The big mathematics divide: between “exact“ and “approximate“ | Sociology and Pure Maths | NJW

Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as “exact theories“ when in fact they are really only “approximate theories“. In this sense they can be viewed either as belonging more properly to applied mathematics, or as being essentially provisional; awaiting a more precise and logically viable treatment. This crucial distinction actually cuts across many areas of modern pure mathematics. It starts of course with arithmetic, and the difference between counting and measurement, that is between intrinsically exact and approximate evaluations, but appears also in modern notions of algebra, topology, function theory, number theory and many other disciplines. In this video we give an introduction to this important distinction, culminating in some unsettling thoughts about the logical validity of the “Riemann zeta function“ and that most revered unsolved problem in pure mathematics: th