In the 1800's, before the advent of sophisticated computer drawing programs, mathematicians interested in visualization built models of surfaces in three dimensions. Mathematical giants such as Gaspard Monge, Felix Klein, Julius Plücker, and Arthur Cayley used wood, string, cardboard, and plaster to construct representations of many types of surfaces, including algebraic surfaces and minimal surfaces.

For a while such models enjoyed an enthusiastic reception. There were exhibitions in London, Munich, and Chicago which included models of surfaces, and manufacturing houses began to distribute copies around the world. By the mid-1900's, however, the old models were being thrown out or left neglected in glass cases. This talk will trace the development of model building and its impact on the mathematical community. We will speculate on the reasons for the eventual decline of model-building and extract some lessons for today. Finally, we will discuss places where one can still see models and what is being done to conserve this part of our mathematical heritage.