The British Society for the History of Mathematics
The Queen's College, Oxford, Saturday 3 March 2012, 11am to 5pm
Organisers: Peter Neumann (peter.neumann@queens.ox.ac.uk), Rosie Cretney(r.e.cretney@open.ac.uk), Jackie Stedall (jackie.stedall@queens.ox.ac.uk), Tony Mann (A.Mann@gre.ac.uk). Please send enquiries to Tony Mann.
Our annual meeting for research students in the history of mathematics to speak about their work. Abstracts can be found at the foot of this page.
Keynote speaker: Henrik Kragh Sorenson (Aarhus), on What's Abelian about Abelian groups?
Student speakers:
Nicole Bloye (Plymouth), The obtuse history of conformal geometry
Davide Crippa (Paris), Impossible Problems in Cartesian geometry: the case of the squaring of the circle
Stefanie Eminger (St Andrews), Viribus unitis! shall be our watchword: the first International Congress of Mathematicians, held 9-11 August 1897 in Zurich
Jasmine Kilburn-Toppin (Victoria and Albert Museum / Royal College of Art), Mastering Crafts: the Mathematical Measuring Text and Artisanal Epistemology in Seventeenth-Century England
Liz Rudge (St Andrews), P.G. Tait’s schoolboy introduction to complex numbers
Sam Hatfield (Warwick), Poincare Dodecahedral Space
Dave Kaye (Warwick), Clifford’s theorem and algebraic curves
Mairi Walker (University of Warwick), Poincare's constructions for Riemann surfaces
Meeting fee: 20 pounds including sandwich lunch. There is a discounted fee of 15 pounds for students and unwaged. The fee is payable on the day, If you are coming to this meeting please register by emailing Tony Mann (A.Mann@gre.ac.uk) by Friday 24 February.
Abstracts
Nicole Bloye, The obtuse history of conformal geometry
The interpretations of conformal geometry are many and varied, and have evolved significantly throughout its history. It is a history that spans several hundred years from the early geographical projections of Mercator in the 16th century, via Riemann’s extraordinary insight, to modern conformal differential geometry.
I will consider some of the significant points and changes in the history of conformal geometry, and try to understand the connections and influences, if any, between them.
Davide Crippa: Impossible Problems in Cartesian geometry: the case of the squaring of the circle
We can find, in Descartes' corpus, few remarks on the impossibility of solving the problem of squaring the circle geometrically. However, Descartes' confidence seems not fully justified in the backdrop of early XVIIth century mathematics context: extant evidence suggests that the squaring of the circle was considered an open problem.
Despite such awareness, it must be observed that Descartes himself obtained interesting results on the quadrature of the circle. The aim of my talk is to examine one of these results, published posthumously in the Excerpta ex Mss. R. Descartes as a short fragment (n, 6 of the Excerpta mathematica, according to Tannery's numbering).
I surmise this piece is interesting both for its mathematical features, since it employs a suggestive application of well-known geometric progressions in order to determine the radius of a circle whose circumference is known (although the problem, as stated by Descartes, does not directly concern the quadrature of the circle, it is immediate, by the first proposition of Archimedes' Dimensio circuli, to derive from its solution the solution of the quadrature too), and for the clues it offers in order to understand Descartes' notion of “impossible problem”. For these reasons, I will provide its reconstruction, a possible dating of the fragment, and few considerations on the interplay between existence and constructibility of geometrical items, that can be made on the ground of Descartes' own study of the squaring of the circle.
Stefanie Eminger: Viribus unitis! shall be our watchword: the first International Congress of Mathematicians, held 9-11 August 1897 in Zurich
Georg Cantor voiced the need for opportunities facilitating international mathematical cooperation as early as in 1888. A decade and efforts by a number of mathematicians later, the first International Congress of Mathematicians marked the beginning of an era where personal relations between mathematicians were considered to be of great importance. Furthermore, it set the standards for future congresses. As well as talking about the pre-history and the organisation of the congress, I hope to put it into a wider historic context and to conjecture on the reasons why it was held in Zurich and why such a great emphasis was placed on the social aspect of the congress.
Jasmine Kilburn-Toppin: Mastering Crafts: the Mathematical Measuring Text and Artisanal Epistemology in Seventeenth-Century England
Instructive printed texts as aids for measurement, produced by a range of self-styled mathematical practitioners throughout the seventeenth century, presented measuring as a form of precise, mathematical knowledge which might be applied by any individual with the appropriate theoretical grounding and tools. Such texts were allegedly intended to remedy the chronic errors perpetuated by practising craftsmen; inaccuracies that were supposedly based on the general artisanal ignorance of geometry.
It will be suggested in this paper that contrary to the claims of these mathematical practitioners’, measurement and the valuation of artisanal labour was a complex, nuanced process, not easily reducible to basic mathematical principles. Archival accounts of disputes over the relative worth of labour, conducted by master craftsmen working on major building projects of the 1630s, suggest that measurement of materials and craftsmanship was a process of arbitration and compromise, involving communities of skilled artisanal practitioners. The claims of the mathematical authors’ for the remedy of ‘vulgar errors’ were almost certainly part of broader intellectual trend which systematically attempted to put the ‘mechanical’ English craftsman in his social and epistemological place.
Liz Rudge: P.G. Tait’s schoolboy introduction to complex numbers
The Tait-Maxwell school-book was intended as a fair-copy book in which Tait and Maxwell (principally Tait) could preserve mathematical propositions, theorems and worked-through examples while at the Edinburgh Academy. My transcription of the school-book (preserved by Edinburgh’s Maxwell Foundation) includes Tait’s notes on a lecture he had heard on the geometrical representation of complex numbers. The lecture, delivered by no less than the Right Rev. Bishop of Edinburgh, surely constitutes Tait’s first introduction to complex numbers and as such merits discussion along with associated historical insights.
Sam Hatfield, Poincare Dodecahedral Space
The famous Poincare conjecture grew out of Poincare’s discovery of a space that had the same homology as a 3-dimensional sphere but was not homeomorphic to it. However, the geometrical picture of the space in terms of a dodecahedron was discovered only between 1929 and 1931. I will discuss how this discovery fitted in with the work of Poincare and others in the early development of 3-manifolds.
Dave Kaye, Clifford’s theorem and algebraic curves
William Kingdon Clifford was the first English mathematician to respond to the work of Riemann, and in a paper of 1878 he found a result that is now named after him and still used today concerning the embedding of algebraic curves in projective space. I will describe the result and its historical context.
Mairi Walker, Poincare's constructions for Riemann surfaces
It is well known that the sphere can be subdivided in only five ways to provide the regular or Platonic solids. Henri Poincare made his name in the early 1880s with a series of papers in which he gave new constructions for Riemann surfaces using non-Euclidean geometry, and it has only recently been shown that all these surfaces can display patterns analogous to the regular solids. I will trace aspects of this work.
The British Society for the History of Mathematics is registered as a company limited by guarantee, no. 3326816, and as a charity, no. 1061229. Its registered office is c/o Andrew Thurburn & Co, 38 Tamworth Road, Croydon, Surrey CR0 1XU, UK.