***THIS WILL BE A HYBRID EVENT***

Zoom Meeting Link:

https://princeton.zoom.us/j/98741681443

Abstract: Euclid's Elements were considered the paradigm of the scientific method for centuries. This was mainly due to the explicit use of first principles of demonstration (axioms), which was later applied to many other disciplines. The talk investigates the significance of such principles of demonstration in Euclid and ancient mathematics, showing that it was totally different from the modern understanding of axioms. It then discusses the major transformations that the concept of axiom underwent over the centuries, leading to the idea that different mathematical theories can be based on different axiomatic systems (non-Euclidean geometries). This transformation can be understood as a complete redefinition of the highest model of the scientific method.