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.
"Doubly Impossible Staircase," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)
Traversing along the outside, the stairs always rise; but traversing along the inside, they always descend. Finally, alternating between the exterior and interior, it behaves like a normal staircase. -- Jean-Francois Colonna