In the late 1800's and early 1900's mathematicians were producing models of mathematical surfaces out of plaster, wire, and other materials. These models were used to illustrate research and for university instruction. Gradually, mathematical interest in these models faded, but the models themselves were still on display in universities and museums. Here they were found by several artists from the Constructivist and Surrealist movements, two movements of abstract art that were active in the early 20th century. Artists from each of these movements drew some inspiration from these models of surfaces. We trace the paths of this influence, concluding with some locations in which models can still be found as well as some current artistic interest.