Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse Joel David Hamkins
Lex Fridman Podcast
Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More. Thank you for listening ❤ Check out our sponsors: lexfridman.com/sponsors/ep488-sc See below for , transcript, and to give feedback, submit questions, contact Lex, etc.
Transcript: lexfridman.com/joel-david-hamkins-tra...
CONTACT LEX: Feedback – give feedback to Lex: lexfridman.com/survey AMA – submit questions, videos or call-in: lexfridman.com/ama Hiring – join our team: lexfridman.com/hiring Other – other ways to get in touch: lexfridman.com/contact
EPISODE LINKS: Joel’s X: @JDHamkins Joel’s Website: jdh.hamkins.org Joel’s Substack: infinitelymore.xyz Joel’s MathOverflow: mathoverflow.net/users/1946/joel-davi... Joel’s Papers: jdh.hamkins.org/publications Joel’s Books: Lectures on the Philosophy of Mathematics: amzn.to/3MThaAt Proof and the Art of Mathematics: amzn.to/3YACc9A
SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to perplexity.ai Fin: AI agent for customer service. Go to fin.ai/lex Miro: Online collaborative whiteboard platform. Go to miro.com CodeRabbit: AI-powered code reviews. Go to coderabbit.ai/lex Chevron: Reliable energy for data centers. Go to chevron.com/power Shopify: Sell stuff online. Go to shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to drinkLMNT.com/lex MasterClass: Online classes from world-class experts. Go to masterclass.com/lexpod
OUTLINE:
- (00:00) – Introduction
- (01:58) – Sponsors, Comments, and Reflections
- (15:40) – Infinity & paradoxes
- (1:02:50) – Russell’s paradox
- (1:15:57) – Gödel’s incompleteness theorems
- (1:33:28) – Truth vs proof
- (1:44:52) – The Halting Problem
- (2:00:45) – Does infinity exist?
- (2:18:19) – MathOverflow
- (2:22:12) – The Continuum Hypothesis
- (2:31:58) – Hardest problems in mathematics
- (2:41:25) – Mathematical multiverse
- (3:00:18) – Surreal numbers
- (3:10:55) – Conway’s Game of Life
- (3:13:11) – Computability theory
- (3:23:04) – P vs NP
- (3:26:21) – Greatest mathematicians in history
- (3:40:05) – Infinite chess
- (3:58:24) – Most beautiful idea in mathematics
Raw Description
<p>Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More.<br /> Thank you for listening ❤ Check out our sponsors: <a href="https://lexfridman.com/sponsors/ep488-sc">https://lexfridman.com/sponsors/ep488-sc</a><br /> See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.</p> <p><b>Transcript:</b><br /> <a href="https://lexfridman.com/joel-david-hamkins-transcript">https://lexfridman.com/joel-david-hamkins-transcript</a></p> <p><b>CONTACT LEX:</b><br /> <b>Feedback</b> – give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a><br /> <b>AMA</b> – submit questions, videos or call-in: <a href="https://lexfridman.com/ama">https://lexfridman.com/ama</a><br /> <b>Hiring</b> – join our team: <a href="https://lexfridman.com/hiring">https://lexfridman.com/hiring</a><br /> <b>Other</b> – other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a></p> <p><b>EPISODE LINKS:</b><br /> Joel’s X: <a href="https://x.com/JDHamkins">https://x.com/JDHamkins</a><br /> Joel’s Website: <a href="https://jdh.hamkins.org">https://jdh.hamkins.org</a><br /> Joel’s Substack: <a href="https://www.infinitelymore.xyz">https://www.infinitelymore.xyz</a><br /> Joel’s MathOverflow: <a href="https://mathoverflow.net/users/1946/joel-david-hamkins">https://mathoverflow.net/users/1946/joel-david-hamkins</a><br /> Joel’s Papers: <a href="https://jdh.hamkins.org/publications">https://jdh.hamkins.org/publications</a><br /> Joel’s Books:<br /> Lectures on the Philosophy of Mathematics: <a href="https://amzn.to/3MThaAt">https://amzn.to/3MThaAt</a><br /> Proof and the Art of Mathematics: <a href="https://amzn.to/3YACc9A">https://amzn.to/3YACc9A</a></p> <p><b>SPONSORS:</b><br /> To support this podcast, check out our sponsors & get discounts:<br /> <b>Perplexity:</b> AI-powered answer engine.<br /> Go to <a href="https://lexfridman.com/s/perplexity-ep488-sc">https://www.perplexity.ai/</a><br /> <b>Fin:</b> AI agent for customer service.<br /> Go to <a href="https://lexfridman.com/s/fin-ep488-sc">https://fin.ai/lex</a><br /> <b>Miro:</b> Online collaborative whiteboard platform.<br /> Go to <a href="https://lexfridman.com/s/miro-ep488-sc">https://miro.com/</a><br /> <b>CodeRabbit:</b> AI-powered code reviews.<br /> Go to <a href="https://lexfridman.com/s/coderabbit-ep488-sc">https://coderabbit.ai/lex</a><br /> <b>Chevron:</b> Reliable energy for data centers.<br /> Go to <a href="https://lexfridman.com/s/chevron-ep488-sc">https://chevron.com/power</a><br /> <b>Shopify:</b> Sell stuff online.<br /> Go to <a href="https://lexfridman.com/s/shopify-ep488-sc">https://shopify.com/lex</a><br /> <b>LMNT:</b> Zero-sugar electrolyte drink mix.<br /> Go to <a href="https://lexfridman.com/s/lmnt-ep488-sc">https://drinkLMNT.com/lex</a><br /> <b>MasterClass:</b> Online classes from world-class experts.<br /> Go to <a href="https://lexfridman.com/s/masterclass-ep488-sc">https://masterclass.com/lexpod</a></p> <p><b>OUTLINE:</b><br /> (00:00) – Introduction<br /> (01:58) – Sponsors, Comments, and Reflections<br /> (15:40) – Infinity & paradoxes<br /> (1:02:50) – Russell’s paradox<br /> (1:15:57) – Gödel’s incompleteness theorems<br /> (1:33:28) – Truth vs proof<br /> (1:44:52) – The Halting Problem<br /> (2:00:45) – Does infinity exist?<br /> (2:18:19) – MathOverflow<br /> (2:22:12) – The Continuum Hypothesis<br /> (2:31:58) – Hardest problems in mathematics<br /> (2:41:25) – Mathematical multiverse<br /> (3:00:18) – Surreal numbers<br /> (3:10:55) – Conway’s Game of Life<br /> (3:13:11) – Computability theory<br /> (3:23:04) – P vs NP<br /> (3:26:21) – Greatest mathematicians in history<br /> (3:40:05) – Infinite chess<br /> (3:58:24) – Most beautiful idea in mathematics</p>
Chapters (1/19)
Show Notes
Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More. Thank you for listening ❤ Check out our sponsors: lexfridman.com/sponsors/ep488-sc See below for , transcript, and to give feedback, submit questions, contact Lex, etc.
Transcript: lexfridman.com/joel-david-hamkins-tra...
CONTACT LEX: Feedback – give feedback to Lex: lexfridman.com/survey AMA – submit questions, videos or call-in: lexfridman.com/ama Hiring – join our team: lexfridman.com/hiring Other – other ways to get in touch: lexfridman.com/contact
EPISODE LINKS: Joel’s X: @JDHamkins Joel’s Website: jdh.hamkins.org Joel’s Substack: infinitelymore.xyz Joel’s MathOverflow: mathoverflow.net/users/1946/joel-davi... Joel’s Papers: jdh.hamkins.org/publications Joel’s Books: Lectures on the Philosophy of Mathematics: amzn.to/3MThaAt Proof and the Art of Mathematics: amzn.to/3YACc9A
SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to perplexity.ai Fin: AI agent for customer service. Go to fin.ai/lex Miro: Online collaborative whiteboard platform. Go to miro.com CodeRabbit: AI-powered code reviews. Go to coderabbit.ai/lex Chevron: Reliable energy for data centers. Go to chevron.com/power Shopify: Sell stuff online. Go to shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to drinkLMNT.com/lex MasterClass: Online classes from world-class experts. Go to masterclass.com/lexpod
OUTLINE:
- (00:00) – Introduction
- (01:58) – Sponsors, Comments, and Reflections
- (15:40) – Infinity & paradoxes
- (1:02:50) – Russell’s paradox
- (1:15:57) – Gödel’s incompleteness theorems
- (1:33:28) – Truth vs proof
- (1:44:52) – The Halting Problem
- (2:00:45) – Does infinity exist?
- (2:18:19) – MathOverflow
- (2:22:12) – The Continuum Hypothesis
- (2:31:58) – Hardest problems in mathematics
- (2:41:25) – Mathematical multiverse
- (3:00:18) – Surreal numbers
- (3:10:55) – Conway’s Game of Life
- (3:13:11) – Computability theory
- (3:23:04) – P vs NP
- (3:26:21) – Greatest mathematicians in history
- (3:40:05) – Infinite chess
- (3:58:24) – Most beautiful idea in mathematics
Raw Description
<p>Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he’s the #1 highest-rated user on MathOverflow. He is also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More.<br /> Thank you for listening ❤ Check out our sponsors: <a href="https://lexfridman.com/sponsors/ep488-sc">https://lexfridman.com/sponsors/ep488-sc</a><br /> See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.</p> <p><b>Transcript:</b><br /> <a href="https://lexfridman.com/joel-david-hamkins-transcript">https://lexfridman.com/joel-david-hamkins-transcript</a></p> <p><b>CONTACT LEX:</b><br /> <b>Feedback</b> – give feedback to Lex: <a href="https://lexfridman.com/survey">https://lexfridman.com/survey</a><br /> <b>AMA</b> – submit questions, videos or call-in: <a href="https://lexfridman.com/ama">https://lexfridman.com/ama</a><br /> <b>Hiring</b> – join our team: <a href="https://lexfridman.com/hiring">https://lexfridman.com/hiring</a><br /> <b>Other</b> – other ways to get in touch: <a href="https://lexfridman.com/contact">https://lexfridman.com/contact</a></p> <p><b>EPISODE LINKS:</b><br /> Joel’s X: <a href="https://x.com/JDHamkins">https://x.com/JDHamkins</a><br /> Joel’s Website: <a href="https://jdh.hamkins.org">https://jdh.hamkins.org</a><br /> Joel’s Substack: <a href="https://www.infinitelymore.xyz">https://www.infinitelymore.xyz</a><br /> Joel’s MathOverflow: <a href="https://mathoverflow.net/users/1946/joel-david-hamkins">https://mathoverflow.net/users/1946/joel-david-hamkins</a><br /> Joel’s Papers: <a href="https://jdh.hamkins.org/publications">https://jdh.hamkins.org/publications</a><br /> Joel’s Books:<br /> Lectures on the Philosophy of Mathematics: <a href="https://amzn.to/3MThaAt">https://amzn.to/3MThaAt</a><br /> Proof and the Art of Mathematics: <a href="https://amzn.to/3YACc9A">https://amzn.to/3YACc9A</a></p> <p><b>SPONSORS:</b><br /> To support this podcast, check out our sponsors & get discounts:<br /> <b>Perplexity:</b> AI-powered answer engine.<br /> Go to <a href="https://lexfridman.com/s/perplexity-ep488-sc">https://www.perplexity.ai/</a><br /> <b>Fin:</b> AI agent for customer service.<br /> Go to <a href="https://lexfridman.com/s/fin-ep488-sc">https://fin.ai/lex</a><br /> <b>Miro:</b> Online collaborative whiteboard platform.<br /> Go to <a href="https://lexfridman.com/s/miro-ep488-sc">https://miro.com/</a><br /> <b>CodeRabbit:</b> AI-powered code reviews.<br /> Go to <a href="https://lexfridman.com/s/coderabbit-ep488-sc">https://coderabbit.ai/lex</a><br /> <b>Chevron:</b> Reliable energy for data centers.<br /> Go to <a href="https://lexfridman.com/s/chevron-ep488-sc">https://chevron.com/power</a><br /> <b>Shopify:</b> Sell stuff online.<br /> Go to <a href="https://lexfridman.com/s/shopify-ep488-sc">https://shopify.com/lex</a><br /> <b>LMNT:</b> Zero-sugar electrolyte drink mix.<br /> Go to <a href="https://lexfridman.com/s/lmnt-ep488-sc">https://drinkLMNT.com/lex</a><br /> <b>MasterClass:</b> Online classes from world-class experts.<br /> Go to <a href="https://lexfridman.com/s/masterclass-ep488-sc">https://masterclass.com/lexpod</a></p> <p><b>OUTLINE:</b><br /> (00:00) – Introduction<br /> (01:58) – Sponsors, Comments, and Reflections<br /> (15:40) – Infinity & paradoxes<br /> (1:02:50) – Russell’s paradox<br /> (1:15:57) – Gödel’s incompleteness theorems<br /> (1:33:28) – Truth vs proof<br /> (1:44:52) – The Halting Problem<br /> (2:00:45) – Does infinity exist?<br /> (2:18:19) – MathOverflow<br /> (2:22:12) – The Continuum Hypothesis<br /> (2:31:58) – Hardest problems in mathematics<br /> (2:41:25) – Mathematical multiverse<br /> (3:00:18) – Surreal numbers<br /> (3:10:55) – Conway’s Game of Life<br /> (3:13:11) – Computability theory<br /> (3:23:04) – P vs NP<br /> (3:26:21) – Greatest mathematicians in history<br /> (3:40:05) – Infinite chess<br /> (3:58:24) – Most beautiful idea in mathematics</p>