Object-Oriented Versus Expression-Oriented Mathematics - Arithmetic and Geometry Math Foundations

Explore the distinction between object-oriented and expression-oriented mathematics in this 46-minute lecture from the MathFoundations series. Delve into the key example of the unit circle to understand how 21st-century mathematics may shift towards a more expression-oriented approach. Learn about projective bipolynumbers, various interpretations of mathematical concepts, and the polar/pole correspondence. Gain insights into the logical foundations of modern pure mathematics and discover how this new perspective could reshape mathematical thinking.

Intro to distinction between object and expression oriented maths
The unit circle
Expression-oriented approach
A Projective bipolynumber
Interpretation A
Interpretation B
Simple case of a Projective polynumber
The second most circle
Interpretation C
Polar / pole correspondence