For the artist, mathematics does not consist of the various branches of mathematics. It is not necessarily a matter of calculation but rather of the presence of a sovereign power; a law of infinite resonance, consonance, organisation. Rigour is nothing other than that which truly results in a work of art, whether it be a Leonardo drawing, or the fearsome exactness of the Parthenon (comparable in the cutting of its marble even with that of machine-tools), or the implacable and impeccable play of construction in the cathedral, or the unity in a Cézanne, or the law which determines a tree, the unitary splendour of roots, trunk, branches, leaves, flowers, and fruit. Chance has no place in nature. Once one has understood what mathematics is – in the philosophical sense – thereafter one can discern it in all its works. Rigour, and exactness, are the means behind achieving solutions, the cause behind character, the rationale behind harmony.

Le Corbusier, 1948

Probably everyone reading this article has heard of Le Corbusier, no doubt the most famous architect this century, but the images he will arouse in their minds may vary greatly. Some will blame him for those theories promoting standardized high rise construction, which have dominated town planning policy in post-war Europe. Others will admire his highly individual, sculptural buildings such as the church at Ronchamp (1950–55) (see Figure 1), the revolutionary public housing scheme of the Unité d'Habitation at Marseilles (1946–52) (Figure 2), its ground-level pillars (pilotis) and roof-level service stacks alike transformed into enigmatic statues, or his pre-war Purist villas in the Paris suburbs (1920s). His work displayed a wide variety of forms and spaces at any one time, and his career spanned almost sixty years, during which he was constantly questioning, and reformulating theories, and in consequence changing his formal language.