The Decline of Rigour in Modern Mathematics - Real Numbers and Limits

Explore the decline of mathematical rigour in modern times through this 27-minute lecture from the MathFoundations series. Examine the concept of rigour in mathematics, its historical importance, and the role of Euclid's Elements. Delve into the nature of proof and the hierarchy of mathematical topics. Identify problematic areas in high school and undergraduate mathematics that hinder logical consistency. Gain insights into why rigour has diminished in the 20th century and understand the implications for mathematical education and research. Learn about the characteristics of rigorous mathematics and the inadequacies of modern college math courses in addressing foundational issues.

Intro to loss of rigour
Characteristics of rigorous mathematics
Primary model for mathematical rigour
Inadequacies of modern college math courses
The nature of proof
The hierarchy of mathematical topics
Problematic topics
Problematic problems are ignored