Modern "Set Theory" - is it a religious belief system? | Set Theory Math Foundations 250

Modern pure mathematics suffers from a uniform disinterest in examining the foundations of the subject carefully and objectively. The current belief system that "mathematics is based on set theory" is quite misguided, and in its current form represents an abdication of our responsibility to the integrity of our discipline. We have essentially outsourced the very heart of our subject to philosophy. In this video we set out our campaign to put modern "Set Theory", in the sense of "hierarchies upon hierarchies of infinite sets" on trial. And we give an overview of how and why we got into the current sad state where everyone believes and dissent is considered scandalous. Cantor and Dedekind and then Hilbert are perhaps mostly responsible for the big changes pushed, against the will of most of their contemporaries, into modern pure mathematics, culminating in the axiomatic frameworks introduced by logicians in the first half of the 20th century. Mathematics needs to find a more sensible, and logical starting position---not only to make the subject cleaner and more exciting for students and researchers, but also to make room for the new forces about to be unleashed into pure mathematics: the next generation of AI machines. Video Content: 00:00 Does modern set theory really work as a logical foundation? 01:40 Modern set theory 03:41 Arithmetic with natural numbers as the mathematical foundation 05:11 How to model the continuum in mathematics 08:51 Ancient Greeks, 17th and 18th century, analysis 09:33 19th century mathematical analysis 13:11 20th century mathematical analysis NOTE: This important topic is now also being developed at the Wild Egg Maths channel: see the first two Playlists below (for Members of that channel) ************** Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon: Patreon: njwildberger Your support would be much appreciated. Insights into Mathematics YT channel: njwildberger Insights into Mathematics Playlists: The Algebra of Boole, Logic and Circuit An... (31 videos) Box Arithmetic: a new framework for Mathem... (18 videos) Hypergroups and Diffusion Symmetry: an int... (6 videos) Rational Trigonometry for maths, physics a... (4 videos) Sociology and Pure Maths (44 videos) Old Babylonian mathematics and Plimpton 322 (8 videos) Math Foundations (226 videos) Math Seminars N J Wildberger (26 videos) Math History (ancient to modern) (45 videos) Geometric Linear Algebra (43 videos) Algebraic Topology (40 videos) Universal Hyperbolic Geometry (55 videos) Differential Geometry (34 videos) Elementary Probability and Statistics (8 videos) Math Terminology for Incoming Uni Students (9 videos) Famous Math Problems ( 46 videos) Wild Egg Maths Playlists: Box Arithmetic Book: A finite multiset fou... (NEW!!) Intro to Algebraic Calculus with Box Arith... (4 videos) Classical to Quantum (for Members) (64 videos) Solving Polynomial Equations and the Geode... (45 videos) De Casteljau Bezier curves and associated ... (20 videos) Exploring q-series (for Members) (8 videos) Six: A mathematical exploration (9 videos) Algebraic Calculus One: a new foundation f... (52 videos) Advice to prospective research mathematici... (9 videos) The Hexagrammum Mysticum: a Geometric Gem ... (14 videos) Algebraic Calculus Two (8 videos) Special (Polynomial) Functions and Maxel N... (25 videos) Dynamics on Graphs: The ADE Phenomenon & B... (30 videos)