Schedule of Talks for the 2007-2008 Academic Year

Date:	Wednesday, October 10, 2007
Speaker:	Prof. Len Berggren Department of Mathematics Simon Fraser University Email: len dot berggren at gmail dot com
Title:	Artistic Problems in Islamic Geometry
Abstract:	Islamic architecture is famous for its striking tile designs - those of the Alhambra being the most well-known. In the tenth century C.E. the mathematician Abu al-Wafa' al-Buzjani wrote a book on the mathematical techniques needed by artisans, in which we find much material relating to the design of such tilings. Abu al-Wafa is known to have discussed these problems with artisans, and was sensitive to their requirements, but he also exposed their errors and treated his problems strictly from a mathematical point of view. In this talk we shall survey Abu al-Wafa's problems and his solutions, including problems dealing with so-called 'rusty compass' constructions and geometrical dissections.

Date:	Wednesday, November 7, 2007
Speaker:	Dr. Emili Bifet emili dot bifet at gmail dot com
Title:	Paolo Ruffini and the Beginnings of Group Theory
Abstract:	In 1799 Paolo Ruffini published La teoria generale delle equazioni, a lengthy book with a revolutionary claim: general equations of degree higher than the fourth cannot be solved by radicals. In this talk we shall have a look at Ruffini's mathematics and its influence on subsequent events.

Date:	Wednesday, December 5, 2007
Speaker:	Prof. Lee Stemkoski Department of Mathematics & Computer Science Adelphi University Email: stemkoski at adelphi dot edu
Title:	Euler's Notebooks and Unpublished Manuscripts
Abstract:	Leonhard Euler (1707-1783) is one of the most important and prolific mathematicians in history, having written over 800 articles and books. The republication of his complete works has been underway for over 100 years, and is still in progress today. We will examine these efforts and survey some of the contents of Euler's notebooks and unpublished manuscripts, placing them in the context of his life and published work.

Date:	Wednesday, February 6, 2008
Speaker:	Larry D'Antonio School of Theoretical and Applied Sciences Ramapo College of New Jersey Email: ldant at ramapo dot edu
Title:	Henry Smith contra Minkowski: a 19th century Cause Célèbre
Abstract:	The British mathematician Henry John Stephen Smith (1826-1883) is perhaps best known for how often he is forgotten. This talk will tell the tale of his most famous overlooked work. In 1882 the Paris Academy set a prize contest to find the number of representations of an integer as a sum of five squares. The only difficulty was that Smith had already solved the problem in 1867. When questioned about this, Hermite assured Smith that he had only to submit his solution and the prize would be his. Smith feverishly worked on polishing his previous paper to beat the fast-approaching prize deadline. The stress of his efforts apparently played a role in Smith's demise. He never lived to see the findings of the prize committee and the subsequent international furor. The committee decided that the prize should be shared by Smith and a previously unknown eighteen year-old Hermann Minkowski. Was Minkowski aware of Smith's earlier work? Did the Paris Academy act shamefully towards Smith? What role did national sentiment play in discussions of the controversy? We will examine these questions and also look at the history of the problem of representing integers as the sum of squares. This problem has a rich history and is very worthy of consideration on its own merits.

Date:	Wednesday, April 2, 2008
Speaker:	Christopher Baltus Department of Mathematics State University of New York, Oswego Email: baltus at oswego dot edu
Title:	Euler, Continued Fractions, and the Pell Equation
Abstract:	Euler did not invent continued fractions, but he invented the subject. Where Wallis had given a couple pages of formulas, Euler established ties to differential equations and infinite series, and studied a variety of special forms. In the broad context of his continued fraction work, we will look at his solution to the Pell equation, illustrating Euler's brilliant exploitations of examples to arrive at general forms and the intense interest in computation. We will also see that his lesser interest in theory limited his achievement in the case of the Pell Equation, where the young Lagrange quickly surpassed him.

Date:	Wednesday, April 9, 2008
Speaker:	Jean-Paul Pier University of Luxembourg Email: jppier at pt dot lu
Title:	Bourbaki, an epiphenomenon in the history of mathematics
Abstract:	The constitution of Bourbaki was one of the most striking and the most influential moments in the history of 20th century mathematics. The phenomenon is quite unique due to its conception as well as its exceptionally long duration. Thirty-five years after David Hilbert's fully axiomized treatise on elementary geometry, the Bourbaki group launched the axiomatized presentation of large mathematical domains, in their utmost useful generality. The Bourbaki archives up to the 1950's have been disclosed. They will be progressively available online, accompanied by comments and explanations.

Date:	Wednesday, May 7, 2008
Speaker:	George Rosenstein Franklin and Marshall College Email: george dot rosenstein at fandm dot edu
Title:	Granville, the Man and the Book
Abstract:	Arguably, the most used calculus book in the United States during the first half of the 20th century was Granville, Smith, and Longley. I have described it elsewhere as the first 20th century text in the U.S. The first edition, appearing in 1904, was authored by Granville alone. In this talk, I will describe the twists and turns of this Minnesota farm boy as he becomes a faculty member at Yale, the author of a best selling text, the president of a Pennsylvania college, and a Chicago insurance executive. I will also talk about the first edition itself and how it differed from its predecessors.

Date:	Monday, June 23, 2008
Speaker:	A Special Summer Colloquium Talk by Ivor Grattan-Guinness Middlesex University
Title:	Solving Wigner's mystery: the reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences
Abstract:	Abstract: In 1960 the physicist Eugene Wigner published a very influential article on "The unreasonable effectiveness of mathematics in the natural sciences." I counter the claim stated in its title with an interpretation of science in which many of the uses of mathematics are shown to be quite reasonable, even rational, though maybe somewhat limited in content and indeed where ineffectiveness can be found. The alternative view emphasizes two factors which Wigner largely ignores: the effectiveness of the natural sciences in mathematics, in that much mathematics has been motivated by interpretations in the sciences, and still is; and the central place of theories in mathematics and the sciences, especially theory-building, in which analogies drawn from other theories play an important role. A major related feature is the desimplification of theories, which attempts to reduce limitations on their effectiveness. Significant also is the ubiquity and/or generality of many topics and notions in mathematics. It emerges that the connections between mathematics and the natural sciences are, and always have been, rationally though fallibly forged links, not a collection of mysterious parallelisms.