The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art, and the Nude by Allan McRobie (review)

In many ways this is a remarkable book. It is unquestionably on fine art, but the author is an academic engineer who is obviously very mathematically knowledgeable. The question is: Does the marriage work? That it might is to a large extent down to the writing skill of McRobie. When commenting on a topic such as the beauty of curves, one is usually firmly into opinion, not fact. When describing curves and surfaces precisely, one is in mathematical fact, not opinion. The author plays it safe in that the examples he cites certainly are beautiful, and the book can be simply seen as fine art, words largely unread. But that would be a pity. Following a general introductory chapter, the next five chapters are grounded by direct comparison between his examples and the five so-called catastrophic folds (the fold, the cusp, the swallowtail, the butterfly and the wigwam). These will certainly interest those, like this reviewer, who are mathematical or scientific. I am less sure they will captivate the fine artist, though; do they care about such classifications? Maybe they should. The book then develops a wider remit and finds mathematically relevant descriptions of surfaces and curves also described precisely through the physics of optics (reflections, rainbows, gravitational lenses); then it is back to René Thom with stability and the Russian sculptor Naum Gabo, whom Thom sadly never met. The book finishes with summaries of the mathematician Thom and the surrealist Salvador Dalí. Both controversial, they did meet late in Dalí's life and got on very well.

The book is a very brave attempt to marry the precise mathematics of catastrophe theory and other related mathematics to what is meant by beauty, an attempt to link the very precise with the imprecise. This reviewer thinks it mostly successful, but credit is due to the erudition of the author plus the quality of the production both in the illustrations used and in the general elegance of the book itself. It would grace the grandest of coffee tables and provide the basis for interesting debates.