Date: Friday 6 November 2009
Location: Royal Statistical Society, London
The conference will be dedicated to tracing the history of social, professional, and academic networks, which in some way influenced the creation of new mathematical concepts or disciplines.
East London, where the conference will be held, was the fermenting ground where one of the first mathematical societies was founded, the Spitalfields Mathematical Society (1717). The history of the area has inspired, in many ways, the contributions to the conference, and we hope that both mathematicians and the historians of mathematics will find this a fascinating opportunity to explore the ways in which mathematics developed from its applications and in which applications inspired the creation of new mathematical techniques.
Abstracts
Professor Victor J. Katz, University of the District of Columbia
Quadratic and Cubic Equations: Can We Really Apply Them?
Abstract: The solution of quadratic equations was at the center of the first algebra textbook, written by Mohammad al-Khwarizmi around 825 CE. Later Islamic authors extended al-Khwarizmi’s work and even attempted, unsuccessfully, to find algebraic solutions to cubic equations. It was this Islamic work that was transmitted to Europe in the late Middle Ages and became the core of Europe’s own work in algebra. But certainly the mathematicians of the Middle Ages and the Renaissance were interested not only in theoretical mathematics but also in applying algebra to solve genuine real-world problems. We will consider the work of several early English mathematicians who wrote on algebra and see how they attempted to find real problems to which they could apply the techniques of solution of both quadratic equations and – later – cubic equations.
Biography: Victor J. Katz received his Ph.D. in mathematics from Brandeis University in 1968 and was for many years Professor of Mathematics at the University of the District of Columbia. He has long been interested in the history of mathematics and, in particular, in its use in teaching. The third edition of his well-regarded textbook, A History of Mathematics: An Introduction, appeared in 2008. A brief version of this text was published in 2003. Katz is also the editor of The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook, published in 2007. Professor Katz has written many articles on the history of mathematics and its use in teaching and has spoken widely on the subject. He presented an invited lecture, “Stages in the History of Algebra with Implications for Teaching,” at ICME-10 in Copenhagen in 2004. He has edited or co-edited two recent books dealing with this subject, Learn from the Masters (1994) and Using History to Teach Mathematics (2000). He also co-edited two collections of historical articles taken from journals of the Mathematical Association of America in the past 90 years, Sherlock Holmes in Babylon and other Tales of Mathematical History (2004) and Who Gave You the Epsilon and Other Tales of Mathematical History (2009). He has directed two NSF-sponsored projects that helped college teachers learn the history of mathematics and how to use it in teaching and also involved secondary school teachers in writing materials using history in the teaching of various topics in the high school curriculum. These materials, Historical Modules for the Teaching and Learning of Mathematics, were published on a CD by the MAA in 2005. Professor Katz is currently the editor of Loci: Convergence, the MAA’s online magazine in the history of mathematics and its use in teaching.
Norman Biggs, London School of Economics and Political Science
Mathematics in the Textile Trade
Abstract: The decline of the Huguenot silk weavers of Spitalfields was due to competition from other parts of the textile trade, in particular the cotton trade. Originally cotton could only be spun into coarse yarn, which was unsuitable for fashionable clothes, but in the second half of the eighteenth century it became possible to produce cotton yarn that was both fine and cheap in relation to silk.
In this talk I shall discuss the part played by mathematical ideas in the explosive growth of the cotton trade. Mathematics was relevant because it was important to control accurately the fineness of the yarn. The fineness of cotton (and woollen) yarn was expressed in a way that seems strange to us nowadays, because it was based on centuries of trade practice, rather than scientific principles. This inevitably led to complicated calculations, and one way of avoiding the difficulty was to use a specially-designed instrument. One such instrument was the ‘bent-lever’ balance, the theory of which was analysed by William Ludlam in 1765, using mechanics, trigonometry and calculus. For the sake of comparison, I shall also describe the mathematics of an ‘equal-arm balance’ patented by Thomas Knowles in 1883, for use in the cotton trade.
The general background to the talk can be found in two articles in Textile History: Vol 35 (2004) 120-129, Vol 40 (2009), to appear.
Biography: Norman Biggs is Emeritus Professor of Mathematics at the LSE. In addition to numerous books and papers on mathematics, he has written extensively on the history of weighing instruments. He was formerly Librarian and General Secretary of the London Mathematical Society, and is currently a member of the Council of the British Numismatic Society, and Chair of the International Society of Antique Scale Collectors (Europe). Further information can be found on his website.
Ioan James, Mathematical Institute, University of Oxford
Some Early Jewish Mathematicians
Abstract: In the words of Thorstein Veblen ‘the intellectual pre-eminence of Jews in modern Europe was due to a break with the past, not its resurrection. The cultural heritage of the Jewish people may be very ancient and very distinguished but these achievements of the Jewish ancients neither touch the frontiers of modern science nor do they follow in the lines of modern scholarship.’ The vast majority of observant Jews held rabbinical authority superior to scientific authority; this was an obvious barrier to their acceptance in the scientific community. Rabbis regarded secular science as a pagan invention, outside the Jewish tradition. However the study of law and medicine was permissible, as was mathematics, including logic and astronomy.
It is generally held that the first Jewish mathematician to enter the mainstream of modern mathematics was Carl Jacobi (1804-1851). However there were other notable early Jewish mathematicians who are not so well-known internationally, even within the Jewish community. Histories of mathematics mention them only briefly, if at all. because they did not contribute very much to research, but nevertheless their life-stories, as far as we know them, are not without interest. In this lecture I profile four, who were born in the eighteenth century, namely Israel Lyons (1739-1775), Abraham Jakub Stern (1768-1842), Benjamin Gompertz (1779-1865), Olry Terquem (1782-1862), Olinde Rodrigues (1795-1851). At the end of his distinguished career Gompertz was the last president of the Spitalfields Mathematical Society, before it was taken over by the Royal Astronomical If time allows I would like to include more Jewish mathematicians from the first decade of the nineteenth century.
Biography: Ioan James is a fellow of the Royal Society and an honorary fellow of two Oxford colleges. As Savilian professor of geometry from 1970 to1995 he led research at Oxford in the field of algebraic topology. He also served first as Treasurer and then as President of the London Mathematical Society. Since he retired he has written books on a variety of subjects, the latest being Driven to Innovate, in which he described the lives of Jewish mathematicians. and physicists born in the nineteenth century.
Dr Benjamin Wardhaugh, University of Oxford
“Two Viols were Mathematically set out…”: Thomas Salmon (1647–1706) and the practicalities of mathematical music
Abstract: In 1705 Thomas Salmon, a Bedfordshire clergyman, had the distinction of organising a musical performance at a meeting of the Royal Society: it was intended to support his theories about the mathematics of musical tuning. Although his theories have since sunk without trace, the lengths to which he went to form relationships with musical instrument makers and performers illustrate that even the most abstruse of mathematical theorising could have a vital practical and social dimension. In this talk I will trace what we can reconstruct of the path Salmon walked between theory and practicalities.
Biography: Dr Benjamin Wardhaugh is a post-doctoral research fellow at All Souls College, Oxford, where he studies the social history of early modern mathematics. He is the author of Music, Experiment and Mathematics in England, 1753–1705 and is also working on a textbook, How to Read Historical Mathematics.
Martin Campbell-Kelly, University of Warwick
The rise and decline of mathematical table making
Abstract: For three hundred years, mathematical tables were the most important aid to calculation. Some 10,000 different tables were produced during this period. Examples of tables included traditional logarithms and trigonometric functions, astronomical and navigational tables, professional tables for actuaries and engineers, and tables for military applications. This lecture traces the evolution of table-making techniques: from the solitary calculators of logarithmic tables in the 16th century; through organized teams of human computers and Babbage’s difference engines in the 18th and 19th centuries; the use of analogue and digital machinery between the two world wars; and finally the development of electronic computers during World War II. Ironically, the electronic computer—originally invented for the production of mathematical tables—led to their obsolescence and demise.
Biography: Martin Campbell-Kelly is a professor in the Department of Computer Science at the University of Warwick, where he specializes in the history of computing. His publications include Computer: A History of the Information Machine, co-authored with William Aspray, and an edited volume Sumer to Spreadsheets: The History of Mathematical Tables. He is editor of the Collected Works of Charles Babbage.
Jan van Maanen, Freudenthal Institute for Science and Mathematics Education, Utrecht University, NL
Applications convince. The case of the early calculus
Abstract: One of the main reasons for mathematicians to accept the calculus was that it had such wonderful applications (extreme value calculations, the solution of differential equations, the determination of areas and more). I shall discuss a whole range of applied problems, and demonstrate one of these (a physics problem about an equilibrium, designed by Johann Bernoulli and published by L’Hospital in the first textbook about the diffrential calculus, 1696). At that time the foundations of the calculus were more or less absent, or at any rate not yet made explicit. But the applications spoke for themselves.
Biography: Jan van Maanen is professor of mathematics education at Utrecht University and chair of the Freudenthal Institute. In his former position at the University of Groningen Jan chaired the Mathematics Education group and as of 2004 he also was chair of the Mathematics Department. He is much interested in the history of mathematics and its application in mathematics teaching. In the years 1997 to 2000 he co-chaired a large-scale international study about this topic under the auspices of the International Commission on Mathematical Instruction (ICMI). On Wednesdays Jan pays the cello in a string quartet, and sings in a choir.
| PhD | History of mathematics, 1987, Utrecht University |
| M.S. | Mathematics, 1977, Utrecht University |
| 2006- | Professor, Mathematics Education, Chair of the Freudenthal Institute, Utrecht University |
| 1992-2006 | Assistant Professor of Mathematics, later Associate Professor of Mathematics Education, University of Groningen, Netherlands |
| 1977-1992 | Secondary school teacher, combined with various research projects |
Selected publications
- Jan van Maanen, ‘L’Hôpital’s weight problem’, for the learning of mathematics 11 No. 2 (June 1991), pp. 44–47.
- —, ‘New Maths may Profit from Old Methods’, for the learning of mathematics 17 No. 2 (June 1997), pp. 39–46.
- John Fauvel, Jan van Maanen (eds.), History in Mathematics Education. The ICMI-Study, Dordrecht: Kluwer Academic Publishers 2000 (ISBN 0-7923-6399-X, 456 pp.).
- Jan van Maanen, ‘Precursors of Differentiation and Integration’, pp. 41–72 in: Hans Niels Jahnke (Ed.), A history of analysis, Providence, RI: American Mathematical Society & London Mathematical Society, 2003.
Programme
| 09.30 | Registration |
| 10.00 | Opening – Snezana Lawrence (Bath Spa University), Applied mathematics and mathematics practitioners: Spitalfields – the home of the first mathematical society |
| 10.15 | Victor J. Katz (University of the District of Columbia), Quadratic and Cubic Equations: Can We Really Apply Them? |
| 11.00 | Break |
| 11.15 | Norman Biggs (London School of Economics and Political Science), Mathematics in the Textile trade |
| 12.00 | Professor Ioan M James (Mathematical Institute, University of Oxford), Some Early Jewish Mathematicians |
| 12.45 | Lunch |
| 13.45 | Benjamin Wardhaugh (University of Oxford), Two Viols were Mathematically set out… |
| 14.30 | Martin Campbell-Kelly (University of Warwick), The rise and decline of mathematical table making |
| 15.15 | Jan van Maanen (Freudenthal Institute for Science and Mathematics Education), Applications convince. The case of the early calculus |
| 16.30 | Plenary discussion and coffee |
Conference Fees
| Non IMA Member: | £85.00 |
| IMA Member: | £70.00 |
| Student: | £60.00 |
Travel Notes
Delegate notes can be downloaded below.
Location map can be downloaded below.
For all enquiries, contact the organisers:
Snezana Lawrence (snezana@mathsisgoodforyou.com)
IMA Conference Officer (conferences@ima.org.uk).
Related Documents
Download History of Mathematics Delegate Notes [PDF]
Download History of Mathematics Location Map [PDF]
