Simons Center Exhibition Brings Altgeld Math Models into Focus

In the late 19th and early 20th centuries, mathematical models were created - primarily in Germany - to visualize complex geometric forms and abstract mathematical concepts.

Crafted from plaster, wood, metal, string, and even cardboard, these objects were used for research and university instruction. The models transformed abstract mathematical principles into visual teaching tools, reflecting an era that valued visualization for scientific understanding.

An exhibition at the Simons Center for Geometry and Physics (SCGP), "The Altgeld Math Models," brings math to life, displaying 12 models from the University of Illinois Urbana-Champaign Collection, one of the most significant mathematical model collections in the world. The models, which are being presented to the public for the first time, will be on display in the Simons Center Gallery until September 25.

Curated by SCGP Art Director Lorraine Walsh in collaboration with the Department of Mathematics and the University Library at the University of Illinois Urbana-Champaign, the exhibition allows students and researchers to literally view concepts, physically illustrating multi-variable calculus, differential geometry, algebraic topology and complex analysis.

"These models are as exquisite as anything you would see in nature," said Walsh. "Math and art are always curious and want to learn about the world. A mathematician will see the forms through the eyes of geometry and topology. An artist will see form and structure and shape. But both share a love of form, space, proportion and symmetry."

The Altgeld models trace their origins to German mathematician Felix Klein - a proponent of visual learning - who famously showcased them at the 1893 Chicago World's Fair, inspiring American universities to purchase and import the teaching tools.

Before computer graphics, these physical models were the only way to transform abstract mathematical principles into tangible, three-dimensional reality. Today, they stand not only as artifacts of mathematical inquiry, but also as remarkable examples of the intersection of science, art and craftsmanship.

"Prior to the turn of the 20th century, most art was representational, and the surrealists and constructivists saw things differently, in dreamscapes and geometrically," said Walsh. "So it's not surprising that they were really beholden to these models, which were very abstract and mysterious. I think that in some ways all human beings can intuit something deeper in an object or painting, even if they don't understand the underlying nature."

Although Germany dominated the production of mathematical models, important collections were subsequently acquired by universities throughout Europe and the United States. The University of Illinois Urbana-Champaign today houses one of the world's largest historical collections of mathematical models, featuring nearly 400 from the late 19th and early 20th centuries. The models demonstrate abstract mathematical principles in a three-dimensional way, offering a unique value to scholars on campus as well as around the world.

"This exhibition is really perfect for the Simons Center, and it aligns with the mission of the gallery in that it embraces both math and art," said Walsh. "It has a lot of historical value in that it shows teaching tools created at a time when universities were using equations to teach their mathematics. Eventually that would evolve through technology and the computer. But this history that crosses math and art is something that I believe is really important and brings value to the Simons Center and to Stony Brook University at large."

- Robert Emproto