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.
"A Strange Dream," by Karl Kattchee, University of Wisconsin - La Crosse (2008)
Oil crayon on paper, 20" x 24". "This drawing is composed of round shapes, mainly. The arrangement of the round shapes is itself round, so that roundness is occurring on multiple levels. On the other hand, the drawing depicts multiple levels of thinking or being, like a sleeper who dreams within his dream within his dream. A Strange Loop, in the sense of Hofstadter, is evident." --- Karl Kattchee, Associate Professor of Mathematics, University of Wisconsin-La Crosse, La Crosse, WI