The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths

Explore the fundamental divide in modern pure mathematics between "exact" and "approximate" theories in this 41-minute video lecture. Delve into the often-overlooked schism that permeates various mathematical disciplines, from arithmetic to topology and number theory. Examine how this distinction impacts the logical validity of concepts like the Riemann zeta function and the Riemann Hypothesis. Gain insights into the implications of this divide for areas such as algebra, function theory, and other mathematical fields. Investigate the transition from counting to measurement, and how it relates to exact and approximate evaluations. Consider the provocative idea that some aspects of pure mathematics may be more akin to applied mathematics or provisional theories awaiting more precise treatments. Engage with this thought-provoking discussion that challenges conventional understanding of mathematical exactness and approximation.

Exact versus approximate in mathematics
Associating applied maths to approximate values
Solving equations and ''real numbers''
Topological spaces
Functions
Number theory sigma and zeta functions
Riemann hypothesis issues