, 1910
Portrait of Daniel-Henry Kahnweiler,
Art Institute of Chicago , 1910,
Nu à la cheminée (Nude). Exhibited at the 1910 Salon d'Automne. Black and white scan from
Les Peintres Cubistes by Guillaume Apollinaire, 1913. Dimensions and whereabouts unknown. , 1913,
Portrait de l’éditeur Eugène Figuière (The Publisher Eugene Figuiere),
Musée des Beaux-Arts de Lyon French
mathematician Maurice Princet was known as "le mathématicien du cubisme" ("the mathematician of cubism"). An associate of the
School of Paris—a group of
avant-gardists including
Pablo Picasso,
Guillaume Apollinaire,
Max Jacob,
Jean Metzinger, and
Marcel Duchamp—Princet is credited with introducing the work of
Henri Poincaré and the concept of the "
fourth dimension" to the cubists at the
Bateau-Lavoir during the first decade of the 20th century. Princet introduced Picasso to
Esprit Jouffret's
Traité élémentaire de géométrie à quatre dimensions (
Elementary Treatise on the Geometry of Four Dimensions, 1903), a popularization of Poincaré's
Science and Hypothesis in which Jouffret described
hypercubes and other complex
polyhedra in four
dimensions and projected them onto the two-dimensional page. Picasso's
Portrait of Daniel-Henry Kahnweiler in 1910 was an important work for the artist, who spent many months shaping it. The portrait bears similarities to Jouffret's work and shows a distinct movement away from the
Proto-Cubist fauvism displayed in ''
Les Demoiselles d'Avignon'', to a more considered analysis of space and form. Early cubist
Max Weber wrote an article entitled "In The Fourth Dimension from a Plastic Point of View", for
Alfred Stieglitz's July 1910 issue of
Camera Work. In the piece, Weber states, "In plastic art, I believe, there is a fourth dimension which may be described as the consciousness of a great and overwhelming sense of space-magnitude in all directions at one time, and is brought into existence through the three known measurements." Another influence on the School of Paris was that of
Jean Metzinger and
Albert Gleizes, both painters and theoreticians. The first major treatise written on the subject of Cubism was their 1912 collaboration
Du "Cubisme", which says that: "If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidian mathematicians; we should have to study, at some length, certain of
Riemann's theorems." The American modernist painter and photographer
Morton Livingston Schamberg wrote in 1910 two letters to
Walter Pach, parts of which were published in a review of the
1913 Armory Show for
The Philadelphia Inquirer, about the influence of the fourth dimension on avant-garde painting; describing how the artists' employed "harmonic use of forms" distinguishing between the "representation or rendering of space and the designing in space":If we still further add to design in the third dimension, a consideration of weight, pressure, resistance, movement, as distinguished from motion, we arrive at what may legitimately be called design in the fourth dimension, or the harmonic use of what may arbitrarily be called volume. It is only at this point that we can appreciate the masterly productions of such a man as Cézanne. Cézanne's explorations of geometric simplification and optical phenomena inspired the Cubists to experiment with
simultaneity, complex multiple views of the same subject, as observed from differing viewpoints at the same time. == Dimensionist manifesto ==