Norman Wildberger (Mathematician)
Videos
- The Emperor's functions have no clothes!
- Description: Unfortunately the modern set-theoretic definition of a function f: A to B generally does not make logical sense. Are we able to think clearly about this crucial concept? If we don't, our AI machines soon will, and the results will embarrass us. The truth is that much of modern pure mathematics is a logical mirage, sustained by giddy levels of wishful thinking and denial.
- Videodan: [The modern theory of functions] is very sad. What is the alternative? How do we really make progress? I think what we need to do is to return to understanding of the Pythagoreans of 2500 years ago. Namely that at the core of mathematics there rest number. Natural numbers, ratios of numbers, like fractions, and proportions between numbers. These are exact, these are proper solid computational basis for mathematics. […] I think that it's exciting to think that we really need to return to classical Greek thinking to create a more sensible, logical correct, computational verifiable mathematics. If mathematics to remain honest it must confront the illusion at the heart of analysis and find a more solid foundation in number.
- Description: Unfortunately the modern set-theoretic definition of a function f: A to B generally does not make logical sense. Are we able to think clearly about this crucial concept? If we don't, our AI machines soon will, and the results will embarrass us. The truth is that much of modern pure mathematics is a logical mirage, sustained by giddy levels of wishful thinking and denial.