Book Review: ii Mathematics and Art: A Cultural History

Last time I suggested that philosophy is missing from the title. Architecture is another very welcome theme in the book, the significance of perspective to art being obvious, but not the only focus. As mentioned the preface is an invitation to dive in. The oldest star atlas (xi), Chinese, sets the scientific and global tone to follow. My interest in diagrams, was quickly awoken as there are many in this book. I recalled the lunar cycle depicted on cave walls and bone. The first diagrams from prehistory. The preface works brilliantly as an introduction, such that I couldn't wait for chapter 7: "Scientists describe such symmetries using the mathematics of group theory" (xv).

Mathematics + Art

For young scholars the book plays the role of sign-posting schools and history of thoughts and ideas. [Paraphrasing..] Adorno and Horkheimer ... wrote the first in-depth analysis of the loss of confidence in enlightenment ideals, a condition that came to be called postmodernism (xviii). There's an observation of artists being inspired by mathematics, but not mathematicians drawing upon art - with some rare exceptions. When possible, Gamwell's approach to the personality and intellectual environment of mathematicians and artists is psychological (noting key traumas), at others the author adopts a more sociological and cultural stance. The prose throughout is clear and flows very well, even with some inevitable and necessary cross-referencing.

Chapter 1 Arithmetic and Geometry brings home the relationships and dependencies between maths, arts, belief and changes in our understanding of the Universe. When I learned in my teens of the destruction of the Library of Alexandria, which Ptolemy would have visited, (p.30) I was shocked and still am at this loss. Sadly a loss that is not just an ancient phenomenon.* Interested in astronomy, the loss of Hipparchus's globes and co-ordinate system is a further blow. A cross-cultural perspective is maintained throughout the book, with Islamic mathematics, South America and Asia. Do you know the difference between philosophy and mathematics? There is an opinion here. From the Greeks - Neoplatonism, early Christian and medieval thought and the 'liberal arts', I knew the modern book version of the 'Quad-rivium' on my shelf was of significance:

"In the late Roman and early Christian era, scholars continued to study the ancient texts based on a curriculum - arithmetic geometry, music, and astronomy (the quadrivium, Latin combination of quadri and via meaning "the place where four roads meet") - first described by the Pythagoreans and adopted by Plato for his Academy." (p.37)

An original purpose for Hodges' model, remains curriculum planning and development, the definition of the core disciplines of learning has always been a roll call of sorts. The book can serve all, but younger scholars especially, as it sets out the formulation of scholastic traditions which have a chapter each:

1. logicism (chapter 5): Realism - St Augustine - Platonic realm
2. intuitionism (chapter 6) - Conceptualism - Peter Abel - distinct objects only in the mind
3. formalism - (chapter 4) Nominalism - William of Okham - mere signs or names (p.37)

Even today we must ponder on the status of the seven liberal arts, the quadrivium plus the trivium of grammar, rhetoric and logic. To classics scholars this will be introductory, but invaluable grounding for many learners - young and more senior.

There is an account of eastern and western cultures and the relative development of mathematics. The sciences and theology feature markedly as human reason made progress - increasing certainty only to suffer from doubt with new discoveries. The 'via negativa' (Latin for "negative way", p.47) reminded me of two books on ignorance I purchased in London. I arrived there March 12th and soon thought; "What on Earth (as a nurse too) am I doing here?" Especially, being in the basement for Jazz Live at Pizza Express, Soho. These are indeed uncertain and challenging times.

You may have noticed I have not mentioned the art thus far. Well there is plenty. By page 47 we are up to plate 1.52 'The Cloud of Unknowing' 1998 by Roman Verostko.

Post iii soon.

*In lockdown I followed a conversation on the destruction of libraries from the digital Hay Festival:

https://www.crowdcast.io/e/hayfestival_event32

(This does require a subscription to Hay Player.)