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.
"Streamlines," by Anne Burns (professor emerita, Long Island University, Huntington, NY)
48 x 32 cm, digital print, 2016
I began my studies as an art major, but switched to mathematics. When I went to my first conference on fractals I was hooked. Visualizing mathematical concepts allowed me to combine both of my interests. The streamlines of the vector field dx/dt = x^2 - y^2, dy/dt = 2xy (the real and imaginary parts of the complex function f(z) = z^2 ) are the directed paths along which the tangent vector is equal to (dx/dt, dy/dt). They are circles tangent to the real axis. the attached vectors are colored according to their slope. --- Anne Burns