What sense can we make of the part of mathematics that admits constructions we can never write down or compute?

I take up this question in defense of infinite processes and analysis with NJ Wildberger, professor of mathematics at the University of New South Wales and host of the Youtube channel Insights Into Mathematics,    / @njwildberger  


Timestamps:
0:00 Intro
3:13 NJ outlines his issue with real numbers and infinite sequences
6:55 Exact vs. approximate; the equation x^3 = 15.
17:44 Statement of my position. When pure mathematics diverged from applied mathematics.
23:25 My first objection: we can make sense of the constructions in real analysis.
27:34 Objects defined by choice or by algorithm
32:46 What constrains what we can speak of in mathematics?
34:30 My explanation of Cauchy sequences in terms of measurement
37:05 Solving polynomial equations computationally. Power series as formal objects or as functions.
40:53 My second objection: analysis is a very successful theory
48:10 Is there a crisis that necessitates a rejection of infinities?
54:06 Do we have to get the foundations right before proceeding? The sum pi + e + sqrt(2).
1:01:40 My third objection: what is computable?


Norman's online course Algebraic Calculus One: https://www.openlearning.com/courses/...


Check out my other podcast episodes for interesting discussions of math and other topics:    • Daniel Rubin Show, Full episodes  


And check out my Tricky Parts of Calculus playlist    • Tricky Parts of Calculus   for careful exposition of the subtle and difficult parts of calculus, including treatments of pi, e, and other topics mentioned in this video.