The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Tryptique," by Radmila Sazdanovic (University of Pennsylvania) and Aftermoon studio (Paris, France)
Ink/brush, 24" x 8", 2010
Tryptique is a drawing of three different kinds of diagrams used in categorifications of the one-variable polynomial ring with integer coefficients. These diagrams are elements of three distinct algebras: on the level of Grothendieck rings, projective modules spanned by these diagrams correspond to Chebyshev polynomials, integer powers of x and (x-1), and Hermite polynomials. Asgar Jorn's comment about Pierre Alechinsky's work could as well apply to the signs Aftermoon studio created based on our diagrams.
"L'image est écrite et l'écriture forme des images... on peut dire qu'il y a une écriture, une graphologie dans toute image de même que dans toute écriture se trouve une image." --- Radmila Sazdanovic (http://www.math.upenn.edu/~radmilas/)