# Outreach and general interest

A Very Brief History of Number Theory

Talk to UKMT Summer School, The Queen's College, Oxford, 23 August 2023

A tour of some highlights of the history of number theory, focusing on prime numbers and perfect numbers.

A Very Brief History of the Early International Congresses of Mathematicians

Talk to Balliol Undergraduate Maths Society, Oxford, delivered online, 2nd May 2022

I will give a brief overview of the formation of the International Congresses of Mathematicians at the end of the nineteenth century and the way in which they were affected by events in the wider world, up to the Second World War.

Ada Lovelace: The Making of a Computer Scientist

Talk for One Day University, delivered online, 24th January 2022

Augusta Ada King, Countess of Lovelace (1815–1852), was a nineteenth-century British aristocrat who has become known in the modern world as a pioneer of computing. Her fame stems from her speculations, published in 1843, concerning the capabilities of the so-called ‘Analytical Engine’ designed by the polymath Charles Babbage (1791–1871). Although it was never built, the Engine was to have been a steam-powered general purpose programmable computer. To Babbage, it was little more than a sophisticated calculating machine, but Lovelace recognised that it might be capable of much more. Her speculations on what it might be programmed to do, such as compose music, resonate with modern ideas about computers, and indeed with the abilities of the machines that we have around us.

In this lecture, I will give an account of Lovelace’s life and influences, focusing in particular on her education and the way in which this prepared her for her collaboration with Babbage. As well as looking at her writings on the Analytical Engine, I will examine her later life and legacy.

Side-stepping absurdity: Some strange ideas about algebra in 19th-century Britain

Talk to the Oxford Invariants, Mathematical Institute, Oxford, 23rd November 2021

By the end of the 18th century, mathematicians had developed a range of powerful techniques for manipulating and solving polynomial equations. Many new ideas, such as complex numbers, had emerged along the way, and these had been accepted (mostly) without trouble into the mathematician’s day-to-day toolkit. In 1790s, however, some mathematicians in Britain began to question the validity not only of complex numbers but even of negative numbers, and proposed to rebuild algebra in such a way that negative numbers could never appear. Although few practicing mathematicians ever seriously considered rejecting negative numbers in this way, the debate did raise questions about the way in which algebra should be approached - in particular, how it should be taught. In this talk, I will look at this episode in the history of algebra and describe where it fits into the mathematical landscape of 19th-century Britain.

Mathematics, from Ancient Egypt to Modern Academia (with R. B. Parkinson)

Talk to the Oxford Invariants, delivered online, 9th November 2020

The subject of ancient Egyptian mathematics typically features, alongside its Babylonian counterpart, at the beginning of almost any general history of mathematics. But how do we know what Egyptian mathematics looked like? The understanding of ancient Egyptian arithmetic and geometry emerged slowly during the nineteenth and early twentieth centuries, thanks to the work both of Egyptologists and of mathematicians. However, the two groups often had different interpretations of the surviving evidence. In this talk, we'll describe how ancient Egyptian arithmetic worked, and use this to contrast these different approaches to the subject.

Unsung Heroes of Ancient Egypt: the anonymous mathematicians

Unsung Heroes of Science Celebration Day, Hertford College, Oxford, delivered online, 30 June 2020

Among the ultimate unsung heroes of science are those who developed scientific ideas in ancient civilisations – because we don't even know their names. In this talk, I will give a short account of what (mostly) unknown people achieved in mathematics in ancient Egypt.

Parallel lines down the centuries

Bodleian Library Lates: Thinking 3D, Weston Library, Oxford, 12th June 2019

In the third century BC, Euclid of Alexandria stated as one of his basic assumptions of geometry that parallel lines must meet at infinity. For Euclid, this was an obvious truth about the way that geometry works in the real world around us; unlike his other assumptions, however, it clearly could not be tested. Thus, in the centuries that followed, mathematicians worried a great deal about Euclid’s assumption on parallel lines: do we really need to assume it, or is it in fact a consequence of his other assumptions? Is it possible to make geometry ‘work’ without it? It was not until the nineteenth century that these questions received satisfactory answers – but these were answers that caused mathematicians to reassess the fundamental nature of geometry, and even of mathematics itself.

Ada Lovelace: Mathematical Learner

Talk to Oxford Mirzakhani Society, Mathematical Institute, Oxford, 24th February 2019

A biographical account of Lovelace life and work, and a survey of recent research thereon.

Mathematics and competition: scientific communication during the Cold War

Talk to STEM Society, Oxford High School, 12th March 2018

A brief survey of the ups and downs of East-West scientific communication during the twentieth century, and during the Cold War in particular, with a focus on mathematics, and an indication of how some Western and Soviet approaches to the same mathematical topics differed.

What is algebra?

What do historians of mathematics do? Mathematical Institute, Oxford, 8th May 2017

I will address the question of "What do historians of mathematics do?" by turning to another: "What is algebra?" In answering this second question, and surveying the way that the answer changes as we move through the centuries, I will highlight some of the problems that face historians of mathematics when it comes to interpreting historical mathematics, and give a flavour of what it means to study the history of mathematics.

Skype lecture for Ada Lovelace Day, University of Edinburgh, 11th October 2016

A brief summary of the education and scientific work of Ada Lovelace, with a particular focus on the figures who influenced her either as tutors or mentors.

Meeting under the integral sign? The 1936 Oslo International Congress of Mathematicians

Queen's College Symposium, Oxford, 7th June 2016

The International Congresses of Mathematicians (ICMs) have taken place at (reasonably) regular intervals since 1897, and although their participants may have wanted to confine these events purely to mathematics, they could not help but be affected by wider world events. This is particularly true of the 1936 ICM, held in Oslo. In this talk, I will give a whistle-stop tour of the early ICMs, before discussing the circumstances of the Oslo meeting, with a particular focus on the activities of the Nazi-led German delegation.

Ebbe og flod: Cold War scientific communication

Talk to visiting students, Lady Margaret Hall, Oxford, 5th April 2016

I give a brief overview of the ups and downs of East-West scientific communication during the twentieth century, and during the Cold War in particular.

Ada Lovelace: 19th-century mathematician and computer scientist

STEM Access Event, Wadham College, Oxford, 24th November 2015

A short account of Ada's life, and an indication of why she is famous.

Sistemas de algarismos não-posicionais

Talk to 'C-infinito': Clube de Matemática da FCUL, 1st October 2009

Com muitos exemplos da história, falarei sobre os sistemas de algarismos em geral, e os sistemas não-posicionais em particular. Examinarei o desenvolvimento destes sistemas e compararei sistemas diferentes.

With lots of examples from history, I will speak about systems of numerals in general, and non-positional systems in particular. I will examine the development of these systems and compare different systems.