Piotr Błaszczyk: Synthetic Non-Archimedean Geometry: New Foundations for Newton's Mathematics

Organized by the Centre for Science, Technology, and Society Studies

Detailed information

Piotr Błaszczyk (Institute of Mathematics, Pedagogical University, Krakow)

Abstract:

Synthetic Non-Archimedean Geometry: New Foundations for Newton’s Mathematics
In [1], we show how to reconstruct Newton’s mathematical techniques without referring to the concepts of the Riemann integral or the derivative. In [2], we show that Newton’s techniques combined Euclidean geometry with the concept of the infinitesimal. In this talk, we present a more systematic approach: we develop a synthetic, non-Archimedean Euclidean plane geometry that aims to provide foundations for the mathematical methods used by Newton in the Principia.

References
[1] Błaszczyk, Reading Newton’s De Analysi by Hyperfinite Sums. Foundations of Science.
[2] Błaszczyk, Reading Newton’s Principia through Euclidean Proportion and Nonstandard Analysis.