The 1998 Nexus conference on architecture and mathematics continues the dialogue begun two years ago with Nexus '96. It is certainly not surprising to find mathematics in architecture: architecture has dimension, and therefore has number; it is composed of various related elements, and therefore contains proportion. But on a more profound level, architecture and mathematics are both symbol systems aimed at expressing ideas, such as infinity, or identity. The presentations at this year's conference examine in depth some of the ideas underlying both architectural compositions and the properties of some special families of numbers, thus bringing into sharper focus the sympathies between our two disciplines.

The Romans' particular notion of their unique place in the universe provided the point of reference for the design and construction of the Pantheon in Rome. Gert Sperling addresses this as well as the role of arithmetic, geometry, music and astronomy--the Quadrivium--in Rome's most enduring monument. The massive dome of the Pantheon presented an engineering problem of no small measure. It wasn't equaled in size until the Renaissance. Salvatore di Pasquale looks at what Galileo learned from Alberti and Brunelleschi as he developed what we now call the "theory of structures". Holger Falter provides an overview of the role of mathematics in the determination of structural form.

Alberti was as concerned with the sublime as with the practical. Graziella Federici Vescovini discusses the philosophical roots for his use of the special proportions so essential to Renaissance architecture. While some of the proportions used in the Renaissance were rational, others were "specially" irrational. Vera W. De Spinadel explains how the mathematical properties of the "Metallic Means" make them such flexible design tools. But was the "Divinam Proportionem" as commonly used as claimed? Marco Frascari and Livio Volpi Ghirardini reveal the controversy surrounding its supposed omnipresence. Henry Crapo and Claude Le Conte de Poly Barbut bring to light the properties of another special family of numbers, the equiangular numbers. Can architects make use of this tool?

Paulus Gerdes reminds us that the application of mathematics to art and architecture isn't found only in Western architecture. He finds a source for architectural form in the geometry of traditional African basket weaving. As straightforward as basket weaving may appear, it often addresses such problems as squaring the circle. Michelangelo was no stranger to such problems, either, often giving to them his own special twist. Architect Ben Nicholson has teamed up with mathematician Jay Kappraff and architecture graduate student Saori Hisano to try to decipher the hidden pavement of the Laurentian Library. Two-dimensional pattern design needed necessarily be symmetrical. Michael Ostwald examines the use of aperiodic Penrose tiling in Melbourne's Storey Hall.

As dedicated to maintaining mathematical rigor as to satisfying the needs of his clients, Palladio designed the villas in which we all dream of living. Stephen Wassell takes us on a mathematical tour of "rustic" country residences. Many of Palladio's clients were Venetian, who lived in a city with a special relationship with mathematics. Michele Emmer shows us "La Serenissima" in all her geometrical splendor.

One outgrowth of the 1998 Nexus Conference was the decision to establish our new e-journal, the Nexus Network Journal. The NNJ will provide an ongoing means of communication between biennial conferences, and a venue for the publication of studies in architecture and mathematics.

I am grateful to the Accademia Nazionale Virgiliana and the Centro Leon Battista Alberti for making possible this year's meeting in Mantua. I also wish thank the Graham Foundation for Advanced Studies in the Fine Arts for having supported the publication of the 1996 Nexus publication, as well as for the grant awarded to Nexus '98 contributor Stephen R. Wassell. But our dialogue is not finished: we'll see you again at Nexus 2000 in Ferrara, Italy, 4-7 June 2000.