This volume of essays on topics in the history of mathematics consists of the term papers prepared by the participants in a Seminar on the History of Algebra conducted within the Honors Program of Rutgers University in Spring, 2002. About half of these essays deal with topics in the history of algebra as such, and the remainder with other topics in the history of mathematics generally, or, indeed, with the place of mathematics in contemporary popular culture. The essays are arranged here in reverse chronological order.
Melissa Schofer, our local journalist, leads off with a discussion of representations of mathematics in contemporary culture, and what seems to be a heightened interest in that field, as a source of news and artistic inspiration. (We are grateful to Susan Picker for supplying several references to scientific studies of attitudes toward mathematics and mathematicians.) Jonathan Salinas then takes us back to World War II and the development of proto-computers at the hands of Alan Turing, work which was highly classified and only began to be revealed in any detail about 1974. We then jump to the late 17th century, the time of Newton and Leibniz, with Ari Pattanayak taking the side of Leibniz (with the assistance of both Joseph Hofmann and Rupert Hall), and Anand Kandaswamy examining the complex personality of Newton.
Before Newton, of course, we have Copernicus and Kepler on the astronomical side, and Descartes on the purely mathematical side. Nilay Patel, our scientist, discusses the role of Kepler both as a defender of the Copernican system and a harbing er of a new kind of mathematical physics, while Deepak Kandaswamy discusses Descartes' role as the putative founder of analytic geometry (with a nod to the ancient Greek Apollonios, and others). Standing behind Descartes is the shadowy but impressive figure of Frangois Viète, elucidated by Jennifer Orlansky. It is not very easy to extract clear information about his role from secondary sources, and the estimable Jacob Klein is hardly a model of clarity; while it may not be entirely clear from this account what Descartes, for one, managed to find in Viète, the essay should shed some light on the matter. With Descartes and Viète we arrive at the culmination of the development of high school algebra.
Moving backward, we jump to the medieval period, leaping over the other high points of the European Renaissance school, back before the invention of the system of printing from movable type, and we land in the thirteenth century: here Teresa Kuo recounts something of the extraordinary mathematics of Leonardo of Pisa, known as Fibonacci, and his near contemporary Jordanus de Nemore, of far more modest stature, more representative of the age. Our last essay, by Patricia DiJoseph, summarizes the convoluted history of the classical unsolved Greek problems: duplication of the cube, trisection of the angle, and quadrature of the circle, a subject which spans the whole period from the 6th century B. C. down to the 19th century A.D., linking the ancient (pre-Euclidean Greeks) with Descartes and Viète, and eventually Gauss and his contemporaries. This is a large topic, to which one could easily devote a semester (and indeed, Professor Gindikin did exactly that, once).
Biographical sketches of the authors are included. Where the information supplied by the authors was inadequate, we have allowed our unbridled imagination to fill in the gaps. This way of proceeding is not original with us (Proclos comes to mind).
G. Cherlin, Rutgers University, May 2002
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