#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

**Lex Fridman** (0:00)
The following is a conversation with Joel David Hamkins, a mathematician and philosopher specializing in set theory, the foundation of mathematics, and the nature of infinity. He is the number one highest rated user on math overflow, which I think is a legendary accomplishment. Math overflow, by the way, is like stack overflow, but for research mathematicians. 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, infinitelymore.xyz.
This is a super technical, super fun conversation about the foundation of modern mathematics and some mind bending ideas about infinity, nature of reality, truth, and the mathematical paradoxes that challenged some of the greatest minds of the 20th century. I have been hiding from the world a bit. Reading, thinking, writing, soul searching, as we all do every once in a while. But mostly just deeply focused on work and preparing mentally for some challenging travel I plan to take on in the new year. Through all of it, a recurring thought comes to me. How damn lucky I am to be alive and to get to experience so much love from folks across the world. I want to take this moment to say thank you from the bottom of my heart for everything. For your support, for the many amazing conversations I've had with people across the world. I got a little bit of hate and a whole lot of love and I wouldn't have it any other way. I'm grateful for all of it. Now, a quick few second mention of a sponsor, check them out in the description or at lexfridman.com/sponsors. It is in fact the best way to support this podcast. We got Perplexity for Curiosity-Driven Knowledge Exploration, Fin for Customer Service AI Agents, Miro for Brainstorming Ideas with Your Team, Code Rabbit for Code Review, Chevron for Liable Energy that Powers Data Centers, Shopify for Selling Stuff Online, Element for Electrolytes and Masterclass for Learning. Choose wisely, my friends. Well, a bunch of sponsors this time because it's the end of the year and I haven't been publishing podcasts. I've been laying low, as I mentioned in the introduction. I'm just really grateful for the patience and the support of the sponsors. The companies and the humans behind those companies have been really amazing over the years. I don't think I would be able to do many of the crazy and the difficult things I'm doing with this podcast without the support of the sponsors. Please go check out their stuff. Please go support them. Please buy whatever they're selling. Really, it helps a lot. It is the best way to support the podcast. I'll do the full ad reads now. I try to make them interesting. But if you skip, please still do check out the sponsors. I enjoy their stuff. Maybe you will too. To get in touch with me for whatever reason, go to lexfridman.com/contact.
In case I don't get a chance to say this, Happy New Year. Let's make this 2026 a fun one. All right, let's go. This episode is brought to you by Finn, the number one AI agent for customer service. 65% average resolution rate. Trusted by over 6,000 customers, including some incredible companies, incredible technology companies, incredible AI companies. When an AI company trusts you to do the customer service, you know you're legit. Built to handle complex, multi-step queries like returns, exchanges and disputes. I really do think a big part of what makes a product or a company incredible is the customer service. And getting that right, where you can handle, you can help take care of the needs of the customer and the complicated problems. Sometimes it's hand holding, never talking down to them, trying not to do too basic a solution to a very unique particular kind of problem because each customer problem, yes, might look like a common problem, but it has unique certain characteristics to it. If you pay attention to them and you take care of them, you can really make a person happy. And a company that makes a large number of people happy is going to be a great company. Anyway, go to fin.ai/lex to learn more about transforming your customer service and scaling your support team. That's fin.ai/lex. This episode is also brought to you by Miro, an online collaborative platform. They have this innovation workspace that blends AI and human creativity to turn ideas into real things, into results. One of the things I love the most recently getting back into the research environment, working on a lot of fun robotics projects with a lot of brilliant mechanical engineers, software engineers, machine learning people, robotics people, is just the conversations we have. Sometimes the aimless exploration of ideas, sometimes banter, sometimes humor, sometimes real rigor over mathematical models of a particular phenomena. Whether it's the controllers, whether it's the perception of the robots, whether it's the different stages of the ML process, whether it's the different layers of the stack of the robotics platforms, from the theory to the software to the hardware, and just talking through it, tossing ideas back and forth. Talking shit back and forth. It's such a fun thing to do. It makes it fun. And I think Miro is striving to do that in the cyberspace. Yeah, saves time. Yeah, it's user-friendly, but it also tries to make the whole ideation team, brainstorming team work fun. Help your teams develop great ideas into results with Miro. Go to miro.com to find out how. That's miro.com. This episode is also brought to you by Code Rabbit, a platform that provides AI-powered code reviews directly within your terminal. As more and more code is generated, developers end up spending more and more time reading and reviewing code. And if you're trying to ship code, production code, code you can rely on, there's this whole process of reviewing it. And that's what Code Rabbit specializes in, used by over 100,000 open source projects. It's a very specific application of AI to handle this very specific part, but a crucial part of the software engineering process. If you want to ship a thing, you want to make sure the thing runs. And to make sure that it runs, you have to understand the code deeply. It supports basically all programming languages. To try it out, you want to install the Code Rabbit CLI today at coderabbit.ai/lex. That's coderabbit.ai/lex.