Women’s participation in mathematics in Scotland, 1730-1850


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It’s great to see Amie Morrison and my paper appear in print. The paper grew out of Amie’s honours project and she did a fantastic job unearthing all sorts of primary source evidence for women’s participation in mathematics – at all levels from basic numeracy upwards – and then building an argument. We concluded that certain elements of Scottish Enlightenment culture promoted wider participation by women in mathematical activities than has previously been recognized, but that such participation continued to be circumscribed by societal views of the role of women within family formation. The paper is open access, so everyone can read it.


Earl Sweeting and the Historiography of African Mathematics


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A couple of days ago I published a blog post with this title on the BSHM (British Society for the History of Mathematics) website – a topic that has been occupying a lot of my time during lockdown.

In Our Time – Kinetic Theory


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The podcast of In Our Time – Kinetic Theory, on which I contributed, is now available.

A Mathematical and Scientific Walk Around St Andrews


I have finally amplified into a self-guided walk, the Mathematical and Scientific Walk Around St Andrews  that I developed for the Mathematical Biographies conference in 2016. This is a work in progress, that I expect to expand and update – and make better web-integrated – at some point.

If you are in St Andrews, enjoy.

If you would like to add to it, let me know (contributions will be credited).

What did Maxwell’s Mother Know?


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Following a question at the end of my recent talk (Maxwell in Six Objects) at the Edinburgh International Science Festival, I’m thinking of writing a book series – “What Maxwell’s Mother Knew,” “What Gregory’s Mother Knew,” etc. They are just two of the many scientists who received their early education from their mothers – but we don’t know what their mothers were able to teach them. It seems likely it was more than watercolours, the piano, and the Bible. Legend has it that Gregory’s mother, whose brother (or possibly uncle – the sources are confused) was a mathematician, taught Gregory geometry. But Maxwell’s mother?

Tracing women’s education and learning is really difficult, and I’ve not come up with any answers yet. But I’ve found out more about her maternal line than appears in other Maxwell biographies, and I’ve some leads for further places to look.

Maxwell’s mother, Frances Cay (1792-1839) was the daughter of Robert Hodshon Cay, and Elizabeth Liddell, an artist. Frances’ brother, John Cay, became a Fellow of the Royal Society of Edinburgh – there is a catalogue of his library in the National Records of Scotland. Unfortunately, the books were dispersed by auction, so tracking them would be difficult. It might be more possible to track Maxwell’s own books, bequeathed to the Cavendish Laboratory, to see whether any might have come to him through his mother’s family.

The Cay side of Frances’ family is well covered in John Arthur’s book, Brilliant Lives, but far less is known about the Liddell side. Frances Cay may have learnt anything she knew from her own mother, Elizabeth Liddell, an artist with connections to Archibald Skirving, Sir Henry Raeburn, and Thomas Bewick. The Liddell family seem to have been reasonably well-to-do, based in the North Shields area of Northumberland. Neil Jeffares, in his Dictionary of Panellists, guesses from their address in Dockwray Square that Elizabeth’s father, John Liddell, was a ship-owner. However, John’s will shows that he also had at least a farm and coal-mining interests at Shire Moor at Murton (I haven’t read it all yet, the writing is difficult). The will also names two surviving sons (Albert and George) and four daughters (Sarah, Elizabeth, Barbara, Isabella). The family memorial in Tynemouth Parish church, gives their dates, married names, and those of further children who died young. Many of the Liddells or their husbands, including Robert Hodshon Cay, sold out of Murton Colliery in 1809.

Elizabeth Liddell’s sister, Barbara, remained unmarried. At some point she moved to Edinburgh, possibly to be near Elizabeth, and lived at 19 Great Stuart St. Her will left most of her estate to her niece Jane Cay (i.e. Frances Cay’s sister – Maxwell’s “Aunt Jane”). The inventory of her estate is in the National Records of Scotland. Again, I haven’t read either will or inventory yet, but they provide further possible leads to Frances Cay’s background.

So, it looks as though Maxwell’s mother did know how to paint. Although we still don’t know what else she knew, we might be a little nearer finding out.

Phases of Physics paper accepted

Oops… I don’t seem to have added anything here for two years. Too many ideas and not enough time to commit them to the blog 😦   I’ll try to do better.

I’m delighted to have got confirmation that the paper I have been working on for the past 18 months has been accepted (PhasesofPhysics_Forbes_Final).  This paper is for a special issue of History of Science on “Phases of Physics”, about the formation of physics as a discipline in the nineteenth-century.

The paper takes James David Forbes’ Encyclopaedia Britannica entry, Dissertation Sixth, as a lens to examine physics as a cognitive, practical, and social, enterprise. Forbes wrote this survey of eighteenth- and nineteenth-century mathematical and physical sciences, in 1852-6, when British “physics” was at a pivotal point in its history, situated between a discipline identified by its mathematical methods – originating in France – and one identified by its university laboratory institutions. Contemporary encyclopaedias provided a nexus for publishers, the book trade, readers, and men of science, in the formation of physics as a field. Forbes was both a witness, whose account of the progress of physics or natural philosophy can be explored at face value, and an agent, who exploited the opportunity offered by the Encyclopaedia Britannica in the mid nineteenth century to enrol the broadly educated public, and scientific collective, illuminating the connection between the definition of physics and its forms of social practice. Forbes used the terms “physics” and “natural philosophy” interchangeably. He portrayed the field as progressed by the natural genius of great men, who curated the discipline within an associational culture that engendered true intellectual spirit. Although this societal mechanism was becoming ineffective, Forbes did not see university institutions as the way forward. Instead, running counter to his friend William Whewell, he advocated inclusion of the mechanical arts (engineering), and a strictly limited role for mathematics. He revealed tensions when the widely accepted discovery-based historiography conflicted with intellectual and moral worth, reflecting a nineteenth-century concern with spirit that cuts across twentieth-century questions about discipline and field.

J.D. Forbes and the development of curve plotting


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Belatedly, I have uploaded the slides from my presentation at the MAA Mathfest last year, on J.D. Forbes and the developent of curve plotting. Here’s the basic idea.

When, in 2012, experimental evidence for the Higgs boson was announced, it came in the form of a curve with a blip, immediately understood by the audience. Yet 190 years earlier, in 1823, the practice of curve plotting was so unusual that S. H. Christie felt it necessary to explain not only the meaning of the curve for magnetic variation that he presented in the Philosophical Transactions but also the process of defining the axes, representing the data as dots, and drawing the curve.

The development of curve plotting as a technique for relating observational data to mathematized theory appears to have been surprisingly difficult. Early promoters, such as Lambert, were not followed, and not until the 1830s did the method start to spread, following the work of Playfair and Quetelet in statistics, and Herschel and Forbes in natural philosophy (Beniger & Robyn 1978; Hankins, 1999; Tilling 1975).

Tilling identifies a step change in the ubiquity of curve plotting among scientists, initiated by J.D. Forbes, Professor of Natural Philosophy at Edinburgh 1833-1859. Beginning in 1834, he used curves both to present and to analyse observational results relating to heat, meteorology, and glacial flow. This was really handy for me, as Forbes later  became Principal of the United College of St Andrews University (effectively Principle of the whole university), and all his archives are here on my doorstep.

Based on an investigation of Forbes’ notebooks, the paper looks in particular at his curve for daily oscillations in atmospheric pressure, to analyse the the influences on his use of curves. I tentatively conclude that:

  • The form of the horary oscillation curve is a response to very particular circumstances of Forbes’ life in 1831-3. In most other work he used  curves as labour saving and calculational tools
  • Transactions of the RSE encapsulates a strongly visual culture in Scottish science in the 1820s-30s
  • The implicit assumption of an analogue space may have been a barrier to the adoption of curve plotting techniques until the 1830s when increasing confidence in instruments and new ways of seeing allowed their acceptance by authors and audiences


Beniger, James R., and Dorothy L. Robyn. ‘Quantitative Graphics in Statistics: A Brief History’. The American Statistician 32, no. 1 (1 February 1978): 1–11. doi:10.2307/2683467.

Hankins, Thomas L. ‘Blood, Dirt, and Nomograms: A Particular History of Graphs’. Isis 90, no. 1 (1 March 1999): 50–80.

Tilling, Laura. ‘Early Experimental Graphs’. The British Journal for the History of Science 8, no. 03 (1975): 193–213. doi:10.1017/S0007087400014229.


Entry of ‘mechanism of the heavens’ into English


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You’ll have gathered that I like playing around with google’s Ngram viewer.

Having been thinking about Mary Somerville recently, I thought I’d use it to assess in some sense the impact of her first book Mechanism of the Heavens, an interpretation of Laplace‘s Mécanique Céleste for the British (published 1832). The results are intriguing. Because the Ngram viewer is case sensitive, one can distinguish between deliberate references to the book, and occasions when the phrase is being used as part of the language (slightly complicated by being in an age when writers still capitalised important words even when they were not titles). But, basically, the phrase was bumbling along at a very low incidence in the English language until the run up to the publication of the book, when usage suddenly increases dramatically. It looks as though Somerville was largely responsible for popularising the phrase in English, as well as for explaining Laplace.


Mary Somerville and John Herschel


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Mary Somerville, in her reminiscences, gives the impression (though she does not say definitely) that she first met John Herschel when she visited his father, William Herschel, in 1816.

However, a letter I came across in the summer in the Herschel papers at St John’s College in Cambridge, shows that they had actually met in 1812 – though he did not mention her by name, and he doesn’t seem to have made an impression on her. But the dates correspond to the Somervilles’ visit to London soon after they were married, and it seems unlikely that there were two such ladies around at the same time.

In August 1812, John Herschel wrote to his friend Rev. John William Whittaker :

I had the happiness of an introduction to a Dulcinea who reads the Mec. Cel__ and Mec. Analytique _ What say you to that?_ To use Playfair’s expressions she “possesses a degree of Math. Knowledge rarely found in the other sex and is at once an ornament & example to her own – to her Country & to the human race!! _ No mortal however would have been able to read a page of La Grange in her eyes. Or to discover the Analyst in her manner, her conversation or her appearance  NB. Corol. She is Confoundedly not-beautiful. Of course one ought never positively to affirm the reverse of beauty to belong to any woman_  (St John’s College, Herschel papers, Herschel/box1/letter 1)

His views on whether female mathematicians can or should be beautiful are intriguing and well worth exploring, and play very well to the themes that Eva Kaufholz explored in her talk on Sofja Kowalewskaja at the Mathematical Biography conference last month.

No Actual Measurement was required…


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I’ve just put a preprint of my article, ‘No actual measurement … was required: Maxwell and Cavendish’s null method for the inverse square law of electrostatics’ on the Arxiv. It has grown and developed from my conference presentation last year – with thanks for great comments and stimulating discussions with Daniel Mitchell and the referees. It’s been accepted (hooray!), but still some minor corrections before the final published version.