The 19th century was an extraordinary period in the history of geometry, featuring revolutionary work by giants of geometry (such as Plucker, Riemann, Klein and Lie just to name a few), but also suffering from fragmentation and a lack of consensus about what should be studied and how it should be studied.

One line of inquiry, pursued with great enthusiasm from the middle of the 19th century through the beginning of the 20th century, was the investigation and classification of cubic and quartic surfaces. The discovery of the existence of 27 lines on a smooth cubic surface was hailed as a discovery of monumental importance and hundreds of papers were written about cubic surfaces and their lines. Quartic surfaces emerged originally from optics and were vigorously studied by Kummer, Klein, and many others.

During many of these investigations, models were built to illustrate properties of these surfaces. The construction and study of plaster models was especially popular in Germany (particularly in Gottingen under the influence of Felix Klein). Many of the models were mass produced by publishing houses and sold to mathematicians and mathematics departments all over the world. Models were built of many other types of surfaces as well, including surfaces arising from the study of differential geometry and calculus. Such models enjoyed a wonderful reception for a while, but after the 1920’s production and interest waned.

Later, two very different artistic movements, the surrealists and the constructivists, discovered mathematical models at approximately the same time. Constructivist Naum Gabo began to draw direct inspiration from the forms of mathematical models in the early 1930’s, and he seems to be the first constructivist to have done so. Surrealist photographer and painter Man Ray did a series of photographs in 1936 of mathematical models housed at the Poincaré Institute in Paris.

## Things to Explore

- Presentations I have done on connections between constructivists, surrealists, and mathematical models.
- Collections of models. If there are models and your university or institution and you are not on my list, please let me know.
- InJune 2007 I cataloged the 48 models (mostly plaster Brill models) at MIT. If you are interested, you can find my work cataloging and describing the mathematics related to the MIT models.