Blueprints How mathematics shapes creativity

Oxford mathematics professor du Sautoy (Around the World in Eighty Games) offers an impressive if occasionally perplexing exploration of links between math and the arts. He defines mathematics as "the study of structure" and argues that structure is "an integral part of artistic practice." Ranging broadly across both disciplines, he lays out nine "blueprints," or mathematical ideas, that underpin creative endeavors, noting, for example, that the abstract paintings of Jackson Pollock are heavily dependent on fractals, or patterns of repeating shapes. Elsewhere, du Sautoy delves into music, demonstrating how French composer Olivier Messiaen's use of prime numbers brought dramatic tension to his Quartet for the End of Time; investigates architecture, showing how Zaha Hadid's Heydar Aliyev Center in Baku, Azerbaijan, is dependent on Riemannian geometry, a branch of geometry used to describe curved space; and examines the written word, illustrating how circularity enriches the work of writers like Jorge Luis Borges. The book starts off strong, with many clear and eye-opening examples of underlying mathematical ideas, but as the author digs into more advanced concepts, like hyperbolic geometry, readers may find themselves lost. Still, du Sautoy constructs a solid bridge between the arts and sciences. (Sept.)