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Berkeley and Byrne

Whilst the physical Library is closed, research on the collections continues apace. In our latest post Dr Clare Moriarty, IRC Postdoctoral Fellow in Philosophy, writes about her research into the intersection between maths and art and the early nineteenth-century Irish mathematician Oliver Byrne, the ‘Matisse of Mathematics’.

Clare will also be presenting at the The Art + Science Reading Group on 18 June at 6.30pm and registration is via this link. The group is now a virtual gathering of thinkers, researchers and the incurably curious. Organised by PhD candidates Amelia McConville (School of English and Institute of Neuroscience) and Autumn Brown (School of Education and Science Gallery Dublin) and supported by Science Gallery Dublin and the Trinity Long Room Hub, the series will explore the evolutionary and revolutionary kinship between two approaches to understanding the universe and our place within it.

Clare writes;

One is a name familiar to all who know the university: George Berkeley. Berkeley was an 18th century philosopher, Anglican bishop, mathematical malcontent, and Trinity student and tutor. The second, Oliver Byrne, is a different creature altogether. Born in 1810 near Avoca in Wicklow, Byrne mixed a life-long devotion to mathematics and mathematics education with: circulating tracts in America detailing close-combat styles (!) to be used in pursuit of Irish Independence, inventing something called the Byrnegraph, writing colourfully against phrenology, and basically living the hard life of an inventor-cum-educator with his wife Eleanor, who was herself a brilliant meteorologist. Byrne had a connection of sorts to Trinity. He claimed he learned his mathematics here. However, he is not recorded as ever having matriculated. So, we have two figures, a century apart, from very different worlds, but united by lifelong preoccupations with mathematics (regard Berkeley’s ‘Of Infinites’, an essay presented to the Dublin Philosophical Society in 1707).

Byrne—if he is known by people at all—is known for his majestic edition of Euclid’s Elements.

Here, Byrne uses coloured diagrams to present that Junior Cert syllabus treasure, the Pythagorean Theorem. This is not “art for art’s sake”; Byrne had a serious pedagogical insight into the difficulties of teaching maths and believed using colours could more judiciously represent the abstract properties of geometric objects.


Example: It’s a mistake to think of a geometric line as having any breadth. When concentrating on a line in its own right Byrne brings this into focus by using two colours bumping up against each other, to suggest a one dimensional boundary, rather than anything with suggested thickness.

Byrne shows a distinctive philosophy of education here: grappling with overcoming the problems of representing necessarily abstract geometric objects in a 3-dimensional learning scenario.

Byrne continued to use colour as a conceptual tool in his instruction. In the little-known work ‘The Young Geometrician’, which lives in Early Printed Books, Byrne expands his method to describe geometric constructions, or, how things need to move when setting up various geometric problems. This time colour is used to mark fixed versus moving parts. So, in these diagrams, Byrne conveys that the moving one of two set squares is the red one.

The process starts out simply, but we can see that it quickly develops into a procedure for fairly sophisticated direction.

TCD Manuscripts are the custodians of box of treasures given to the university by Byrne’s wife, Eleanor. It includes the beautiful manuscript of Byrne’s last book, The Trinal Calculus. The elaborate pictorial frontispiece suggests that Eleanor Byrne prepared the document.

And again, we have fascinating mathematical connections to Berkeley whose infamous 1734 tract The Analyst criticised the foundations of calculus, and inflamed what became a near-century long search for more rigorous logical foundations. Byrne’s strange treatise is (1) dedicated to solving Berkeley’s problems:

And when we look to see what Byrne provided by way of an appendix, it’s just his copy of The Analyst.

The above shows the possibility of demonstrating significant links between two key thinkers with a few key resources. Distance from primary material during Covid-19 is challenging. Now that archive access is not a short-term option, I find myself reminded that the sources that first struck me as relevant—those that first caused me to photograph them for personal use—are very likely the ones that epitomise the project.

Dr Clare Moriarty

IRC Postdoctoral Fellow, Philosophy, TCD