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International Day of Mathematics

Felix Klein – Insights from the Outside

A cinematic portrait by Ekaterina Eremenko, produced by the Max Planck Institute for Mathematics in the Sciences.

Felix Klein (1849–1925) was not only one of the most influential mathematicians of his time, but also a passionate mediator between science, society, and education. Closely connected to Leipzig and its university, he was particularly committed to strengthening the relationship between school and university mathematics. His groundbreaking contributions to geometry had a lasting impact on modern mathematics and also influenced developments in physics and computer science.

Outside the academic world, Felix Klein is best known as the inventor of the Klein bottle, a mathematical object with no clear distinction between inside and outside. Making mathematics tangible and accessible was one of his central concerns.

The documentary Felix Klein – Insights from the Outside aims to present Klein’s mathematics — in particular his innovative view of geometry — to a wider audience. Geometry is not limited to measuring lengths and angles. It is the study of symmetries and transformations of space. Discover the life and work of Felix Klein, explore his groundbreaking contributions to geometry, including the famous Erlangen Program, and encounter mathematical ideas that continue to have an impact today.

Prof. Dr. Meike Akveld
Eidgenössische Technische Hochschule Zürich, Switzerland
Prof. em. David Rowe
Johannes Gutenberg-Universität Mainz, Germany
Dr. Henrike Allmendinger
Fachhochschule Nordwestschweiz, Switzerland
Prof. Marcus du Sautoy
University of Oxford, England
Prof. Dr. Dorothea Bahns
Georg-August-Universität Göttingen, Germany
Prof. Peter Sarnack
Princeton University, United States of America (USA)
Prof. Dr. Laurent Bartholdi
Université Claude Bernard Lyon 1, France
Prof. Dr. Thomas Schick
Georg-August-Universität Göttingen, Germany
Prof. Dr. Alexander Bobenko
Technische Universität Berlin, Germany
Prof. Richard Schwartz
Brown University, United States of America (USA)
Prof. Dr. Michael Bronstein
University of Oxford, England
Asst. Prof. Steve Trettel
University of San Francisco, United States of America (USA)
Prof. Dr. Jean-Pierre Bourguignon
Institut Hautes Études Scientifiques, France
Dr. habil. Renate Tobies
Friedrich-Schiller-Universität Jena, Germany
Dr. Max Hoffmann
Universität Paderborn, Germany
PD Dr. habil. Rüdiger Thiele
Universität Leipzig, Germany
Prof. Dr. Karl-Hermann Neeb
Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Prof. Dr. Akshay Venkatesh
Stanford University, United States of America (USA)
Prof. em. Dr. Samuel Patterson
Georg-August-Universität Göttingen, Germany
Prof. Dr. Anna Wienhard
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
Prof. Sir Roger Penrose
University of Oxford, England
Prof. Dr. Edward Witten
Institute for Advanced Study, United States of America (USA)
Prof. Dr. Dr. Jürgen Richter-Gebert
Technische Universität München, Germany
 
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Ekaterina Eremenko

Ekaterina Eremenko is the director and writer of the film. In addition to earning a distinguished degree in mathematics, she holds a degree in film directing, and graduated from the Documentary Campus Masterschool in Munich. In 2012, she created “Colors of Math”, an exceptional film exploring the sensory aspects and countless facets of mathematics, followed by a series of other cinematic insights into this fascinating field. Her repertoire also includes documentary films such as “Math Circles around the World”, “Solving the Bonnet Problem”, and “Lake Vostok: At the Mountains of Madness”.

The Klein Bottle

What is inside, what is outside?

The Klein bottle defies this seemingly simple question. It is a mathematical object without clear boundaries—a shape in which the inside and outside merge into one another. At first glance, it appears like a curious art object, almost like a paradox made of glass. 

Discover the Klein bottle in the accompanying video (in German).