Mathematics and Art: A Cultural History

by Lynn Gamwell

A cultural history of the links between mathematics and art, from antiquity to today



This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration.

Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt G�del posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked What is art? in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Beno�t Mandelbrot to Max Bill and Xu Bing.

Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.

Genres: Art, Mathematics, Nonfiction, Science, History, Philosophy, Art History

584 pages, Hardcover

First published October 1, 2015

Reviews

[Brian Clegg · Rating 4 out of 5]

I have to start by saying that I have never really understood the point of coffee table books. There is no way anyone is going to comfortably read Mathematics + Art as it's around 25 cm by 32 cm, and weighs in at a wrist-crunching 3 kg, heavier than many laptops. (The price is fairly wallet-crunching too.) Although it is heavily and beautifully illustrated, though, this is much more than just a picture book of images with a mathematical association. It is a genuinely interesting text, running across over 500 pages, which I found I liked far more than I wanted to.

While there is, as is often the case with this kind of attempt to link science and the arts, sometimes a rather tenuous link to the mathematics, it is still fascinating to discover how the influence of maths on culture at large has had an impact on the arts. Sometimes this is in a quite explicit form, where an image, say, is mathematically derived or features a mathematician at work, while on other occasions it's a much more subtle connection where a topic or context is derived from the way mathematics is influencing the world at large.

Lynn Gamwell does not shy away from including a surprising amount of detail about the maths itself, with occasional boxes explaining everything from calculus to the double slit experiment in quantum physics. Her writing style feels rather closer to that of a textbook than a work intended for a wide audience, but it is nonetheless reasonably approachable, and time and again the illustrations capture the attention and the imagination.

An oddity, then - but a genuinely interesting one.

[Tony Gualtieri · Rating 5 out of 5]

This is that rarest of things: A beautiful coffee table book that contains a text that is not only a pleasure to read but also covers intriguing new ground. Ostensibly about the history of the connection between mathematics and visual art, the book moves quickly from the influence of platonism in classical and Renaissance art to a sophisticated discussion of how mathematicians such as Cantor, Hilbert, Gödel, and Brouwer inspired artworks in the first half of the twentieth century. I was impressed with the author's ability to make connections as well as her clear prose when explaining obtuse topics.

[Sally Sugarman · Rating 4 out of 5]

This is indeed a cultural history linking the work of mathematics and its effect on art throughout the centuries. What strikes one as most interesting is the way in which philosophy, mathematics, social and cultural ideas affect visual artists. Technology also plays a part with photography, film and computers changing the nature of art. As someone who spent many hours at the Museum of Modern Art, growing up in New York City, many of the works reproduced and discussed were familiar from having seen them on the gallery walls. I also thought of some of the art that we saw in the Tate Museum in London. Certainly, math led to perspectives in painting and the changes in the world both social and technological led to abstract art. Traveling between the Metropolitan Museum and the Museum of Modern Art provided many lessons in the history of art even though I did not have the context of the philosophical influences at the time. Reading this book over a rather long period of time was both advantageous and not since the author kept making references back to earlier chapters in the later ones where the impact of ideas about physics as well as the realities of the world wars increasingly affected the work of artists. This was a deeper analysis than offered by the book Art That Changed the World with fortunately a better use of the illustrations of the art works. All of the images were related to the particular discussion in a chapter and didn’t follow the rigid pattern of the other book. The images were not crowded and were larger so that they could be examined in greater detail. I have always been intrigued by the history of science and mathematics and this book did a fine job of discussing them and their relation to their time and their influence on the individual artists. I still have a four volume history of mathematics which I should read, but I did get down my copy of Godel, Escher and Bach to finally read. The effect of deepening understanding of math affected music as well as painting. It became clear how well educated contemporary artists are and the influence of their teachers. Gamwell handled the subject masterfully, explaining complex ideas clearly and relating them to the social context as well as showing how mathematics affected art. There were side bar quotes through the book that were most helpful and thought provoking. This study was worth all the time that it took to complete it.

[Tech Nossomy · Rating 3 out of 5]

A hefty tome, richly illustrated, which is a journey of discovery along the eternal "push" or "pull" debate: are artists inspired by the profound patterns that emerge from a mathematical description of our world, or do mathematicians come up with theorems and proofs that through their elegance are considered artful? The text does not take a side, but provides plenty of examples from either perspective. The art works are mostly from the visual arts, with a few forays into music and filmmaking.

The book reads more like Asimov's-non-fiction however, with many factual details and relations between the sciences and the arts. And this observation also unfolds a fundamental shortcoming: the author often takes the easy route, focusing on historical details and carefully avoiding the real relationships and patterns that govern art in so far they spring from mathematics. The theory of special relativity is mentioned a couple dozen times in the book, but whether the author truly understands the mathematical modelling behind this theory and whence its mathematical foundations came never becomes clear. It is just far easier to throw the name "Albert Einstein" in there for popular scientific reasons and leave the rest to the reader, who hopefully won't ask too many questions either.
And, going in the other direction, the artist Vasarely is mentioned a few times, but what maths he used to arrive at his works is not discussed, just that he made them.
Euler is mentioned and the convex polyhedra are mentioned, but Euler's characteristic is not, the number that relates the vertices, edges and faces of polyhedra.

The author might have drawn some inspiration from the Wikipedia page on the Collatz conjecture, which I think is a prime example of art emanating from simple to understand mathematics.

The text suffers from numerous repetitions, for example the randomness of electrons spinning around their nucleus is mentioned on a few occasions, and even entire sentences are copied verbatim throughout the book.

[Michael McEllin · Rating 4 out of 5]

I As others have remarked it is a very substantial work and not only in the physical sense. It was a revelation (though it ought not to have been) to discover that the intellectual elites in the arts and sciences were often closely connected. (One forgets that the intellectual world was then much smaller. This is a perspective that you do not get in the conventional art histories.) The author does admit that the flow of ideas was generally only in one direction - from maths to art - and I often got the feeling that quite a lot of distortion took place in the communications channel, and I know that there was quite a lot of other important non-mathematical but very influential things going on the same time. Perhaps the new perspective is somewhat overplayed? Nevertheless, I did feel that I was beginning to understand some of the reasons why, for example, there was such an explosion in abstract art starting in the early 20th Century. Well worth a read, and actually remarkably moderately priced for study of this physical and academic weight.

[Vanessa · Rating 5 out of 5]

As others have noted, the physicality of this book is a bit daunting for would-be readers. It’s large and it’s heavy, but nevertheless the text is well worth enduring some discomfort to read.

Gamwell provides a clear and fascinating perspective on art history and the history and philosophy of mathematics as they’ve evolved in parallel. It’s probably the best book I have read on either subject, so I think it deserves a lot more attention.

Definitely recommended if you can afford it, but don’t let it gather dust on your coffee table! Put a pillow in your lap, open it flat (the book is well-bound) and read it cover to cover.

[Debora Ewing · Rating 4 out of 5]

I wish I'd had more time to fully immerse in this book. I was reading it in sections with my book group. Some of the connections between philosophy, math, and art were surprising; some were edifying. I'll bet Gamwell has enough material from her extensive research to write another book peripheral to this one.

[Reina Meza · Rating 5 out of 5]

This is my favorite go to when I'm wanting to feed my brain some knowledge. If you're into science and art it's a must read!

[Mills College Library]

700.105 G194m 2016