In this special video, Steve Patterson interviews N J Wildberger on a range of foundational issues exploring infinities and the role of skepticism in modern mathematics. Steve is a philosopher who runs a popular podcast called Patterson in Pursuit, and you can find more of his work at

http://stevepatterson.com/podcast/

We cover quite a lot of territory, including the core topic at the heart of the modern foundational difficulties with mathematics, the difference between algorithms and infinite choice, conundrums like the Banach Tarski paradox, Wittgenstein's insights, the role of axiomatics in modern mathematics, the nature of space, the direction of future mathematics, and more!

A big thanks to Daniel Mansfield for setting up the studio and videoing our talk, and to Steve Patterson for lots of interesting questions and comments. He is coming from philosophy, and I from mathematics, but there is a lot of common ground and understanding. Hope you enjoy the discussion: I certainly did!

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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.

Here are the Insights into Mathematics Playlists:

   • MathHistory: A course in the History ...  
   • WildTrig: Intro to Rational Trigonometry  
   • Math Foundations  
   • Wild Linear Algebra  
   • Famous Math Problems  
   • Box Arithmetic  
   • Elementary Mathematics (K6) Explained  
   • Year9Maths  
   • Ancient Mathematics  
   • Wild West Banking  
   • Sociology and Pure Mathematics  
   • Sociology and Pure Physics  
   • Old Babylonian Mathematics  
   • Probability and Statistics: an introd...  
   • Boole's Logic and Circuit Analysis  
   • Universal Hyperbolic Geometry  
   • Differential Geometry  
   • Algebraic Topology  
   • MathSeminars  
   • Playing Go  
   • Diffusion Symmetry: A bridge between ...  

Here are the Wild Egg Maths Playlists (some available only to Members!)

   • Algebraic Calculus One  
   • Classical to Quantum  
   • Algebraic Calculus Two  
   • Advice for mathematics exploration  
   • Solving Polynomial Equations | Explor...  
   • The Hexagrammum Mysticum (Members only)  
   • Algebraic Calculus and dCB curves | E...  
   • Dynamics on Graphs  
   • Playlist  
   • Triangle Geometry  
   • Explorations with qseries  
   • Six: An elementary course in Pure Mat...  
   • Maxel Inverses and Orthogonal Polynom...  
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