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

    31/12/2025

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

    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: https://lexfridman.com/sponsors/ep488-sc See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc. Transcript: https://lexfridman.com/joel-david-hamkins-transcript CONTACT LEX: Feedback – give feedback to Lex: https://lexfridman.com/survey AMA – submit questions, videos or call-in: https://lexfridman.com/ama Hiring – join our team: https://lexfridman.com/hiring Other – other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Joel’s X: https://x.com/JDHamkins Joel’s Website: https://jdh.hamkins.org Joel’s Substack: https://www.infinitelymore.xyz Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins Joel’s Papers: https://jdh.hamkins.org/publications Joel’s Books: Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt Proof and the Art of Mathematics: https://amzn.to/3YACc9A SPONSORS: To support this podcast, check out our sponsors & get discounts: Perplexity: AI-powered answer engine. Go to https://www.perplexity.ai/ Fin: AI agent for customer service. Go to https://fin.ai/lex Miro: Online collaborative whiteboard platform. Go to https://miro.com/ CodeRabbit: AI-powered code reviews. Go to https://coderabbit.ai/lex Chevron: Reliable energy for data centers. Go to https://chevron.com/power Shopify: Sell stuff online. Go to https://shopify.com/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex MasterClass: Online classes from world-class experts. Go to https://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

  • The Benchmark With No Instructions — ARC-AGI-3 (winning team!)

    1 Jul

    The Benchmark With No Instructions — ARC-AGI-3 (winning team!)

    Tim Scarfe travels to Zurich to sit down with the Tufa Labs ARC-AGI-3 team — founder Benjamin Crouzier, with Jeroen Cottaar, Dries Smit, Stefano Viel and Michal Tesnar — to work out what their leaderboard-topping system does and what the benchmark is really testing.The cut opens on the games: a walkthrough of the Locksmith game, where you read the rules of an unfamiliar world straight from raw frames. ARC-AGI-3 makes ARC interactive and agentic, so the model has to *discover* the goal rather than transduce a static grid. It stays easy for humans and breaks LLMs, and it runs through everything that follows. Dries traces his StochasticGoose preview win — brute force that only searched actions which changed the frame — and why it collapsed once the organisers added action-efficiency scoring and unseen games.Induction and transduction run through the middle of the conversation — how much of an answer is really priors leaking back the moment a model recognises a maze. The abstraction mountain, and Tim's case that LLMs reach the right answer through fractured, entangled representations — performance, not competence. Whether transformers plan at all or just fake it well enough. Why the score really measures action efficiency, not games solved, and why agents lock onto the wrong goal and cannot climb back out.Crouzier closes on the Tufa Labs thesis — a small lab against the giants, the bitter lesson against hand-built harnesses, and safety — and Tim ties it back to Kenneth Stanley, deep constraints, and creativity as competence. Disclosure: Tufa Labs sponsors MLST. ---TIMESTAMPS:00:00:00 Meet the Tufa team and what makes ARC-AGI-3 hard00:02:11 Locksmith game: reading the rules from raw frames00:03:10 Why build an independent research lab00:04:11 StochasticGoose: a preview win, then the hardened games00:07:58 Induction, transduction, and priors inside LLMs00:10:31 Curiosity, world models, and exploring by frame change00:14:32 Understanding debt and losing sight of your own code00:15:53 Requirements-based agents and human-AI co-creativity00:19:22 Why auto-research misses the big picture00:21:54 The abstraction mountain and fractured representations00:27:36 Constraints and making LLMs act as if they understand00:34:51 Human difficulty calibration, esports priors, and emergence00:41:35 Agency, goal acquisition, and two kinds of planning00:47:31 Harnesses, the 36% number, and wrong-goal loops00:52:33 Rewards, goals, and why ARC-AGI-3 resists brute force01:00:46 Would solving ARC-AGI-3 prove AGI?01:07:53 Stripping language away, then priors leak back01:14:06 Representation and whether language is necessary01:18:04 The bitter lesson versus specialised harnesses01:22:20 Capability research, safety, and the software singularity---REFERENCES:organization:[00:02:11] ARC-AGI-3https://arcprize.org/arc-agi/3[00:03:10] Tufa Labshttps://tufalabs.ai/team/[00:04:20] ARC-AGI-3 Preview Agent Competitionhttps://arcprize.org/competitions/arc-agi-3-preview-agentstool:[00:04:55] StochasticGoose ARC-AGI-3 solutionhttps://github.com/DriesSmit/ARC3-solution[00:07:42] ArcGenticahttps://github.com/symbolica-ai/arcgentica[00:07:49] RGB-Agenthttps://github.com/alexisfox7/RGB-Agent[00:14:38] Claude Codehttps://www.anthropic.com/claude-code[01:03:42] Qwen 3.6 27Bhttps://huggingface.co/Qwen/Qwen3.6-27Bpaper:[00:13:03] On the Measure of Intelligencehttps://arxiv.org/abs/1911.01547[00:27:42] DreamCoderhttps://arxiv.org/abs/2006.08381[00:43:55] On the Biology of a Large Language Modelhttps://transformer-circuits.pub/2025/attribution-graphs/biology.html[01:18:46] ImageNet Classification with Deep CNNs (AlexNet)https://proceedings.neurips.cc/paper_files/paper/2012/file/c399862d3b9d6b76c8436e924a68c45b-Paper.pdfother:[01:18:16] The Bitter Lessonhttp://www.incompleteideas.net/IncIdeas/BitterLesson.html---https://app.rescript.info/share/463d7f031349b4b9db428553eed88230

  • #497 – Biggest Mysteries in Physics: Antimatter, Dark Energy & ToE – Don Lincoln

    29 May

    #497 – Biggest Mysteries in Physics: Antimatter, Dark Energy & ToE – Don Lincoln

    Don Lincoln is a particle physicist at Fermilab who has spent decades working at the frontiers of high energy physics. Thank you for listening ❤ Check out our sponsors: https://lexfridman.com/sponsors/ep497-sc See below for timestamps, and to give feedback, submit questions, contact Lex, etc. CONTACT LEX: Feedback – give feedback to Lex: https://lexfridman.com/survey AMA – submit questions, videos or call-in: https://lexfridman.com/ama Hiring – join our team: https://lexfridman.com/hiring Other – other ways to get in touch: https://lexfridman.com/contact EPISODE LINKS: Don’s Facebook: https://facebook.com/Dr.Don.Lincoln/ Don’s Website: https://drdonlincoln.com/ Don’s LinkedIn: https://bit.ly/4nHeNiF Don’s YouTube Playlist: https://bit.ly/3PCIW67 Don’s X: https://x.com/DrDonLincoln Don’s Books: https://amzn.to/4uYbkOZ Don’s Great Courses: https://shop.thegreatcourses.com/don-lincoln Don’s Audible: https://adbl.co/4wGioRV Fermilab’s YouTube: https://www.youtube.com/fermilab Fermilab’s Website: https://www.fnal.gov/ Fermilab’s X: https://x.com/fermilab SPONSORS: To support this podcast, check out our sponsors & get discounts: Upwork: Platform for hiring freelancers. Go to https://upwork.com/lex Larridin: Measure AI adoption in your business. Go to https://larridin.com Fin: AI agent for customer service. Go to https://fin.ai/lex LMNT: Zero-sugar electrolyte drink mix. Go to https://drinkLMNT.com/lex Shopify: Sell stuff online. Go to https://shopify.com/lex Perplexity: AI-powered answer engine. Go to https://perplexity.ai/ OUTLINE: (00:00) – Introduction (00:34) – Sponsors, Comments, and Reflections (08:52) – Unifying the laws of nature (23:23) – Einstein, special relativity, and general relativity (40:31) – Electroweak force (52:13) – How particle colliders work (1:10:16) – Higgs boson discovery (1:20:35) – Theory of everything (1:50:20) – Physics of empty space (1:57:45) – Antimatter (2:18:35) – Dark energy (2:22:23) – Dark matter (2:50:59) – Future of physics PODCAST LINKS: – Podcast Website: https://lexfridman.com/podcast – Apple Podcasts: https://apple.co/2lwqZIr – Spotify: https://spoti.fi/2nEwCF8 – RSS: https://lexfridman.com/feed/podcast/ – Podcast Playlist: https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4 – Clips Channel: https://www.youtube.com/lexclips

  • Blake Scholl: Breaking the Supersonic Ban

    2 days ago

    Blake Scholl: Breaking the Supersonic Ban

    In 1969, we landed on the moon and flew Concorde. Half a century later, we could do neither. Blake Scholl founded Boom Supersonic (YC W16), the startup building America’s first supersonic airliner, to change that. At Startup School 2026, he shares how a cardboard mockup with Office Depot seats became XB-1, the first independently developed jet to break the sound barrier, and why founders have to build for both the worst day and the best day. He also answers founder questions about teaching yourself hard things, breaking into hardware without the right resume, and finding work-life harmony while building something ambitious.

  • Jensen Huang: The Mindset That Built NVIDIA

    4 days ago

    Jensen Huang: The Mindset That Built NVIDIA

    NVIDIA started with the wrong technology, learned the right one from three textbooks bought at Fry’s, and went on to invent most of the major breakthroughs in modern computing.At Startup School 2026 at Chase Center, Garry Tan sits down with Founder and CEO Jensen Huang to talk about confronting reality, learning your way into new domains, and why resilience — getting through one day at a time — matters more than anything else.

  • How to pursue excellence … in noodles (unlocked bonus)

    17 Jul

    How to pursue excellence … in noodles (unlocked bonus)

    The world right now, seems tilted towards the good enough. The AI-written wedding toast, the half-assed attempt. Despite this, a handmade noodle shop is trying to make perfect noodles. Trying so hard that they have signs admonishing their customers to ONLY EAT THEIR SPICY NOODLES THE CORRECT WAY, DO NOT TAKE THEM TO-GO, THE EXPERIENCE WILL BE RUINED. Why do some people still want to do small things perfectly, even at the expense of profits? An interview with Jason Wang, of Xi'an Famous Foods. Become a premium member!

  • Sam Altman: "Never a Better Time to Do a Startup"

    3 days ago

    Sam Altman: "Never a Better Time to Do a Startup"

    In 2005, Sam Altman was a Stanford sophomore in YC’s first batch, building a startup in a little Cambridge office while Paul Graham cooked the founders dinner. Twenty years later, as co-founder & CEO of OpenAI, he closed Startup School 2026 in conversation with YC's Garry Tan — on agents, ambition, and why the ceiling for what a startup can take on has never been higher.

  • Why is the pool at Buckingham Palace a secret? (classic)

    5 Jun

    Why is the pool at Buckingham Palace a secret? (classic)

    An investigation into a mysterious room. A room that the most famous family in England apparently does not want you to see. Support the show!

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