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The the 4th interdisciplinary workshop will trace the development of geometric thinking from Euclid through Descartes to non-Euclidean theories, illustrating how our concept of space has transformed over time. Participants will also have the opportunity to discuss how these changes have influenced the way we think about the world.

The speakers will address key Euclidean axioms and postulates, as well as the foundations of Greek thought, which relied on ruler-and-compass constructions and maintained an aversion to the infinite. The next topic will be Descartes’ synthesis of geometry and algebra, which made it possible to express even unprecedented forms through equations, opening the path to modern analytic geometry, while at the same time obscuring the older modes of mathematical thinking.

The historical overview will culminate with non-Euclidean geometries, which fundamentally reshaped the modern conception of space, its structure, and its topology. The formulation of elliptic and hyperbolic geometry will be presented as the outcome of attempts to prove Euclid’s fifth postulate.

The interdisciplinary workshop organized by the Department of Mathematics, Faculty of Applied Sciences (FAV), and the Department of Philosophy, Faculty of Arts (FF) aims to serve as an open discussion forum for all members of the pilsner academic community interested in the intersection of philosophy and mathematics. It will take place at the Faculty of Applied Sciences.

Programme

13:00 – Dr Ludmila Dostálová (Department of Philosophy):
Euclidean Geometry – From Ruler and Compass to Infinity

13:30 – Dr Radek Schuster (Department of Philosophy):
Descartes’ Geometry – From Curves to Algebra

14:00 – Assoc. Prof. Jan Vršek (Department of Mathematics):
Non-Euclidean Geometries – From Paradox to a New View of Space

15:00 – Discussion / Collaboration Across Philosophy and Mathematics

This workshop is organized as part of the UWB project PRVA-25-018 “Interdisciplinary Teaching at the Interface of Philosophy and Mathematics.”