People are often a bit puzzled upon learning that I received a B.S. in Architecture (1984) before receiving a Ph.D. in Mathematics (1990) from the University of Virginia. One may state that this seems like an odd combination or question why I switched fields. Fortunately, this then becomes an opportunity for me to profess my interest in the interdisciplinary study of mathematics in architecture. It is important to stress immediately that this does not comprise a study of structure or architectural engineering per se, but rather an investigation into the mathematics inherent in the aesthetics of design.
Although my interest in the study of math in architecture has existed for several years, the organization of my ideas on the subject, as well as my confidence in its validity, were crystallized during the summer of 1994, while in Paris attending the XIth International Congress of Mathematical Physics. I had the opportunity to explore the architecture of this vibrant city and found it to be replete with extraordinary examples of geometry, proportion, and symmetry. This experience inspired me to offer a course entitled "Math in Architecture" during the 1995 Winter Term at Sweet Briar College (the Winter Term is a four-week term ideal for experimental classes). The success of this course, and the fun I had researching for it, led me to continue my studies. Given the opportunity of a sabbatical year, I feel compelled to return to Paris for an extensive exploration of the mathematics inherent in its architecture in order to produce a number of expositions that I can share with my students and with the growing number of scholars who welcome the marriage of these seemingly disjoint disciplines.
The interdisciplinary study of math in architecture, though possessing a rich history in its own right, may best be appreciated in light of more recent developments aimed at bridging the gap between art and science in general. Indeed, the study of the commonalities in these apparently disparate areas has evolved during the second half of this century, in spite of society's inclination toward specialization, into a bona fide field involving a great many scholars representing all of the arts and sciences. From a mathematician's point of view, one may argue that the origins of this modern renaissance can be traced to the 1952 publishing of Symmetry by Hermann Weyl, one of this century's leading mathematicians. This delightful text evolved from courses that Weyl taught at Princeton University, and it includes many examples taken from nature, art, and architecture, as well as several sophisticated mathematical results. Two contemporaries of Weyl were equally influential. The artist M.C. Escher created works which embodied a variety of mathematical concepts, e.g. symmetry, self-similarity, recursion, and topological equivalence. And the engineer and architect R. Buckminster Fuller made an art out of structural purity, using simple geometric forms for aesthetic as well as functional purposes. The works of these influential men showed the potential in blurring the borders between art and science. However, the tendency towards specialization in all matters of life, though necessary to achieve great strides in science and technology, would keep most scholars within their own disciplines for many years.
During the past several years, however, many have begun to embrace working amidst the fringes of artificial borders. A good example of this is Gödel, Escher, Bach: An Eternal Golden Braid, which earned Douglas R. Hofstadter, a professor of computer science and cognitive science at Indiana University, the Pulitzer Prize (General Nonfiction category) and the American Book Award (Science Hardback category) in 1980. This book explores the commonalities between the concepts exhibited in the works of the mathematician Kurt Gödel, Escher, and the composer J.S. Bach, particularly regarding the use of recursion in their works. More recently, in 1991, Jay Kappraff, a mathematician at the New Jersey Institute of Technology, published Connections: The Geometric Bridge Between Art and Science. This thorough "exploration of the mathematics of beauty," with topics including myth, music, architecture, art, and mathematics, shows that, whether the bridge is natural or man-made, the connections between art and science are plentiful and inspiring. A third illustration of the acceptance of crossing disciplines i sht egreat sucess of the Art and Mathematics Conference, organized in 1992 by Nat Friedman, a professor of mathematics at the State University of New York at Albany. This conference has now been held each summer for the past five years, bringing together renowned artists, mathematicians, and other natural and social scientists for a week of sharing art, math, and insights into the relationships between them.
By far the best indication of the validity of the interdisciplinary study of math in architecture, however, was the arrival of the conference Nexus '96: The Relationship Between Architecture and Mathematics, held in Florence, Italy in the Summer of 1996. This conference was organized by Kim Williams, an American architect living and working in Tuscany, who has published several articles on the use of mathematical principles in architectural monuments and in paving designs in journals such as Mathematical Intelligencer and Leonardo. The first major gathering of its kind, Nexus '96 attracted dozens of scholars from around the world; abstracts of the presentations can be found on the web page, http://www.leonet.it/culture/nexus96/.
Ms. Williams has invited me to give a presentation on Palladian villas at Nexus '98, which will occur in the summer after my sabbatical year. After speaking at this conference, and after leading a select number of participants on a two- to three-day excursion through the Veneto to experience several of Palladio's designs first-hand, I will travel to Paris to undertake a comprehensive investigation of its architecture, with an eye on the mathematical qualities of the designs. This experience will lead to the production of a number of articles, and it is my hope eventually to write a book-length manuscript. In any case, I plan to offer an updated version of "Math in Architecture" during the 1999 Winter Term.