Logical weakness in modern pure mathematics | Real numbers and limits Math Foundations 87 скачать в хорошем качестве

Logical weakness in modern pure mathematics | Real numbers and limits Math Foundations 87

We begin PART II of this video course: "Mathematics on trial - why modern pure mathematics doesn't work". This video outlines the case for the prosecution: that modern pure mathematics suffers from: 1. Inconsistent rigour 2. Problematic definitions 3. Reliance on `axioms' 4. Computational weakness 5. Impoverished examples We give some initial orientation to the first two claims, suggesting that contrary to popular opinion, rigour in mathematics has been on a consistent downward trend in the last few centuries, and give an explicit list of problematic definitions, cutting across many areas of modern pure mathematics. In subsequent videos in this series, we will be substantiating the claims made here. We will also be inviting comments and a wide discussion of these highly contentious, but vitally important, issues. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. Video Content: (thanks to Seeker) 00:00 Intro to why modern pure maths doesn't work 1:47 5 Key problems 5:36 Problematic & Non-problematic areas 9:10 Applied and Pure Mathematics 11:09 Inconsistent rigour 13:49 Concepts defined clearly 14:42 Concepts not defined clearly 19:09 3 Consequences of logical weaknesses 23:30 4 Aims ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. *********************** My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Patreon,   / njwildberger   . Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист