At the beginning of the 20th century, geometry based on paper folding flourished. Indeed, it was discovered during the first decades of this century that such geometry was more powerful than the geometry based on compass and straightedge in terms of the constructions that could be made. Moreover, at the end of the 19th century and resp. during the second half of the 20th century, there was a growing recognition of the epistemic power of 3-dimensional material models resp. of 2-dimensional diagrams. However, the end of the 20th century saw a fundamental change in the status of these material practices. With the introduction of computer programs for folding, new mathematical and algorithmic phenomena were discovered that could not have been found using purely manual methods. Moreover, in recent years, the AI-based program AlphaGeometry has managed to find unexpected solutions to problems in plane geometry, solutions that were only retrospectively accompanied by diagrams. In my talk, I would like to explore different stages in the disappearance of such material practices, as well as the new role concerning the status of materiality in the 21st century mathematical research.
