There has been a growing interest in the interaction between mathematics and architecture. That was the reason that the first Nexus conference on this topic was organized in 1996 and these conferences are being organized on a biennial basis ever since. The need for a platform to discuss this interaction on a more continuous basis grew and soon the Nexus Network Journal (NNJ) was started by Kim Williams. It is available since 1999. She and Michael Ostwald, who is the current editor in chief of the NNJ, have collected in this period almost 100 papers on the subject that they have collected in this comprehensive two volume set.
The ambitious goal is to describe both the intimate relation but also the alienation between mathematics and architecture and between mathematicians and architects. The issue is covered both thematically and chronologically which means that concepts such as measurements, composition, skills, etc. are discussed and that such groups of papers are interlaced with sets of papers that deal with a certain period. Of course, as time evolves, new concepts were born, changing the way people look at ideas causing the rise and decline of tools and techniques and the way architecture is realized.
The two volumes consist of 9 parts, each collecting an average of around 10 papers written by experts. That includes architectural historians, designers, mathematicians, engineers, philosophers, and computer scientists. This diversity already illustrates the broadness and the interdisciplinary aspects of the material. Each volume starts with a paper that gives an extensive description of the contents of the books. An obvious start is to try to answer the question what the common or binding concepts between the two disciplines are. This is followed by a discussion of the first period 2000 BC - 1000 AD. Then it is explained how mathematics became important in developing methods of measurements and to guarantee stability of constructions. That is explored in the historical section 1000 - 1400 (from Medieval to Romanesque with early Gothic churches). Next the concepts of proportion, symmetry and periodicity are introduced. While Vitruvius referred to the human body, now ratios were related to a music scale. These concepts of course became important in the Gothic buildings and even more so for the Renaissance in the period 1400 - 1500. Of course several famous buildings are discussed in detail with ample illustrations. The examples cover geographically not only the obvious regions that influenced Western civilization like Egypt, Greece, Rome, Persia, etc., but include also Mayan and Indian elements.
The second volume continues in the same style. There are two historical parts covering the periods 1500 - 1800 and 1800 to the present time respectively. The first period is connected with the introduction of perspective and work by Palladio, Borromini, Michelangelo, Wren,... After 1800, we meet Frank Loyd Wright, Le Corbusier, Louis Kahn, Niemeyer, Gerhy, and many others with all the variants of Modernism and Post-Modernism. In the later parts of this volume also architecture from North America and Oceania enters the picture. It is in the nineteenth-twentieth century that mathematics and architecture somewhat diverged, being in the different continents of science and arts that were drifting away from each other like tectonic plates. Although of course many architectural constructions were only possible because of technical evolution and there were definitely interactions of how mathematics and architecture developed. For example new mathematical findings such as aperiodic tiling were applied by architects and computer systems were used to analyze ancient amphitheaters or laser scans were used for 3D modeling. Towards the end the thematic and historical subdivision becomes more fuzzy. The concluding part of this volume even sheds some light on the future, highlighting opportunities and challenges that arise by increased application of computers in architecture.
Even if you start reading, convinced that mathematics and architecture are related and amply interact, you will still be surprised in how many aspects they are interwoven. Even though sciences and arts have separated, the mutual love between mathematics and architecture has never died, and as you read the later chapters in the book, it will be clear that the mutual attraction is nowadays still very strong, like the Nexus platform, the Nexus journal, and these volumes and several other books illustrate. It is an important and highly inspiring collection of papers that will be of interest to researchers from as many disciplines as illustrated by the diversity of the background of the authors. It revives some of the former polymath idea that has been gradually lost in the 20th century. Highly recommended for readers who do not want to drown or hide in their own abyss of specialization.