Between the middle of the 18th century and the middle of the 20th century, three-dimensional mathematical models of different types were produced for various disciplines. Those objects were able to show aspects that could not be represented on paper, and were important vectors of knowledge. Mathematical models are often neglected by the history of science, being considered only as teaching aids, but, in fact, they are the expression of different epochs of the development of scientific knowledge. Actually, some of the models that were used as teaching aids, became a stimulus for research and vice versa. Models were not confined to laboratories and university classrooms; they were also presented in exhibitions and congresses.
Senior students surround math teacher Helen Shafer during a class. Seated from left to right: [Irene] Searles '85, Helen Merrill, Miss Shafer, Isabel Darlington, Ellen Pendleton. Standing from left to right: Gertrude Brown, Lizzie White, Susan Peabody, Alma Aumack '84, Louella Smith, Grace Dodge.
(from Wellesley College Archives Image Gallery)
Mathematical model production appears to have started in France at the Paris Ecole Polytécnique. Those models were later shown at an exhibition to the Conservatoire des Arts et des Métiers at the end of 1860, where the mathematician Felix Klein had the opportunity to see them. Klein was able to see more mathematical models during the congresses of German mathematicians, like the one held in Gottingen in 1873. During congresses, mathematical models were studied only for didactical purposes; the model allowed the visualization of the surfaces and the curves that the mathematicians were studying. Klein himself, together with Alexander Brill (1842-1935), who had Max Planck among his students, built a workshop to design and construct mathematical models. The workshop was annexed to the Mathematical Institute of the Polytechnic School of Munich.
In the Walldorff-Astoria Grande Hotel Hall, New York, a group of geometers, metaphysicians, theologians, metamathematicians, members of the Society of Skeptics, examine the negative ontology of the pseudosphere, presented by prof. Eugenio Beltrami of Bologna, Italy, on the occasion of the Great Universal Exhibition.
(from website on Imre Thot by Regensburg University)
In Padua, Giuseppe Veronese, one of the most important mathematicians of his time, started a collection of models. He also tried to build in Padua a laboratory to construct mathematical models. His aim was not only to produce those objects, but at the same time give the students of the Faculty of Mathematics and Applied Engineering the possibility to put into practice their theoretical knowledge. Unfortunately, due to the unavailability of adequate funds, Giuseppe Veronese was not able to build his laboratory, and most models were bought in Germany. In the present exhibition we show a selection of them.
he present virtual exhibition aims to show the public a particular aspect of the mathematical models; they played an important role in 20th century art. While the exhibit isn’t complete, we are going to present the work of some artists who were deeply fascinated by those creations.