In the 19th century, 3d-models made of wood, plaster, and other materials started to play an important role in the communication of mathematics both to students and to researchers. 
However, mainly because of technical issues, some of the models did not show all relevant  aspects in a good way. One major problem were the singularities of surfaces.

In the talk, we give a historical overview on the topic of mathematical models
and explain in some more detail how modern computational mathematical as well as technical developments such as 3d-printing and laser-in-glass help to improve the presentation of some abstract mathematical objects.
Actually, this can nowadays be done in such a way that essential features such as the singularities and also the topology of the objects are immediately visible.

We will present lots of pictures, animations and even some real 3d-objects from our collection of more than 200 different new mathematical models 
which we realized in the last two years.
