Cubics and the Prettiest Theorem in Calculus - Arithmetic and Geometry Math Foundations

Explore the fascinating world of cubic polynomials and their algebraic calculus in this 28-minute mathematics lecture. Delve into Taylor expansions, subderivatives, tangent lines, and tangent conics for cubic functions. Discover the "prettiest theorem in calculus" attributed to Etienne Ghys, complete with an elementary and elegant proof. Learn about the MathFoundations series, which aims to establish proper mathematical foundations while addressing logical challenges in modern pure mathematics.

Introduction
Strategy
Tangents
Special cubic
Cubic disjoint tangent conic theorem
Example