IMAGINARY – through the eyes of mathematics


IMAGINARY – through the eyes of mathematics


A project by the Mathematisches Forschungsinstitut Oberwolfach, supported by the Federal Ministry of Education and Research in Germany BMBF from 2008 - 2009 and by the Klaus Tschira Stiftung from 2011 - 2016.

Submitted by


DirectionGert-Martin Greuel
Coordination/CuratorAndreas Daniel Matt
SupportHerwig Hauser
Software/TechnologyChristian Stussak, Steffen Weissmann

IMAGINARY – through the eyes of mathematics” is an interactive travelling exhibition by the Mathematisches Forschungsinstitut Oberwolfach originally developed for the Year of Mathematics 2008 in Germany. Its intention is to display visualizations, interactive installations, virtual realities, 3D objects and their theoretical background in algebraic geometry and in singularity theory in an attractive and understandable manner. It’s a unique science experience!

The exhibition IMAGINARY has visited more than 100 cities in 30 countries and attracted more than 2 million visitors. The exhibition sets out to evoke interest and curiosity in mathematics. Visitors are encouraged to interact with the exhibits and create their own mathematical artwork using special software. Demonstrators are available to give helpful insights into the theoretical background.

The Idea

The idea behind the IMAGINARY exhibition is—as the name suggests—to use the visual and aesthetic component of mathematics as an eye-catcher in order to explain the mathematical backgrounds to the visitors in an interactive manner. The imaginary and unimaginable of mathematics is illustrated, it turns to images which you can generate yourself. 

The exhibition 

In its original form developed for the Year of Mathematics 2008 in Germany, the exhibition consists of four exhibit sections: A gallery of beautiful mathematical images, several interactive installations where visitors can experiment with math art themselves, a film station where mathematical movies are shown, and a showcase with 3D sculptures of algebraic surfaces.


The IMAGINARY cube is a walk-in aluminium cube in which the mathematical images are presented. Most of the pictures show beautiful algebraic surfaces that were created by the Austrian mathematician Herwig Hauser. The algebraic surfaces that are presented together with their defining equations are at the same time beautiful images as well as interesting mathematical objects. The gallery is completed by a series of spectacular mathematical images by Oliver Labs, Aurélien Alvarez, Jos Leys and Étienne Gys, Ulrich Pinkall, Nicholas Schmitt, Charles Gunn and Tim Hoffmann, and some more artistic works by Luc Benard and Richard Palais. All pictures are presented at a size of 85×85 cm on acryl glass and are provided with explanation boards describing their mathematical properties.

Interactive programs

The main attraction of an IMAGINARY exhibition is the SURFER program that calculates and displays algebraic surfaces in real time. Visitors can enter and change polynomial equations on a large touchscreen with their fingers, shift parameters, determine the colours of the surfaces and turn the figures as they like.

Various mathematical and physical phenomena are adressed with the program CINDERELLA. This is a compilation of interactive applications that communicate topics as simulation, chaos or symmetries in a playful way. In addition, the program MORENAMENTS allows to paint symmetrical patterns in one of the 17 space groups in the Euclidian plane.

A unique 3D experience is provided by the program 3D-XPLORMATH. Using 3D glasses, visitors are able to discover mathematics from a three-dimensional point of view. 

Finally, there is the JREALITY program, which generates a virtual mathematical world where visitors can move freely, climb and jump on certain surfaces or fall down. The surfaces used in the program are, among others, the Boy surface, an artful torus or a tetranoid. 

Mathematical films

There are several mathematical movies shown at the exhibition: The multiply awarded film MESH on discrete mathematics explains the history of discrete geometry and its application to computer graphics. Moreover, the film DIMENSIONS is presented. It offers a look into the fourth dimension by explaining the stereographic projection on a generally understandable level. There is also a short film on algebraic surfaces, a film on elliptic curve cryptography and a collection of the winner films of the Math Film Festival 2008.

Surfaces as sculptures

The German companies Voxeljet Technology and Alphaform are engaged, among others, in generative manufacturing of 3D models by selective gluing plastic powder or by means of stereolithography. Both companies have accepted the challenge to print in 3D a selection of algebraic surfaces of the exhibition and present them as sculptures. Ten sculptures at a diameter of about 25 cm are exclusively displayed at the exhibition. They were produced for the exhibition by the two companies free of charge. The 3D data of the sculptures was prepared by the exhibition partner FORWISS Institute, University of Passau.

IMAGINARY Catalogue, Poster Set and Postcards

You can purchase the printed IMAGINARY exhibition catalogue, an IMAGINARY poster set with 12 algebraic surfaces and a set of 5 IMAGINARY postcards in high quality. We also offer the pdf files under an open and non-commercial license.