{"slug": "chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software", "title": "Chris Hsu on How One Programming Language Rewrote Mathematics and Why Software Is Next", "summary": "Lean, a programming language created in 2013 by Leonardo de Moura, has grown into shared infrastructure for mathematics, with its community-built Mathlib library now exceeding two million lines of machine-checked proofs. In July 2025, Alex Gerko committed $10 million to support Mathlib and core language features, and Lean won the ACM SIGPLAN Programming Languages Software Award and the Skolem Award that year. The language's success in formalizing mathematics, including the Liquid Tensor Experiment completed in July 2022 and Terence Tao's Equational Theories Project, has led its developers to believe the same machinery will be needed for AI-written software.", "body_md": "# Chris Hsu on How One Programming Language Rewrote Mathematics and Why Software Is Next\n\nFor most of its history, mathematics has been checked the way it was written: by people. A mathematician submits a proof, referees read it, and the field accepts a result once enough experts vouch for it. Lean replaces the referee with a machine. It is a programming language precise enough that a proof can be written out step by step and a computer can confirm each step, with no room for the gap a tired human reader might miss. Translating ordinary mathematics into that exact form is called formalization, and for years it was laborious enough to stay a curiosity. Then that curiosity started drawing in the field's most celebrated mathematicians, and close behind them the AI labs. The story of the last five years is how a proof checker became shared infrastructure, and why the people who built it now believe the same machinery is what AI-written software will need next.\n\nSomewhere past two million lines, Mathlib stopped resembling anything mathematics had produced before. The community-built library of formalized mathematics, written in the [Lean proof assistant](https://lean-lang.org/use-cases/mathlib/), now spans undergraduate staples through research-frontier results, every line checked by machine rather than by referee. A 2024 Simons Institute workshop page put the count at one and a half million lines; the Lean site now says over two million. Comparable libraries took decades longer to reach similar scale: Mizar's library sits near 3.7 million lines and Isabelle's Archive of Formal Proofs near 4.8 million, [each the accumulation of a generation of specialist labor](https://arxiv.org/html/2508.21593v1).\n\nLean itself was created in 2013 by Leonardo de Moura, then at Microsoft Research and now a senior principal applied scientist in Amazon's Automated Reasoning Group. In 2023 he co-founded the Lean Focused Research Organization with Sebastian Ullrich to develop the language full time. Its supporters include Alex Gerko, the Alfred P. Sloan Foundation, the Simons Foundation International, and Convergent Research.\n\nIn July 2025 Gerko committed $10 million more, split between Mathlib and core language features. That same year Lean won the ACM SIGPLAN Programming Languages Software Award and the Skolem Award: recognition, from the programming-languages community, that a proof checker had become infrastructure.\n\n## When the mathematicians arrived\n\nWhat moved Lean from tool to phenomenon was the caliber of the mathematicians who staked their own work on it. In December 2020, the Fields medalist Peter Scholze challenged the formalization community to verify the central theorem of his and Dustin Clausen's theory of liquid vector spaces, a result he worried might contain an error too deep for human referees to catch. Six months in, he wrote that he found it \"absolutely insane\" that proof assistants could now verify difficult original research within a reasonable time span. The Liquid Tensor Experiment, led by Johan Commelin, was completed in July 2022.\n\nIn November 2023 Terence Tao coordinated a Lean formalization of the freshly proven polynomial Freiman–Ruzsa conjecture, then launched the Equational Theories Project, a crowdsourced effort that settled all 22,028,942 implications among the 4,694 simplest equational laws. The implications were resolved informally in about two months and fully formalized in Lean within roughly seven. The experience turned Tao into an advocate for a [more collaborative, machine-checked style of mathematics](https://www.quantamagazine.org/how-terry-tao-became-an-evangelist-for-ai-in-math-20260608/), one where strangers can contribute to a proof because the computer guarantees correctness.\n\nThe AI labs arrived by a different door. DeepMind's AlphaProof, which reached silver-medal standard at the 2024 International Mathematical Olympiad, trains itself to prove statements in Lean, and its [peer-reviewed methodology](https://www.nature.com/articles/s41586-025-09833-y) describes auto-formalizing roughly one million natural-language problems into some eighty million formal Lean problems for training. At the 2025 IMO, Harmonic's Aristotle produced formally verified Lean 4 solutions to five of six problems, gold-medal-equivalent work.\n\n## First mathematics, now software\n\nDe Moura has been explicit that mathematics was the proving ground rather than the destination. His [recent writing](https://leodemoura.github.io/) asks who verifies the world's software when AI is writing it, and describes a moonshot to verify the Signal messaging protocol and its Rust implementation in Lean. Amazon, announcing what it called the largest donation in the Lean FRO's history, framed the language's purpose the same way: mathematically proving that software, and AI agents, behave as specified for all inputs, not just the tested ones.\n\nThat approach has drawn philanthropic attention from outside mathematics. The investor [Chris Hsu](https://chrishsu.com/) of Kilometre Capital, whose [Infinitude Foundation](https://infinitudefoundation.net/) counts AI safety among its areas of giving and whose grantees include the Lean FRO and the Stanford Center for AI Safety, has emphasized the goal of formal proof as an imperative, eventual bedrock of trust in an AI-saturated world. The underlying thesis is that as machine-generated code outruns human review, the guarantees that matter will be the ones a machine can check.\n\nHsu identified early 2026 as a key inflection point for formal methods, when AI-enabled auto-formalization and specification collapsed years of manual proof engineering into days, and in some cases hours. In that view, the limiting factor ceased to be whether software could be formally verified, and became whether society could deploy the discipline quickly enough to match the accelerating pace of AI-generated code. Formal methods, once constrained by human effort, entered the same era of scale that AI had already brought to software generation.\n\nHsu's argument has gained broader visibility with [Kevin Hartnett's recent book](https://us.macmillan.com/books/9780374620059/theproofinthecode/) \"The Proof in the Code: How a Truth Machine Is Transforming Math and AI,\" which chronicles Lean's journey from an academic theorem prover into a foundational technology for mathematics, programming, and artificial intelligence. The book presents Leonardo de Moura's work as a rare example of infrastructure that quietly reshapes multiple disciplines at once, unifying mathematical reasoning, software construction, and machine-verified proof within a single formal language. Alongside de Moura, Sebastian Ullrich's engineering leadership has transformed Lean into a scalable platform capable of supporting the growing demands of both mathematics and industrial software verification.\n\nThe broader implication extends well beyond mathematics. If AI is becoming the dominant producer of software, then correctness itself must become machine-checkable rather than human-reviewable. In Hsu's view, formal methods represent the next foundational layer of digital infrastructure, replacing confidence based on testing and inspection with confidence grounded in mathematical proof. The ambition is not merely more secure software, but a future in which increasingly autonomous systems can be trusted because their behavior is provably correct before they are ever deployed.\n\nIf Mathlib provided the machine-checked foundation for modern mathematics, CSLib has aimed to do the same for computer science and software itself. Introduced in 2026 by Professor Clark Barrett of Stanford University and collaborators, CSLib is an open-source effort to build a shared, formally verified library of computer science knowledge and software infrastructure, enabling both humans and AI to construct and verify large-scale systems on common, machine-checked foundations. Just as Mathlib transformed Lean into the language of modern mathematics, CSLib aims to make formally verified software engineering practical at civilization scale.\n\nThe trajectory that began with machine-checked mathematics is increasingly pointing toward a broader transformation of software itself. Lean demonstrated that mathematical reasoning could be made precise enough for computers to verify, Mathlib showed that such verification could scale across an entire discipline, and CSLib now seeks to extend the same foundation to computer science and software engineering. If the twentieth century was defined by making software programmable, and the early twenty-first century by making it intelligent, the next era may be defined by making it provably correct. In that future, formal methods cease to be a contained discipline within computer science and become a scalable, foundational layer upon which trustworthy AI, critical infrastructure, and digital civilization itself are built.\n\n© Copyright IBTimes 2026. All rights reserved.", "url": "https://wpnews.pro/news/chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software", "canonical_source": "https://www.ibtimes.com/chris-hsu-how-one-programming-language-rewrote-mathematics-why-software-next-3806974", "published_at": "2026-08-31 14:42:23+00:00", "updated_at": "2026-08-31 14:54:11.592296+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "ai-tools", "developer-tools"], "entities": ["Lean", "Mathlib", "Leonardo de Moura", "Alex Gerko", "Peter Scholze", "Terence Tao", "DeepMind", "Amazon"], "alternates": {"html": "https://wpnews.pro/news/chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software", "markdown": "https://wpnews.pro/news/chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software.md", "text": "https://wpnews.pro/news/chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software.txt", "jsonld": "https://wpnews.pro/news/chris-hsu-on-how-one-programming-language-rewrote-mathematics-and-why-software.jsonld"}}