Dr Benjamin Wardhaugh
My research and publications centre on the history of numeracy and mathematics, and the ways mathematics influences and is a part of cultures. I have worked mainly on topics in early modern Britain, including mathematical music theory in that period and a biographical study of the mathematician, natural philosopher and educator Charles Hutton (1737–1823). My current research project looks at the reception of the Euclidean Elements of Geometry in sixteenth and seventeenth–century Britain. I also have a special interest in practices of mathematical reading and the evidence for them including annotations and marginalia.
I have published a number of more wideranging books, including a textbook for students interested in reading historical mathematics and an anthology of five centuries of popular mathematical writing; I am one of the two general editors of the forthcoming Bloomsbury Cultural History of Mathematics.
I have taught in both the Mathematical Institute and the History Faculty, and am always happy to hear from graduate students hoping to work in my areas of interest.
 History of mathematics
 Early modern British history
 History of education
I have wideranging interests in the history of mathematics and its applications, the history of mathematics education, and the history of numeracy and the mathematics of everyday life. With an intellectual background in mathematics (BA, Cambridge, 2000) and music (MMus, GSMD, 2002) I have always been keen to develop ideas and research projects that cross disciplinary boundaries and to begin and sustain conversations between scholars from different fields.
For my doctoral project (Oxford, 2006) I looked at mathematical theories of music in early modern Britain: theories of pitch and tuning and their relationship to natural philosophical ideas about sound and hearing in the same period. Since completing that project I have published several critical editions of sources in the same field, including writings by René Descartes and Isaac Newton that bear on the nature of sound and its mathematical description. I maintain an interest in this area, and have participated in research projects and given papers on various topics in the early modern study of sound and music.
My postdoctoral work, done at All Souls College, Oxford, focussed on popular and everyday mathematics in Georgian Britain. I explored sources including almanacs, textbooks, school curricula and newsprint for evidence of how mathematical skills were acquired and disseminated, and how mathematics was used and viewed by people whose main fields of interest and expertise lay elsewhere. This research led to a number of publications including my book Poor Robin’s Prophecies (OUP, 2012). The longterm processes of change in this area – how populations acquire or lose numerate skills – remains one of my main interests, and has motivated my subsequent work. Smaller ‘spinoff’ projects have included a study of the mathematics of the natural historian and ‘virtuoso’ Francis Willoughby and an ongoing investigation of marginalia and annotations in early modern mathematical books. The latter has produced two papers on the consumption of mathematical books and the nature(s) of mathematical reading in the period.
More recently I have received AHRC funding for two separate projects. First, a biographical study of the mathematician and educator Charles Hutton (1737–1823). A celebrity in his day, Hutton is now mainly remembered as the enemy of Sir Joseph Banks, whose dismissal from a secretarial role at the Royal Society provoked a row that nearly unseated Banks as President of the Society. But he was also a mathematical editor, compiler, author and patron of exceptional range, as well as a talented experimental natural philosopher and – for perhaps thirty years – the leading voice speaking for mathematics in English. My biography of Hutton will be published in 2017.
Finally and currently, I am the Principal Investigator on the AHRCfunded project ‘Reading Euclid in Early Modern Britain’. Together with Philip Beeley and Yelda Nasifoglu I am investigating the dissemination of the Euclidean Elements of geometry in Britain from the early sixteenth to the late seventeenth century. The Elements was a culturally pervasive text, studied at grammar schools and universities, drawn on by practical manuals and alluded to by literary authors. Ours will be the first study to consider in detail the history of its early modern publication, dissemination and use, using both printed and manuscript evidence from around Britain.
Poor Robin’s Prophecies: A curious almanac, and the everyday mathematics of Georgian Britain (OUP, 2012)
Author, astrologer, journalist, satirist, and ‘wellwiller to the mathematics’, Poor Robin of Saffron Walden was a fantastic, yet invented, figure of British popular culture from the Restoration to the end of the Georgian period. Poor Robin's Almanac first appeared in 1662, developing an enthusiastic following and long outliving its original creator to last until 1828.
Benjamin Wardhaugh tells the great story of Georgian popular mathematics – through Poor Robin’s remarkable life, from his humble beginnings as an almanacwriter through to bestselling stardom, controversy, and decline. Using the character, wit, and columns of Poor Robin, Wardhaugh explores the mathematics of ordinary people, from learning sums to using mathematics in weighing and measuring, in business, agriculture, mapmaking, and navigation.
This is a history of mathematics that is rarely thought about – creative, popular, and led by practical and social needs. It is centred on the ordinary people that used it. Their names remain littleknown; their solutions have vanished along with the situations that required them; but their energy and ideas – as captured by Poor Robin – create a wonderfully rich picture of what mathematics can be, and has been.
Endorsement
‘Bring back the almanac! Wardhaugh's fascinating account of Poor Robin's Almanac persuasively reveals the power of the almanac to give mathematics a human face.’ Marcus du Sautoy
Reviews
‘an inspired thesis …. While the likes of Poor Robin and his pamphlets may have disappeared long ago, mathematics remains a bedrock of our society. This wonderful book goes a long way in highlighting why.’ Jamie Condliffe, NewScientist
‘delightfully chatty and informative … [an] excellent, lively study.’ Patricia Fara, Literary Review
‘Excellent …. A book on the history of mathematics could have ended up dry and exclusive, yet Wardhaugh has written an engaging and entertaining book that never loses its audience.’ Steve Toase, Fortean Times

Gunpowder and Geometry: The Life of Charles Hutton, Pit Boy, Mathematician and Scientific Rebel
2019BookAugust, 1755. Newcastle, on the north bank of the Tyne.Mathematics 
Editorial
2018Journal articleBSHM Bulletin: Journal of the British Society for the History of Mathematics 
James Q. Davies; Ellen Lockhart (Editors). Sound Knowledge: Music and Science in London, 1789–1851. vi + 257 pp., figs., index. Chicago/London: University of Chicago Press, 2017. $55 (cloth).
2018OtherIsis 
The Correspondence of Charles Hutton
2018Book<p>This book contains complete transcriptions, with notes, of the 133 surviving letters of Charles Hutton (1737–1823). The letters span the period 1770–1823 and are drawn from nearly thirty different archives. Most have not been published before. Hutton was one of the most prominent British mathematicians of his generation. He played roles at the Royal Society, the Royal Military Academy, the Board of Longitude, the ‘philomath’ network, and elsewhere. He worked on the explosive force of gunpowder and the mean density of the earth, winning the Royal Society’s Copley Medal in 1778; he was also at the focus of a celebrated row at the Royal Society in 1784 over the place of mathematics there. He is of particular historical interest because of the variety of roles he played in British mathematics, the dexterity with which he navigated, exploited, and shaped personal and professional networks in mathematics and science, and the length and public profile of his career. Hutton corresponded nationally and internationally, and his correspondence illustrates the overlapping, intersection, and interaction of the different networks in which Hutton moved. It therefore provides new information about how Georgian mathematics was structured socially and how mathematical careers worked in that period. It provides a rare and valuable view of a mathematical culture that would substantially cease to exist when British mathematics embraced continental methods from the early nineteenth century onwards.</p> 
The Correspondence of Charles Hutton
2018Scholarly editionThis book contains all the letters that are known to survive from the correspondence of Charles Hutton (17371823).Mathematics 
Editorial
2018Journal articleBSHM Bulletin 
Sing Aloud Harmonious Spheres
2017Chapter 
John Birchensha: Writings on Music
2017Scholarly edition94 His diagrams show that Birchensha is confused here. Arithmetic division should result in a set of notes for which the differences between pairs of string lengths are constant; Birchensha's second and third examples, however, show notes whose string length ratios are constant. the first example shows a set of notes whose string lengths obey no consistent rule. 95 this paragraph is probably intended as a gesture towards the fact that every note (of the diatonic genus) in Birchensha's ...Music 
Thomas Salmon: Writings on music
2017Book© 2013 Benjamin Wardhaugh. All Rights Reserved. This is the second volume in a twopart set on the writings of Thomas Salmon. Salmon (16471706) is remembered today for the fury with which Matthew Locke greeted his first foray into musical writing, the Essay to the Advancement of Musick (1672), and the nearfarcical level to which the subsequent pamphlet dispute quickly descended. Salmon proposed a radical reform of musical notation, involving a new set of clefs which he claimed, and Locke denied, would make learning and performing music much easier (these writings are the subject of Volume I). Later in his life Salmon devoted his attention to an exploration of the possible reform of musical pitch. He made or renewed contact with instrumentmakers and performers in London, with the mathematician John Wallis, with Isaac Newton and with the Royal Society of London through its Secretary Hans Sloane. A series of manuscript treatises and a published Proposal to Perform Musick, in Perfect and Mathematical Proportions (1688) paved the way for an appearance by Salmon at the Royal Society in 1705, when he provided a demonstration performance by professional musicians using instruments specially modified to his designs. This created an explicit overlap between the spaces of musical performance and of experimental performance, as well as raising questions about the meaning and the source of musical knowledge similar to those raised in his work on notation. Benjamin Wardhaugh presents the first published scholarly edition of Salmon's writings on pitch, previously only available mostly in manuscript. 
Charles Hutton and the ‘Dissensions’ of 1783–84: scientific networking and its failures
2017Journal articleNotes and Records: the Royal Society Journal of the History of Science
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Current DPhil Students
 Kevin Baker
I would like to hear from potential DPhil students regarding any area in the history of mathematics or early modern history of science.