Mathematics and Art: A Cultural History

Lynn Gamwell

(Princeton University Press, 2015); hbk, £37.95

Secondary school education seems to continually instil pupils with the concept of the incompatible nature of the discipline of mathematics and the arts. Indeed, such is the acceptance of their opposition that you tend to fall into the category of being good at one and not the other. Lynn Gamwell, however, as the mastermind behind the incredible Mathematics and Art: A Cultural History, must have been part of the lucky few in school who were inexplicably good at both subjects.

That this book falls into the “coffee table” bracket of reading material is highly deceiving of its fine composition and intellectual weight. True, at 25cm by 32cm and 3kg it may constitute a coffee table in its own right; however, across the 500 pages there is a wealth of incredible images, carefully selected to illustrate the ideas discussed in the text. A fine balance is found in the integration of text and image. Flowing between double-page spreads of solely images and solely text, often to a collage of both, the book never ceases to capture your visual attention and intrigue.

Beginning with the origins of mathematics in Greece and Asia, Gamwell attempts to re-evaluate our conception of these foundations. Explaining Taoism’s belief in nature’s self-assembly, Gamwell shows how this naturally inhibited further investigation, whereas the Western belief in a Divine person engendered fascination for the means of their order and chaos. Moving on to a more Germanic focus of philosophy in the last two hundred years, Gamwell notes the reorientation from theology to science as the creation story was continually debunked by our understanding of the body and physical properties of the world. Marking out concurrent developments in both fields and how they have continually influenced each other, there remains a central opposition between reason and intuition. Culminating in Gödel’s “proof by computation”, which in turn influenced Alan Turing’s computer work, we reach our current position of both artists and mathematicians employing the computer in their field of study, though sadly Gamwell does neglects to offer further comment on the future of these relationships.

In most cases we see how the mathematics has inspired the art, showing the links between the two fields, whether in specific historical documents or through the popularisation of maths as way of reaching the artist. Gamwell’s method of investigation is slightly inconsistent, swapping between taking individuals on a psychological basis and at other times sociologically placing them in their context. However, this approach proves successful in how it ultimately seeks to explode the famous yet vague intellectual climates responsible for the huge shifts in our conceptualisation of the world. Interestingly, Gamwell questions the immunity from post-modern critiques of certainty that mathematics has constituted for itself by rooting such concepts of truth deeply in its history.

Her clear commentary does not falter from the resounding message of the intricate relationship and inter-subjectivity present in the two fields.. If maths is the logic of the world- like the code that constructs the world of a computer game- then it is an obvious location for philosophers and artists alike to ponder the operations of nature.

What is central in Gamwell’s discussions, and is crucial in its subtly simple equation of the two fields, is the concept of self-reflection. Gamwell shows that it is no different to ask “what is art” as it is to question the nature of the symbols that hold mathematics together, as David Hilbert and Alexander Rodchenko did respectively. Both practices share an attention to the physical world, and in deciphering its mechanisms the many connections that are thrown up make this book compelling in its revelatory surprises.

The greatest success of the book is how mathematics is completely demystified. Not shirking from its abstract language, clear descriptions and diagrams are used to initiate the view of these symbols’ proximity to “art”, as visualisations of abstract thoughts. The influence this “international language” has provided artists with is notable- and a relationship that is too long neglected considering the universality of “the language of exact thought”. 

Jamie Madden