Uploaded June 2026 | Updated September 2026, 2 weeks ago
Please don't go out of your way to pester Impressive-Mud5074 about his ultrafinitism! Despite the jokes, I hope you will come to understand where he is coming from throughout today's discussion!
"Pi is uncomputable", so said Impressive-Mud5074 on r/learnmath. From there, he was thoroughly discoursed and today we look at the whole saga - digging into computability, the halting problem, and ultrafinitism. #maths #mathmemes
More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Business Inquiries: wrathofmathlessons@gmail.com
SOURCES
human.libretexts.org/Bookshelves/Philosophy/Logic_and_Reasoning/Sets_Logic_Computation_(Zach)/03%3A_III-_Turing_Machines/3.01%3A_Turing_Machine_Computations/3.1.01%3A_Introduction
Real Analysis is a Degenerate Case of Discrete Analysis by Doron Zielberger
https://plato.stanford.edu/entries/philosophy-mathematics/
Hilbert, David (1926), "Über das Unendliche", Mathematische Annalen, 95 (1): 161–190
Computational Complexity: A Modern Approach by Sanjeev Arora and Boaz Barak
What is Mathematics and What Should it Be? By Doron Zeilberger
mathworld.wolfram.com/AxiomofInfinity.html
Meta Math!: The Quest for Omega by Gregory Chaitin
Aristotelian Infinity by John Bowin
Understanding the Infinite by Shaughan Lavine
Computation Finite and Infinite Machines by Marvin L Minsky
Ultrafinitism by Joel David Hamkins
Alan Turing, On computable numbers by Joel David Hamkins
math.stackexchange.com/questions/462790/are-there-any-examples-of-non-computable-real-numbers
mathoverflow.net/questions/44208/is-there-any-formal-foundation-to-ultrafinitism
Constructivism in Mathematics an Introduction Volume 1 by A.S. Troelstra and D. Vandalen
On Computable Numbers, with an Application to the Entscheidungsproblem by A. M. Turing
0:00 Intro
2:02 Computable Numbers
3:49 Impressive Mud's Definition
7:05 Opposing Pi
12:53 Zielberger
15:33 Uncomputable Conception
21:57 Conclusion
Please don't go out of your way to pester Impressive-Mud5074 about his ultrafinitism! Despite the jokes, I hope you will come to understand where he is coming from throughout today's discussion!
"Pi is uncomputable", so said Impressive-Mud5074 on r/learnmath. From there, he was thoroughly discoursed and today we look at the whole saga - digging into computability, the halting problem, and ultrafinitism. #maths #mathmemes
More Math Chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
Business Inquiries: wrathofmathlessons@gmail.com
SOURCES
human.libretexts.org/Bookshelves/Philosophy/Logic_and_Reasoning/Sets_Logic_Computation_(Zach)/03%3A_III-_Turing_Machines/3.01%3A_Turing_Machine_Computations/3.1.01%3A_Introduction
Real Analysis is a Degenerate Case of Discrete Analysis by Doron Zielberger
https://plato.stanford.edu/entries/philosophy-mathematics/
Hilbert, David (1926), "Über das Unendliche", Mathematische Annalen, 95 (1): 161–190
Computational Complexity: A Modern Approach by Sanjeev Arora and Boaz Barak
What is Mathematics and What Should it Be? By Doron Zeilberger
mathworld.wolfram.com/AxiomofInfinity.html
Meta Math!: The Quest for Omega by Gregory Chaitin
Aristotelian Infinity by John Bowin
Understanding the Infinite by Shaughan Lavine
Computation Finite and Infinite Machines by Marvin L Minsky
Ultrafinitism by Joel David Hamkins
Alan Turing, On computable numbers by Joel David Hamkins
math.stackexchange.com/questions/462790/are-there-any-examples-of-non-computable-real-numbers
mathoverflow.net/questions/44208/is-there-any-formal-foundation-to-ultrafinitism
Constructivism in Mathematics an Introduction Volume 1 by A.S. Troelstra and D. Vandalen
On Computable Numbers, with an Application to the Entscheidungsproblem by A. M. Turing
0:00 Intro
2:02 Computable Numbers
3:49 Impressive Mud's Definition
7:05 Opposing Pi
12:53 Zielberger
15:33 Uncomputable Conception
21:57 Conclusion
