The 19th century was an extrordinary 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 illustrateproperties of these surfaces. The contruction 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. See article (in Word format).
Having taken an extended hiatus from this project (due to my dissertation research, among other things), I am slowly picking it back up again. So please send me an email if you have comments or questions.
Things to Explore
- A paper (from 2003, in Word format) on modern art and mathematical models in the early 20th century. This expands on research done in 2000, which can be found in a short article and some additional notes. If you happen to read Hungarian, here's a translation, published in an online magazine I wish I could read more of called Ponticulus Hungaricus.
- References. Includes annotations of many references and a list of things I want but haven't found yet.
- "Cast of Characters:" an annotated list of historical figures involved in building models of surfaces. And check out this family tree I made a few years ago.
- Some pictures of surfaces. New as of June 2007 -- more pictures!
- Collections of models. I am slowly gathering a list of collections of models. If there are models and your univeristy or institution and you are not on my list, please let me know.
- Jonathan Chertok is an architect who is working to recreate a number of mathematical models using rapid prototyping and other technologies. It's really great work, so check out the website.
- I recently (June 2007) finished cataloging the 48 models (mostly plaster Brill models) at MIT. I've put up a few photos and if you are really interested, you can look at the (very very large) pdf file about all of the models.
