If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidean mathematicians; we should have… - Jean Metzinger

Often we were joined by Maurice Princet. Although very young, he held an important post in an insurance company which he owed to his knowledge of mathematics. But outside his profession it was as an artist that he thought of mathematics, as a specialist in aesthetics that he evoked continuities in n dimensions. He liked to interest painters in the new visions of space that had been opened up by Victor Schlegel and several others. He succeeded. After having heard him by chance, Henri Matisse was caught reading an essay on hyperspace. Oh! it was only a potboiler [un ouvrage de vulgarisation]! but at least that shows that for the great 'fauve' the days of the painter who knows nothing, who runs towards a pretty subject with his beard blowing in the wind, was passed.

Already, a conscious courage is coming to life. Here are some of the painters: Picasso, Georges Braque, Delaunay, Le Fauconnier.. ..they are highly enlightened, and do not believe in the stability of any system, even if it were to call itself classical art.. ..Their reason is poised between the pursuit of the fleeting and a mania for the eternal.

"What madman, or what clever-dick with the instincts of a counterfeiter was the first to paint a sphere in trompe l'oeil on a surface that is vertical and rigorously flat! And that's what they teach at the Beaux-Arts [academy]! How could such idiocies ever have survived the verdict of Pascal?" [quote of Albert Gleizes ]. That was how, in 1906, Albert Gleizes was feeling his way towards Cubism and condemned in advance those who never saw anything in it other than a shibboleth [mot d'ordre]. It was still nothing more than a need he felt, the need not for an intellectual art but for an art that would be something other than a systematic absurdity. Quite clearly nature and the painting make up two different worlds which have nothing in common, and what is quite in its place in the one cannot also be in its place in the other.