Math Dispute Breakdown: In Defense of Analysis

Summary of my discussion with Professor NJ Wildberger on whether we can admit the notions of infinity that appear in the theory of analysis. I try to make my arguments more clear, add some comments about what we discussed, and set up the important points for further debate. My discussion with Norman Wildberger: https://youtu.be/edh5bbgSKqo More episodes of my podcast, featuring fascinating discussions of math and other topics: https://www.youtube.com/playlist?list=PLw3pvR_YJeRd5vZUvMbZIzUPYkLNVFMlJ 0:00 What the dispute is about 2:35 My 3 objections to Norman's view 3:54 Norman's example: whether there is a solution to x^3 = 15. Where we disagree 8:58 The Axiom of Infinity 10:45 What do we require of a mathematical theory for it to be comprehensible? 12:19 Analysis is a successful theory, so why attack it? 14:25 My view of Norman's example of the geocentric model of the universe 16:35 Why I think it's not useful to insist on correct foundations at the outset 17:23 Addressing Norman's points about the development of math 20:40 Examples of the success of the modern analytical theory of functions and power series 23:43 Why I don't consider Norman's issue with pi + e + sqrt(2) to be a crisis for the theory of real numbers 27:17 Questions about a finitist framework I make reference here to the view in the philosophy of science put forward by Thomas S. Kuhn. His famous work in which he spells out this view is The Structure of Scientific Revolutions https://amzn.to/3CXlZPN Interestingly, Norman brought up the dispute over the geocentric and heliocentric models of the universe, which is the subject of another of Kuhn's books, The Copernican Revolution https://amzn.to/2VWQvZG Both of these are fantastic books that I highly recommend. The Copernican Revolution explains really well some of the earliest science of astronomy and its historical development. The Structure of Scientific Revolutions is a must-read for anyone remotely interested in the philosophy of science or its history.