University of Oxford. Though perhaps chiefly known to historians of eighteenth-century science for his involvement in the Royal Society's ‘dissensions’ of the 1780s, Wardhaugh describes Hutton as a skilled networker who transitioned from ‘pit boy’ to ‘mathematician and scientific rebel’. Wardhaugh's biography situates Hutton within a social and cultural milieu in which the perception of mathematics, and ways to obtain social position and fame, were in flux. This book offers both the general reader and the historian of science and mathematics a valuable picture of eighteenth-century social and scientific mores.

Chapter 1 considers Hutton's early life and formative experiences, beginning in the coal pits of Newcastle in 1755, and ending with the promise of his taking over a schoolroom the following year. Even at this early stage in his career, Wardhaugh reveals how Hutton's skill at fostering connections was vital in shaping this transition. Chapters 2 and 3 deal respectively with Hutton's career as a teacher in Newcastle and his early experiences as an author, who self-fashioned his mathematical persona by engaging wealthy patrons, writing for popular mathematical periodicals and publishing textbooks. In Chapter 4, Wardhaugh presents Hutton's successful appointment as professor of mathematics at the Royal Military Academy in Woolwich as a pivotal moment in his career, a role he obtained through patronage and mathematical ability.

In Chapter 5, Wardhaugh presents the peak of Hutton's early career and success, as a respected professor with impressive networks and patrons in London society, including the Astronomer Royal, Nevil Maskelyne. Wardhaugh describes Hutton's natural-philosophical investigations, including his experiments with the ballistic pendulum at Woolwich, which won him the Copley Medal and special favour with the president of the Royal Society, John Pringle. This triumph was vital to Hutton's processes of self-fashioning as a natural philosopher.

In Chapter 6, Wardhaugh provides a nuanced account of the Royal Society's ‘dissensions’, a series of events which saw a sharp reversal of fortunes for Hutton. Wardhaugh explores factors behind Banks's dislike of Hutton and his decision to exclude him from the society. These included Hutton's relatively humble origins as well as his connections to Pringle's circle. Banks was also troubled by Hutton's radical connections and Protestant Nonconformism. By focusing on Hutton's identity in relation to Banks's agenda and ambitions for the society, this biography offers a more complex account of the ‘dissensions’.

In Chapters 7 to 9, Wardhaugh presents Hutton's gradual recovery of status. Hutton continued to publish, though he avoided the Royal Society's Philosophical Transactions for his scientific papers. He strengthened his status in novel ways, including by claiming famous ancestry, and a supposed connection to Isaac Newton. He continued to play a key role in shaping military education at the academy, and was presented to the king on the back of his successful Elements of Conic Sections, published in 1787. The image of Hutton that Wardhaugh presents in the 1790s is one of a gentleman recovered, who spent his time producing prestigious monuments to mathematical culture, including his ambitious Mathematical and Philosophical Dictionary.

In Chapters 10 to 12, Wardhaugh describes Hutton's retirement, and his continued efforts to secure his legacy. Having retired from his role at the Military Academy in 1807, Hutton moved to Bedford Row, and turned his efforts to providing patronage for others, some of whom, including Olinthus Gregory, worked to support and strengthen his legacy. This period in Hutton's life was not without controversy, and in his retirement Hutton saw his teaching at the academy called into question, and his approach to mathematics undermined. The character of mathematics was changing in this period, with increasingly elite academic mathematics prevailing in Europe, in contrast to the practical mathematics championed by Hutton in Britain. Despite a series of personal and professional difficulties, Wardhaugh presents Hutton's final years as relatively peaceful. When Banks died in 1820, Hutton was able to rebuild his ties with the Royal Society, which he did under the new president, Humphry Davy. With Banks gone, Hutton's supporters openly commemorated him in his own lifetime. By his death in 1823, Hutton was a celebrated individual.

Wardhaugh's biography offers a rich social history of a variety of Georgian spaces and occupations, from the dust of the coalface in Newcastle to the clamour and stench of the Military Academy at Woolwich. Wardhaugh situates Hutton's major intellectual works within these social worlds, providing a brief introduction to their contents for the general reader, and a strong sense of their relevance within Hutton's efforts to self-fashion his persona. A key strength is Wardhaugh's representation of Hutton not as a lone great man, but as an individual shaped by his social context. Wardhaugh draws attention to the significant role of Hutton's household, a ‘bustling family workshop’ (p. 79), and his second wife, Margaret Ord, who assisted with his mathematical publications, and his daughter Isabella, who served as his trusted amanuensis. Though the names of these women never featured in published works, Wardhaugh stresses the importance of considering Hutton's publications as featuring both male and female voices.

Some themes within Hutton's life might have been explored in greater detail, though it is perhaps owing to the lack of surviving personal manuscripts, such as Hutton's diary, that these have not been explored further. Hutton's interests in both Methodism and Unitarianism are mentioned only briefly, though Wardhaugh conjectures that these may have played a role in shaping his character. The brief notes provided at the end of the book do leave the reader longing for more detail, though an extensive bibliography, including a list of Hutton's manuscripts and published works, can be freely accessed on Wardhaugh's website.

Gunpowder and Geometry is an engaging book, and one that highlights the changing perceptions of mathematics, patronage and social position within a period of immense cultural and intellectual change. It is an insightful biography for anyone with an interest in the Georgian period, and in the history of science and mathematics.