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