IHoM4 abstracts

Joseph Bennett, Institute of Technology, Carlow and Maynooth University

Henry Smith and the Arithmetical Theory of Forms

During his inaugural lecture as Savilian Professor of Geometry at Oxford University in 1920, Godfrey Harold Hardy FRS (1877-1947) acknowledged the significant contribution made by the Irish born mathematician Henry John Stephen Smith FRS (1826-1883) in his memoirs on the arithmetical theory of forms. Henry Smith was Savilian Professor of Geometry from 1860 to 1883. He distinguished himself as a superb lecturer and researcher who brought international recognition to Oxford mathematics. His unique and caring personality ensured he was held in widespread affection and admiration by his students and the University community. In this talk I will discuss Henry Smith’s life and contribution to number theory, particularly his memoirs on the arithmetical theory of forms. I will close by considering why, as Savilian Professor, Godfrey Harold Hardy was considered a `natural heir’ of Henry Smith in number theory.

Michael Brennan, TRIARC, Trinity College Dublin

The enigmas of two 8-9th century brooches

A large high-status brooch from Rogart in Sutherland, Scotland, and another from Ardagh in Co. Limerick, have unusually strong features in common, some geometric, some artistic. These challenge the art historian to understand what may have been in in the minds of their designers. With the help of simple mathematical methods it is possible to help the historian, though some aspects of the brooches’ designs are probably lost in time. The talk will try to use a simple understanding of symmetry and of early medieval knotwork motifs to interpret some of the goldsmiths’ work, In the process we will meet a hazard that waits in the long grass for all those who work in interlace, whether in the 8th or 20th century, or today.

Oisín Coombs, Trinity College Dublin

History of mathematics and its effects on maths anxiety

Maths anxiety is a well-defined cognitive, physiological, and psychological construct that negatively affects the mathematics achievements of students who suffer from it. Maths anxiety does not end when a student leaves school, and can negatively impact their adult life. In the age of big data and evidence based policy it is imperative that people do not avoid nor have distaste for mathematics. This case study investigates the use of the history of mathematics in a second-level class group and its effect on maths anxiety. In this case study a module using history-as-a-tool is taught to a class group of 15-17 year old students by the researcher. An instrument to measure maths attitudes and maths anxiety as they relate to this study was designed by the researcher. The levels of maths anxiety were decreased statistically significantly, and the attitudes of the students toward success in mathematics were statistically significantly improved.

Miguel De Arce, Smurfit Institute of Genetics, Trinity College Dubln.

Educating genius: William Rowan Hamilton’s schooling in Trim, Co. Meath (1808-1823)

William Rowan Hamilton (1805-1865) went through his primary education in the Church of Ireland Diocesan School, based in Talbot Castle in Trim, Co. Meath. He was there for fifteen years, from the age of 3 to 18. The school was operated by William’s uncle and local curate Rev. James Hamilton. This paper explores the character of Rev. Hamilton, his school and his young nephew, paying special attention to his studies and other occupations there, and whether this was a good preparation or a hindrance for his entrance examination in Trinity College and for his future career as an astronomer, theoretical physicist (mechanics and optics) and creative mathematician.

Roderick Gow, University College Dublin

In search of Robert Steell, mathematician and author

As far as we can see, the only Irish mathematical book in Edward Worth’s Library is Robert Steell’s “A treatise of conic sections” (Dublin 1723). A somewhat mathematical book, intended for surveyors, and also in the Library, is “A method to determine the areas of right-lined figures universally” (Dublin 1724) by Thomas Burgh. We know much about Burgh but virtually nothing about Steell. Curiously, contiguous but unrelated poems in Laurence Whyte’s “Poems on various subjects” (Dublin 1740) are dedicated to Steell and to the Burgh family. We will discuss the little we have discovered about Steell and the mathematical circles in which he moved.

Sue Hemmens, Marsh’s Library, Dublin

‘Knotty problems in algebra’: mathematical collections in Marsh’s Library

The four major collections of Marsh’s library were formed at a time of rapid development of the role of mathematics in all its diversity, both as an abstract subject and as a practical support for trade, engineering and the emerging scientific disciplines which made up natural philosophy. The majority of the mathematical books came to the library in the collection of its founder, Narcissus Marsh. He described his studies in Oxford as including ‘old philosophy, mathematics and oriental languages’ and his fascination with mathematics led him to use problems in algebra and geometry as a recreation, to divert his thoughts from the instability he experienced in late seventeenth-century Ireland. His collections are annotated with calculations and commentaries which indicate his attention to mathematical detail. Classical geometry, algebra, engineering and the application of mathematics to music and astronomy are represented in the other three major collections, together with practical arithmetic.

Peter Lynch, University College Dublin

Replication of Foucault’s pendulum experiment in Dublin

Léon Foucault’s pendulum experiment in 1851 generated widespread interest. The experiment was repeated in numerous locations in Europe and the United States of America. The more careful of these demonstrations confirmed the effect of the Earth’s rotation on the precession of the swing-plane of the pendulum. A set of pendulum experiments were carried out by Joseph Galbraith and Samuel Haughton in Dublin and a comprehensive mathematical analysis of them was published in 1851.

Ciarán Mac an Bhaird, Maynooth University

Euler’s methods and their impact on student learning

The History of Mathematics has been taught at Maynooth University since the 1990s. As you would expect, different lecturers focus on different eras and on different aspects of mathematics in these periods. In this talk I will consider three problems of Euler which I work through with my students: his first ‘solution’ to the Basel Problem; his ‘establishment’ of the Taylor Series expansions for sin(x) and cos(x); and his ‘proof’ that eix = cos(x) + i sin(x), for real x.  These problems are selected for two reasons: 1) They involve mathematics that the students have already seen; 2) Euler constructs the ‘proofs’ in a remarkable manner, often employing methods that were not rigorous at the time (but subsequently shown to be).  I will close with a brief discussion on why more students should see how the mathematics they study was constructed and discovered, and give some student feedback on their exposure to Euler’s methods.

Mark McCartney, University of Ulster

‘One of the best of Irishmen’: James Thomson Snr and Mathematics in late Georgian Belfast

At the beginning of the nineteenth century Belfast was a town which was growing rapidly, both in size and in importance within Ireland. Part of this rapid growth saw the opening of the Belfast Academical Institution in 1814. It aimed to be both a school and a college combined, with the college part enabling men from Ulster to be educated at home rather than having to, as was typical,  travel to Scotland. The school’s first mathematics master, and college’s first mathematics professor, was one James Thomson (1786-1849), a bright and ambition farmer’s son from Ballynahinch, some 20 km south of Belfast. During  his career in Belfast Thomson wrote a number of textbooks, on arithmetic, geography, trigonometry and calculus.  This talk will summarise Thomson’s time in Belfast, and examine some of his textbooks.

Colm Mulcahy, Spelman College, Atlanta

The Library of Irish Mathematics

The free online Annals of Irish Mathematics and Mathematicians documents over 2700 mathematical people who are/were Irish, work(ed) in Ireland, or had Irish doctoral advisors. It also documents over 750 associated books by authors in the first two categories, spanning three centuries. We will provide an overview of the diversity of this “virtual library of Irish mathematics”, focussing mostly on the wealth of volumes published from 1900 on.

Maurice OReilly, CASTeL, Dublin City University

Mathematics from the Imprimerie Royale, Paris at the Edward Worth Library, Dublin

There are two volumes of mathematical works from the royal printing house, Paris, in the Edward Worth Library. The older one, from 1676, Recueil des plusieurs traitez de mathematiques de l’academie royale des sciences, is a lavish volume with four articles, three by Edme Mariotte and the fourth by Bernard Frenicle de Bessy. The second volume, Divers ouvrages de mathematique et de physique, dated 1693, contains 31 articles by seven authors, including Christiaan Huygens and Gilles de Roberval. This paper examines the content, authors and context of these two volumes, in the light of other works of French origin at the Worth and of the online exhibition, Mathematics at the Worth Library.

David Wilkins, Trinity College Dublin

The limit concept in the early 18th century

This talk will examine the theory of limits, or prime and ultimate ratios, underlying Newton’s Principia, exploring how it was understood and explained by 18th century mathematicians such as Benjamin Robins, Thomas Bayes, John Stewart and Jean le Rond d’Alembert.  The perspective adopted is that the limit concept as understood in the 18th eighteenth century, and its use in the proof-based mathematics of its times, should be approached in its own terms, similar in some respects, but different in others, from the limit concept developed in the 19th century by Cauchy, Bolzano, Weierstrass and others.