Machine Learning Street Talk (MLST)

Kevin Hartnett is the author of *The Proof in the Code*.SPONSOR:---Cyber Fund built the Monastery to help founders ship products that were impossible a year ago. Applications for Batch 1 are now open.Apply now: https://cyber.fund---In 1998 Thomas Hales finished a proof of the Kepler conjecture that leaned so heavily on computer code that the Annals of Mathematics could not say whether it was true. That impasse opens Kevin Hartnett's book *The Proof in the Code*, and this documentary.Built around Tim's conversation with Hartnett, the film follows Lean from a side project at Microsoft Research to the system mathematicians now use to check their own field. Leonardo de Moura, Lean's creator, explains why everything rests on a small trusted kernel. Jeremy Avigad recalls the argument over foundations that changed Lean. Kevin Buzzard describes his fear that his corner of mathematics was becoming a house of cards, and Paul Lessard separates a correct proof from a useful one. Mathlib, Peter Scholze's Liquid Tensor challenge and Terence Tao's Equational Theories project all pass through.The second half turns to AI. AlphaProof, natural-language olympiad proofs and autoformalisation sharpen the question the book keeps asking: when a machine produces a proof nobody can read, what has actually been checked? The answer lies in the formalisation gap, the distance between the mathematics people mean and the statement a checker certifies. The film closes on the human story behind the software.---TIMESTAMPS:0:00 Cold open: proof, code and the wrong problem1:50 Kepler's oranges and the proof nobody could check6:54 How mathematicians decide a proof is true9:04 Correct is not the same as useful12:17 Sponsor: Cyber Fund12:53 What Lean is, and the small kernel it trusts15:23 From Microsoft's Z3 to Lean18:22 The argument over Lean's foundations24:52 One researcher versus a growing user base26:16 Kevin Buzzard's house of cards30:43 Mathlib as a barn raising37:16 The perfectoid-spaces stunt47:12 Scholze's proof nobody had read: Liquid Tensor53:20 Can AI learn to find proofs? AlphaProof58:43 AI mathematics in 2026 and Tao's experiment1:01:36 Lean's place in AI mathematics1:02:17 AI brute force versus the right abstraction1:05:19 Autoformalisation's Trojan horse1:07:25 The formalisation gap1:11:45 A proof is not understanding1:16:58 Integration hell and the zlib specification1:21:14 Verification in the AI software lifecycle1:22:38 The human story behind Lean1:31:09 The birthday walk1:33:05 Farewell---REFERENCES:[2:12] Thomas Hales, A proof of the Kepler conjecture (Annals of Mathematics, 2005)https://annals.math.princeton.edu/2005/162-3/p01[2:12] The Flyspeck project (the formal proof of the Kepler conjecture)https://github.com/flyspeck/flyspeck[12:53] Leanhttps://lean-lang.org/[30:43] Mathlibhttps://github.com/leanprover-community/mathlib4[30:43] Kevin Hartnett, "Building the Mathematical Library of the Future" (Quanta Magazine, 2020)https://www.quantamagazine.org/building-the-mathematical-library-of-the-future-20201001/[47:12] The Liquid Tensor Experimenthttps://github.com/leanprover-community/lean-liquid[53:20] AlphaProof (Google DeepMind): AI achieves silver-medal standard solving International Mathematical Olympiad problemshttps://deepmind.google/blog/ai-solves-imo-problems-at-silver-medal-level/[59:23] The Equational Theories Project (Terence Tao)https://github.com/teorth/equational_theories[1:18:30] lean-zip (the zlib proof)https://github.com/kim-em/lean-zipFrontierMath Erdős (Epoch AI, 2026)https://epoch.ai/benchmarks/frontiermath-erdosBook: Kevin Hartnett, *The Proof in the Code* (Quanta Books, 2026)https://www.quantabooks.org/books/the-proof-in-the-code/---RESCRIPT: https://app.rescript.info/share/8604a0cd6ea4604a368028a05f4e6be4Support MLST on Patreon: https://www.patreon.com/mlstDiscord: https://discord.gg/HNnAwSduud

A lot of people in AI treat evolution as a dumb fallback, basically random search for when you can't take a gradient. Akarsh Kumar thinks that is wrong. Selection hangs on to partial solutions, so mutations only need to be useful about 1% of the time for the search to keep making progress.Akarsh is a PhD student at MIT working with Phillip Isola, works with Sakana AI, and is first author of the Fractured Entangled Representation paper with Kenneth Stanley, Jeff Clune and Joel Lehman. He tells Tim Scarfe why the path a learner takes may shape the structure of what it learns, and why that is a different way of looking at intelligence from the statistical one.Most of the conversation is about ASAL, the method he led for searching whole spaces of artificial worlds. Rather than predict what a rule will do, ASAL runs the simulation and asks a foundation model what happened. Mapped across all 262,144 Life-like rules, the most interesting worlds sit on one small island. Along the way: Game of Life, Lenia (with a clip from its creator, Bert Chan), neural cellular automata, Boids, Particle Life and the emergence of persistence.---TIMESTAMPS:00:00:00 Intro: artificial life, ASAL and Core War in four minutes00:04:19 Life as it could be, not just as it is00:05:46 Why the order you learn things in matters00:08:33 No shortcuts: Wolfram, novelty search and regularisation00:10:44 Kenneth Stanley: the path matters, not just the destination00:11:31 Statistical intelligence vs regularity-based intelligence00:13:49 Artificial chemistry and other possible universes00:15:59 Convergent patterns: shadows of the substrate?00:18:02 How Conway's Game of Life works00:20:49 Change one cell, change everything?00:22:31 Lenia (with Bert Chan) and neural cellular automata00:25:26 Boids, Particle Life and cell-like creatures00:28:47 Persistence, entropy and what life is00:30:15 ASAL: a foundation model as the critic00:34:04 Impostors inside the simulation00:36:50 From primordial soup to alien animals00:38:26 262,144 rules and the island of open-endedness00:40:17 From artificial life to AGI00:41:35 Core War: Game of Thrones, Turing edition00:43:22 LLMs as the mutation step: evolving warriors00:46:03 Evolution is anything but random---REFERENCES:paper:[00:04:19] ASAL (Kumar et al.)https://arxiv.org/abs/2412.17799[00:08:08] Assembly theory https://www.nature.com/articles/s41586-023-06600-9[00:09:54] FEP paperhttps://arxiv.org/abs/2505.11581[00:22:38] Lenia: Biology of Artificial Life (Bert Chan)https://arxiv.org/abs/1812.05433[00:23:20] Growing Neural Cellular Automata (Mordvintsev et al.)https://distill.pub/2020/growing-ca/[00:41:35] Digital Red Queen: Core War with LLMs (Kumar et al.)https://arxiv.org/abs/2601.03335[00:43:42] MAP-Elites https://arxiv.org/abs/1504.04909[00:44:55] AlphaEvolve https://arxiv.org/abs/2506.13131[00:47:03] AutoML-Zero (Real et al.)https://arxiv.org/abs/2003.03384book:[00:07:04] Why Greatness Cannot Be Planned (Stanley and Lehman)https://link.springer.com/book/10.1007/978-3-319-15524-1tool:[00:18:12] Conway's Game of Lifehttps://en.wikipedia.org/wiki/Conway%27s_Game_of_Life[00:25:27] Boids (Craig Reynolds)https://www.red3d.com/cwr/boids/[00:27:12] Particle Life (Tom Mohr)https://github.com/tom-mohr/particle-life[00:41:50] Core Warhttps://corewar.co.uk/other:[00:08:49] Computational irreducibility (Stephen Wolfram)https://www.wolframscience.com/nks/p737--computational-irreducibility/[00:10:46] MLST: Why Every AI Model Is an Impostor (Kenneth Stanley, FER documentary)https://www.youtube.com/watch?v=o1q6Hhz0MAg[00:28:30] MLST: Blaise Agüera y Arcas on life emerging from codehttps://www.youtube.com/watch?v=rMSEqJ_4EBk---LINKS:Akarsh Kumar: https://akarshkumar.com/ASAL project page and demos: https://pub.sakana.ai/asal/Digital Red Queen project page: https://sakana.ai/drq/RESCRIPT:https://app.rescript.info/public/share/Qfv3T0EVzqOXL_CYYeRr9Blv8HnNm4JsXBh7ByFjJbc

Tsung-Hsien (Shawn) Wen, CTO of PolyAI, tells Tim Scarfe why voice agents are harder than text agents. Voice adds time, and a good conversation depends on adapting to the person on the line, not just on reasoning to the best answer. Shawn describes an audio-native model (Dialog-RSN-1) that first predicts a turn-taking signal, then replies in text with citations, and writes the transcript last so enterprises can audit it.Along the way: training on real, noisy calls with synthetic noise added, and why over-cleaned audio made the new model worse. Latency, and what a voice agent should do while it thinks. Why a voice with a hint of regional accent beats a generic one. Why public benchmarks fall short for voice, why enterprises want to own their agent harness, and whether behaviour belongs in the harness or in the weights.The last stretch is about working with agents: cognitive debt, the shift from producing content to checking it, Wispr Flow, building tools that agents can use, and whether slop is in the eye of the reader.This episode was produced in partnership with PolyAI.https://poly.ai CHAPTERS0:00 Why voice agents are harder than text4:27 What enterprises want, and why PolyAI built its own model9:04 How an audio-native voice model works15:21 Training data, spectrograms and synthetic noise20:36 The cocktail party problem and the future of turn-taking25:21 Latency, adaptive reasoning and keeping callers' trust31:33 Voices, personality and the uncanny valley36:32 How do you benchmark a voice agent?42:00 Harness engineering and owning the intelligence45:09 Well-specified problems and auditable agents49:46 Weight adaptation and cognitive debt56:31 Agents at work: Wispr Flow, voice and tool building1:02:50 The next decade of voice, and what counts as slopREFERENCESThe Bitter Lesson: http://www.incompleteideas.net/IncIdeas/BitterLesson.html [9:05]Retrieval-augmented generation: https://arxiv.org/abs/2005.11401 [13:23]Mel scale: https://en.wikipedia.org/wiki/Mel_scale [17:16]Victor Zue: https://en.wikipedia.org/wiki/Victor_Zue [17:45]Cocktail party effect: https://en.wikipedia.org/wiki/Cocktail_party_effect [20:39]Speaker diarisation: https://en.wikipedia.org/wiki/Speaker_diarisation [21:16]

Leonardo de Moura created Lean and co-created Z3. ---This episode is sponsored by Parallel.Parallel, where agents find answers: web search, extraction and deep research APIs built for AI agents.Start free with the Parallel MCP server and $5 of credits every month: https://parallel.ai/mlst?utm_source=creator&utm_medium=podcast&utm_content=MLST---Tim Scarfe talks with Leo about how Lean escaped its original audience, why dependent types and Mathlib made it useful to working mathematicians, and what happens when formal verification leaves the lab. De Moura explains the small trusted kernel and independent checkers, and gives his account of the recent Collatz incident, in which a purported proof was accepted by both Lean's official kernel and Nanoda, apparently by exploiting a different bug in each.---TIMESTAMPS:00:00:00 Cold open: the green checkmark can lie00:00:59 Cathedral or bazaar: who controls Lean's core?00:04:55 Why Lean's core stays small and protected00:08:07 The Slack purge, Brandolini's law and the Lean FRO00:11:12 The Collatz exploit: two kernels, two bugs00:16:44 More kernels, reward hacking and safety by transparency00:21:04 Sponsor: Parallel00:21:59 Kim Morrison, Claude and the zlib proof00:25:25 Can we specify complex systems?00:28:04 Specs change: proofs are cheaper to redo with AI00:31:27 From Lean 1 to Lean 400:34:57 Dependent types in plain terms00:37:25 Lean 4's extensibility and Mathlib's growth00:41:44 Mathlib as infrastructure: Formal Frontiers00:44:15 Creativity, abstraction and nut-sniping00:48:46 Breadcrumbs, not learning: what AI agents lack00:53:03 Competence without comprehension, and verified guardrails00:56:21 Is the human still the author?01:01:44 AlphaProof, LLMs and why certificates still matter01:06:38 What's next for Lean, and its legacy01:11:42 How to start learning Lean---REFERENCES:tool:[00:00:48] Leanhttps://lean-lang.org/[00:01:24] Mathlibhttps://github.com/leanprover-community/mathlib4[00:12:09] nanoda_libhttps://github.com/ammkrn/nanoda_lib[00:12:19] CollatzLeanhttps://github.com/xrchz/CollatzLean/blob/a79357462a33d2a6babd4cf6c8d8bcd25425d653/README.md[00:13:06] Lean issue 14576https://github.com/leanprover/lean4/issues/14576[00:13:21] Lean pull request 14577https://github.com/leanprover/lean4/pull/14577[00:13:45] nanoda_lib pull request 22https://github.com/ammkrn/nanoda_lib/pull/22[00:15:33] Lean comparatorhttps://github.com/leanprover/comparator[00:18:02] Lean4Leanhttps://github.com/digama0/lean4lean[00:19:50] ARC-AGI-3https://arcprize.org/arc-agi/3[00:21:59] lean-ziphttps://github.com/kim-em/lean-zip[00:29:45] CompCerthttps://compcert.org/[00:29:45] seL4https://www.sel4.org/[00:30:23] Z3https://github.com/Z3Prover/z3[00:38:10] Veilhttps://github.com/verse-lab/veil[00:38:10] Velvethttps://github.com/verse-lab/velvetorganization:[00:00:52] Lean FROhttps://lean-lang.org/fro/[00:42:39] Mathlib Initiativehttps://mathlib-initiative.org/about/person:[00:05:11] Ilya Sergeyhttps://ilyasergey.net/[00:10:31] Joachim Breitnerhttps://www.joachim-breitner.de/[00:32:58] Adam Chlipalahttps://adam.chlipala.net/[00:38:42] Kevin Buzzardhttps://www.ma.imperial.ac.uk/~buzzard/[01:10:16] Terence Taohttps://terrytao.wordpress.com/book:[00:08:19] The Proof in the Codehttps://us.macmillan.com/books/9780374620059/theproofinthecode/other:[00:10:05] Brandolini's lawhttps://en.wikipedia.org/wiki/Brandolini%27s_law[00:45:33] A new result on unit distanceshttps://openai.com/index/model-disproves-discrete-geometry-conjecture/[01:01:08] Fermat's Last Theorem formalisationhttps://imperialcollegelondon.github.io/FLT/paper:[00:34:36] The Lean 4 theorem prover and programming languagehttps://doi.org/10.1007/978-3-030-79876-5_37---RESCRIPT:https://app.rescript.info/share/7d3d4a0059443236a01f6c9acbf4db58https://app.rescript.info/api/public/sessions/b007264c0ce89047/pdf

Weco let an AI coding agent rewrite the harness around another agent for eight days: its code, prompts and tools, while the underlying language model stayed fixed. Tim Scarfe asks Weco co-founder Zhengyao Jiang what the reported gains over two years of human engineering actually demonstrate.The discussion examines AIDE 85's generated code, held-out evaluation and the difficulty of separating useful discoveries from reward hacking. Jiang explains Weco's four levels of recursive self-improvement and compares the experiment with AlphaEvolve and the Darwin Gödel Machine.The limits matter as much as the gains. Jiang explains why the experiment did not establish that the system had become a better improver. The conversation closes with open-ended search, human-designed primitives and Parameter Golf: where does the next useful idea come from when the agent is searching inside a space that people designed?---TIMESTAMPS:00:00:00 Eight days of self-improvement: what counts?00:03:25 AIDE and the puzzle of useful spaghetti code00:08:38 Four levels of recursive self-improvement00:12:02 What AIDE 85 changed and how it was tested00:20:04 AlphaEvolve, Darwin Gödel Machine and the RSI claim00:26:21 Reward hacking and the limits of detection00:33:09 Open-ended search, harness tuning and creativity00:39:43 Parameter Golf and the limits of self-improvement---REFERENCES:organization:[00:00:30] Weco AIhttps://www.weco.ai/other:[00:00:33] AIDE²: The First Evidence of Recursive Self-Improvementhttps://www.weco.ai/blog/first-evidence-of-recursive-self-improvement[00:14:11] Faulty reward functions in the wildhttps://openai.com/index/faulty-reward-functions/[00:29:59] The Hugging Face incident and the road aheadhttps://openai.com/index/hugging-face-incident-and-the-road-ahead/tool:[00:03:29] AIDEhttps://github.com/WecoAI/aideml[00:04:29] MLE-benchhttps://github.com/openai/mle-bench[00:04:33] ALE-Benchhttps://github.com/SakanaAI/ALE-Bench[00:04:52] WeatherBench 2https://github.com/google-research/weatherbench2[00:08:18] ReActhttps://react-lm.github.io/[00:39:43] Parameter Golfhttps://github.com/openai/parameter-golfpaper:[00:20:08] AlphaEvolve: A coding agent for scientific and algorithmic discoveryhttps://arxiv.org/abs/2506.13131v1[00:21:35] Darwin Gödel Machine: Open-Ended Evolution of Self-Improving Agentshttps://arxiv.org/abs/2505.22954v3[00:23:45] Hyperagentshttps://arxiv.org/abs/2603.19461v1[00:27:01] SpecBench: Measuring Reward Hacking in Long-Horizon Coding Agentshttps://arxiv.org/abs/2605.21384book:[00:33:14] Why Greatness Cannot Be Planned: The Myth of the Objectivehttps://link.springer.com/book/10.1007/978-3-319-15524-1---LINKS:https://app.rescript.info/share/3a9dc6189cb539c6a05fcc4f75c101b3PDF:https://app.rescript.info/api/public/sessions/9eda60ede2b31c92/pdf