Other articles

'One hundred years of commutative rings', Mathematics Today 57(6) (December 2021), 222–224.

In October 1920, Emmy Noether submitted a paper entitled 'Idealtheorie in Ringbereichen' ('Ideal theory in ring domains') to the journal Mathematische Annalen. Its appearance in print the following year not only gave initial impetus to the theory of commutative rings, but also introduced a whole new outlook into mathematics. In this article, we briefly introduce Noether and her work, and describe how her 1921 paper fits into twentieth-century mathematics.

Guest Facebook post for Westminster City Archives, marking Ada Lovelace Day 2021.

A few brief introductory comments about Ada Lovelace, accompanying photographs of her former home in St James's Square, City of Westminster.

'Peter M. Neumann OBE (1940–2020)', British Journal for the History of Mathematics 36(2) (2021), 67–75.

A tribute and obituary, focusing on Peter's work in the history of mathematics.

'Historical notes: Uncovering ancient Egyptian maths', Mathematics Today 57(3) (June 2021), 100–101.

A short account of the rediscovery of ancient Egyptian mathematics during the nineteenth and twentieth centuries, and approaches that were taken to it.

'Peter M. Neumann OBE (1940–2020)', Mathematics Today 57(2) (April 2021), 43.

A short tribute, with very brief comments on mathematical, historical, and educational work.

'400 years of the Sedleian Professors', Round up: The Oxford Mathematics Annual Newsletter 2021, 22.

A brief note of the 400th anniversary of Oxford's Sedleian Chair of Natural Philosophy.

'Bridging the gap between science and the arts: Clifford Norton Fellows and Students at Queen's', The Queen's College Record 2020, 105–108.

A brief account of the foundation of the Clifford Norton Junior Research Fellowship (subsequently the Clifford Norton Studentship) at The Queen's College, Oxford. A slightly longer footnoted version may be found here.

'Ægyptisk matematik fortolket' ('Egyptian mathematics interpreted') (with R. B. Parkinson; translated into Danish by Lise Manniche), Papyrus (Dansk Ægyptologisk Selskab) 40(2) (2020), 18–23.

A slightly modified Danish version of this article.

'Differing approaches to ancient Egyptian mathematics' (with R. B. Parkinson), London Mathematical Society Newsletter, no. 490 (September 2020), 28–33.

We discuss some developments in the understanding of ancient Egyptian mathematics that took place during the early decades of the twentieth century. In particular, we highlight the differing views of the subject by mathematicians on the one hand and Egyptologists on the other.

'The Oslo International Congress of Mathematicians in 1936 and the first Fields Medals', Oxford Mathematics Research Case Study, April 2020

A short overview of the impact of world events on the Oslo ICM and the award of the first Fields Medals.

'Mathematics Emerging: from Colorado to Oxford' (with Marlow Anderson and Robin Wilson), PRIMUS 29(5) (2019), 461–473

History of mathematics courses based on original source materials are becoming increasingly common. But are they more suitable for particular types of students? Here we compare two such upper-level courses, with a similar structure and using the same textbook, taken by liberal arts students at Colorado College and mathematics specialists at Oxford University.

'The need for closure', The Mathematical Gazette 103(557) (July 2019), 248–256

When defining a group, do we need to include closure? This is a detail that is often touched upon when the notion of a group is introduced to undergraduates. Should closure be listed as an axiom in its own right, or should it be regarded as an inherent property of the binary operation? There is no clear answer to this question, although there are firm opinions on both sides. Indeed, a very brief survey of group theory textbooks suggests that there is a rough 50:50 split between authors who include closure explicitly and those who do not. In this article, we go back to the beginning of the twentieth century to provide some historical perspective on this problem.

'Transcendental numbers (and politics)', Plus Magazine, August 2018

A short account of the understanding of complex numbers, with a focus on Hilbert's seventh problem, and Gel'fond's solution thereof.

'Maths and politics', Plus Magazine, August 2018

A short survey of the early history of the International Congresses of Mathematicians, and the impact of world politics thereupon.

'How to handle partial transformations II', Mathematics Today 54(4) (August 2018), 154–156

This article is a follow-up to an earlier one in which I explored some of the basic ideas surrounding the study of partial transformations. The focus there was upon partial transformations on a single set. However, at the end of that prior article, I hinted at the possibility of studying partial transformations between two different sets through the introduction of an appropriate ternary operation. I expand here upon those earlier comments, and describe some of the contributions made in this area by the Russian geometer V. V. Wagner (1908–1981).

'Tinkering with postulates. How some mathematics is now redundant. Or is it?', Oxford Mathematics Research Case Study, June 2018

A brief indication of the nature of the work on so-called postulate analysis that was carried out by a group of American mathematicians at the beginning of the twentieth century.

'Ada Lovelace, determined learner', Oxford University – Medium, 18th June 2018

A short account of Ada Lovelace's mathematical education, presenting the point of view that 'Ada the determined learner' is a far more useful image for encouraging girls into the sciences that is 'Ada the genius'.

'How Ada Lovelace's notes on the Analytical Engine created the first computer program' (with Ursula Martin and Adrian Rice), Science Focus, 15th June 2018

Also available on the Bodleian Library's Ada Lovelace blog

A short account of Ada Lovelace's contributions to the understanding of Charles Babbage's Analytical Engine.

'Ada Lovelace in the archives', The Queen's College Newsletter, no. 29 (Trinity Term 2017), 14–15

A brief account of working with the Lovelace–Byron archive in the Bodleian Library.

'R. S. Ball's Mechanics: bringing Newton to the masses?', The Mathematical Gazette 101(551) (July 2017), 280–288

In 1879, the Irish astronomer Robert Stawell Ball published a slim book entitled simply Mechanics. This book appeared as part of the series of 'London Science Class-Books', published by Longmans, Green & Co. These books were intended as elementary science texts for use in schools, and, as a consequence, their mathematical content was quite basic – even for those books on supposedly mathematical topics. In this article, I will look at Ball's handling of his subject, and compare his book to its distant ancestor: Newton's Principia.

'How to handle partial transformations', Mathematics Today 53(3) (June 2017), 121–123

A number of concepts in modern algebra have arisen as abstract versions of systems of functions of one type or another, the most famous example of course being groups: the abstractions of systems of bijections or permutations. Going further, the articulation in the 1920s and 1930s of the fact that non-invertible transformations are no less ubiquitous than bijective ones, led to the abstraction of systems of arbitrary transformations and the beginning of the theory of semigroups. Various other types of functions have also been studied in a similar manner. One particularly interesting instance, though one that is arguably lesser known, is that of partial transformations. In this article, I give a taste of the study of partial transformations and the corresponding abstract theory.

'Mathematics and Politics: The International Congresses of Mathematicians', Oxford Mathematics Research Case Study, February 2017

A brief summary of the ways in which the International Congresses of Mathematicians were affected by the broad political events of the twentieth century.

'Celebrating Ada Lovelace' (with Ursula Martin), Oxford Mathematical Institute Newsletter, no. 15 (Spring 2016), 2

A short account of the life and work of Ada Lovelace and an indication of the events that took place in Oxford in 2015 in celebration of her bicentenary.

'I, Claudius and the cipher extraordinary', The Mathematical Gazette 96(537) (November 2012), 466–470

We investigate two ciphers, supposedly used by Augustus, which appear in Robert Graves' I, Claudius. We focus in particular on the more complicated (and therefore more secure) of the two, the so-called cipher extraordinary, and relate it to another, better-known cipher.

'The case of Evgenii Sergeevich Lyapin', Mathematics Today 48(4) (August 2012), 184–186

One of the major issues facing mathematics at present is the demand for immediate applications. Another (historical) example of such a policy may be found in Soviet ideological interference in mathematics, of which I will give a short description, before illustrating it with an account of an ideological attack on the Russian algebraist E. S. Lyapin.

'The fabulous positional system', Plus Magazine 48 (September 2008)

1, 2, 3, 4, 5, 6, 7, 8, 9, 0 are commonplace symbols, so we rarely appreciate just how special our system of numerals really is. Fifteen hundred years of development have given us an extremely succinct method for writing down even very large numbers. The key to the success of this system is its positional nature. One of the first things we all learn at school is that our numbers are arranged in columns; reading from right to left, we first have the units column, then the tens, the hundreds, the thousands, and so on. Thus, it not only matters which symbols we write down, but also where we place them in this arrangement. But why should the need for a positional system arise in the first place? In this article, I demonstrate why positional number systems are so special by taking an historical approach and looking at the development of numeral systems in general.

'Some first tantalizing steps into semigroup theory', Mathematics Magazine 80(5) (2007), 331–344

Semigroup theory is a thriving field in modern abstract algebra, though perhaps not a very well-known one. In this article, we give a brief introduction to the theory of algebraic semigroups and hopefully demonstrate that it has a flavor quite different from that of group theory. In the first few sections, we build up some basic semigroup theory, always with the group analogy at the back of our minds. Then, once we have established enough theory, we break free of this restriction and see some truly 'independent' semigroup theory. In the final section, we consider the application of semigroups to the study of 'partial symmetries'.