An interesting review of cubism in the Guardian talks of the influence Henri Poincaré had on Picasso.
Cubism was never a style in that sense. It was an inquiry. Picasso and Braque were lucky enough to be young - Picasso was 28 in 1909, Braque 27 - at a time of intellectual revolution. Habits of perception and assumptions about the nature of things that had been stable since the 17th century were falling away. Arthur I Miller's 2001 book Einstein, Picasso: Space, Time and the Beauty that Causes Havoc demonstrates how uncannily Picasso's discovery of cubism parallelled Einstein's contemporary theories of special and general relativity. In science, mathematics and philosophy, the laws of a clockwork universe established by Sir Isaac Newton in the Baroque age were giving way before the first world war to extraordinary notions - that time and space are one, that light waves curve, that no two observers ever see exactly the same thing.
Picasso and Einstein, Miller has shown, were both influenced by the French thinker Henri Poincaré, who published his book La Science et l'Hypothèse in 1902.
Picasso learned about his ideas through the mathematician Maurice Princet, who was a regular at Montmartre cafe tables. Picasso's friend André Salmon wrote that Princet "preoccupies himself especially with painters who disdain ancient perspective. He praises them for no longer trusting the illusory optics of not long ago... "