Today, 17 July 2012, is the centenary of the death of the great French polymath Henri Poincaré, once described as the "last of the universalists". His achievements span mathematics (he set the basis for chaos theory), physics (his mathematical methods are still used in studying elementary particles), philosophy (his framework for exploring scientific theories is still controversial) and the psychology of creativity (he studied the workings of the unconscious).

Poincaré also acted as a surprising link between Einstein and Picasso, who were both inspired by his best-selling Science and Hypothesis, published in 1902.

Working as a patent clerk in Bern, Switzerland, Einstein was at the core of a study group, his "think tank", one of whom described how Poincaré's book had "held them spellbound". In it Poincaré moves from an analysis of scientific theories to analysing perceptions to probing thought itself, transporting the reader in crystal-clear prose to the very frontiers of knowledge. As Einstein wrote years later: "Poincaré realised the truth [of the relation of everyday experience to scientific concepts] in his book."

But Einstein found Poincaré's dependence on everyday experience and laboratory data too restricting. In spring 1905, he went one step further. The result was his theory of relativity.

Far from being a stereotypical scientist, Poincaré's thinking was closer to that of an artist. Édouard Toulouse, a psychologist specialising in creativity, interviewed him in 1897 and wrote that Poincaré's thought "was spontaneous, little conscious, more like dreaming than rational, seeming most suited to works of pure imagination".

So it's hardly surprising that Picasso too was inspired by his work. But how did he hear of him? Picasso had a "think tank", of avant-garde literati who kept him up to date on the latest developments in science and technology. One rather unlikely member was Maurice Princet, an insurance actuary with a keen interest in advanced mathematics and philosophy. After bistro dinners he gave impromptu lectures – often on Science and Hypothesis.

Picasso was particularly struck by Poincaré's advice on how to view the fourth dimension, which artists considered another spatial dimension. If you could transport yourself into it, you would see every perspective of a scene at once. But how to project these perspectives on to canvas? Poincaré's suggestion in Science and Hypothesis was to do so one at a time, showing each in succession. Picasso disagreed. He wanted to depict them all at once.

Listening to Princet, Picasso realised that geometry offered the language to express the deep meaning of primitive Iberian art, which he was working on at the time. In Les Demoiselles d'Avignon, he depicts one of the demoiselles simultaneously full face and in profile, two perspectives at once, a projection from the fourth dimension. He had gone beyond Poincaré.

But though Einstein and Picasso transcended Poincaré, his work spurred them towards the proper path by making them think beyond their disciplines.

Einstein met Poincaré in 1911; they disagreed on relativity theory. Picasso never met either and was unaware of Einstein's existence when he created Les Demoiselles d'Avignon, which contained the seeds of Cubism.

So who was Henri Poincaré? Born 29 April 1854, in Nancy, France, he was a precocious child and had a stellar university career, launching into mathematical research of extraordinary originality. In 1889, he received the King Oscar II Prize for research into the stability of the solar system. This led him to create topology and then, in 1904, to the conjecture that the sphere is the simplest shape in three dimensions. Not as trivial as it sounds: it took almost a hundred years before his conjecture was proved by an eccentric Russian mathematician, Grigori Perelman, who then dramatically refused the million dollar prize for solving it. In 1905 Poincaré worked out the mathematical method for exploring how electrons move at velocities close to that of light. This would become essential for framing Einstein's relativity theory in four-dimensional space-time (three spatial dimensions with a fourth dimension – time).

Of medium height, Poincaré was portly and slightly stooped, with a full beard, thick glasses and a legendary air of distraction. His manuscripts, which I discovered in 1976, contain page after page of abstract mathematics and detailed calculations in physics and astronomy, with hardly a line crossed out. In his philosophical works and essays too, a single draft sufficed. He won every scientific prize except the Nobel – for which much lobbying took place on his behalf.

A highly cultured man, he was director of l'Académie Française (the pre-eminent French literary academy), as well as President of l'Académie des Sciences, an extraordinary honour.

He once wrote: "It is only through science and art that civilisation is of value." He straddled two worlds, inspiring both Einstein and Picasso and played a pivotal role in sparking the explosion of creativity in both art and science that set the tenor of the 20th century.

• Arthur I Miller is the author of Einstein, Picasso: Space, Time and the Beauty that Causes Havoc