Finite versus infinite and number systems | Sociology and Pure Mathematics | N J Wildberger

A social scientist wanting to understand the culture of mathematics needs also to have at least some familiarity with the role of number systems throughout history. This is a rich and surprising topics, and in subsequence videos in the series we will be investigating quite different historical roles, starting with the fascinating Egyptian and Mesopotamian number systems and then move forward towards to modern European epochs and eventually the current difficulties that beset the so-called theory of "arithmetic with real numbers". There are many important sociological questions that arise when looking at the almost deliberate attempt by the academy to ignore discussion of this crucial topic. The rift between the realities of computational mathematics and the dreaming of pure mathematics in the direction of "real numbers", "infinite series" and "transcendental functions" (just to get started) is now so pronounced that it is become impossible to dismiss. One place to anchor the discussion in the difference between studying a finite discrete system, say a list or sequence , and the corresponding "infinite or unbounded" concepts --which are at their core quite different mathematical objects and need to be treating quite differently. So let's start a wide ranging discussion about the role of numbers in mathematics, and how to explain the sociological forces that maintain the pretense that all is well despite obvious evidence to the contrary. ******* 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:   / njwildberger   Your support would be much appreciated. 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)    • Elementary Mathematics Explained (K-6)   (40 videos)    • Ancient Mathematics and insights of Howard...   (7 videos)    • Wild West Banking: A mathematician goes We...   (7 videos)    • Playing Go: the ancient oriental board game   (19 videos)    • Maths and Music   (21 videos)    • Year 9 Mathematics (review fractions, deci...   (10 videos)    • Wild Trig: An introduction to Rational Tri...   (94 videos) Wild Egg Maths Playlists: ttps://www.youtube.com/channel/UCriFv3G22iOU...    • 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)