Discovering the sole source of an artistic movement is problematic. More often than not, a myriad of obscure factors gradually and subtly accrete until a creative explosion occurs. Much of the credit for inspiring the cubism of Pablo Picasso and Georges Braque has been given to Paul Cezanne, the post-impressionist painter who reduced objects to their essential forms. His reductive and distinct analysis of human perceptions and primary qualities clearly preludes the pioneering efforts of young artists working in Paris immediately before and after the First World War. However, another less reported influence on Cubism must be included in any adequate appraisal of that movement – the influence of mathematics.
Several posthumous shows in Paris from 1904-1907 revealed the extent of Cezanne’s exploration of form and perspective. The young men and women who walked through those galleries and beheld the brilliance of Cezanne’s originality realised the irreversible effect his work would have on future artistic endeavours. The emergence of primitivism – the idea that less materially developed cultures are closer to the truth of nature – and the increasing popularity of African masks, helped inform the rigidity and clarity of depicting subjects via basic shapes. The derivation of style from Cezanne and primitive pieces offered the avant-garde a direction away from what Braque called ‘the false tradition’, but the largely forgotten mathematician, Maurice Princet, also deserves recognition for his contribution to the genesis of Cubism.
Maurice Princet was a French mathematician who worked as an actuary. He loafed around Montparnasse and Saint Germain during the turn of the century, drinking with painters and poets while divulging the major breakthroughs in modern mathematics. His translations of formal mathematical developments into layman terms lent his creative companions an analytical edge over their contemporaries. He gleefully provided casual lectures for aesthetic cenacles who regularly gathered at the notorious Bateau-Lavoir and inspired a healthy interest in new ways of comprehending reality. In 1903, Princet showed his friend, Picasso, the works of Henri Poincare and explained the concept of the fourth dimension to the budding genius. He gifted the prodigious Spaniard a text entitled ‘Traité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions)’ by Espirit Jouffret in which the author expatiates the geometric layout of hypercubes and polyhedra, showing his readers how to portray these notions in two-dimensions upon a page. In the sketches Picasso drew towards his cubist masterpiece, Les Demoiselles d’Avignon, historians have noted the lessons the painter evidently learned from Princet and Jouffret, with some deeming Picasso’s mathematical education seminal in his approach to Cubism. In 1907, Princet’s close relationship with the artistic community of Paris came to an abrupt end. His wife suddenly left him for the famous Fauvist, Andre Derain, and a distraught Princet quietly drifted away, avoiding as many reminders of this deep humiliation as possible. However, his popularity with artistically inclined thinkers in France meant he soon gravitated back to meetings where talks about theories of painting and the application of newfound mathematics on the medium were passionately and assiduously conducted.
Some of the biggest names in modern art acknowledged Princet’s intellectual leadership during the evolution of cubism. Maurice de Vlaminck wrote ‘I witnessed the birth of cubism, its growth, its decline. Picasso was the obstetrician, Apollonaire the midwife, Princet the godfather’. Marcel Duchamp said to a friend ‘we weren’t mathematicians at all, but we believed in Princet’. And in his memoir, Metzinger describes Princet as follows – ‘it was as an artist that he conceptualised mathematics, as an aesthetician that he invoked n-dimensional continuums. He loved to get the artists interested in new views on space…..he succeeded at that’.
Since ancient times, mathematics has exerted an enormous influence over the arts. Fundamentally connected though obviously divergent, mathematics, like philosophy, seeks to clarify and prove, whereas art tries more to mystify and amaze. But the lucidity of mathematics certainly has the power to refresh an artistic perspective, opening alternative avenues of understanding to those tasked with expressing the condition of human existence. In the 4th century, the Greek sculptor, Polykleitos, proposed the proportions of the perfect male nude. Those proportions are believed to be based on the ratio 1:√2. Ancient ideals akin to the aforementioned would determine the styles of later phases such as the Renaissance. The Renaissance itself was affected by contemporary geometric theorems and mathematical conceptions, chiefly derived from the works of Luca Pacioli. And the prevailing aesthetic proclivity of Islam clearly shows an indebtedness to mathematics.
In moments of extraordinary artistic progress, an inventive and imaginative appreciation of mathematics seems to spur artists on to reveal the unseen and adumbrate the abstract. When the next Copernican leap in the visual arts ensues, scan its origins for the fingerprint of at least one mathematician. She or he will be owed as much praise as we owe Maurice Princet.