February 18, 2026
Proofs, puns, and pedants collide
Learning Lean: Part 1
Mathematician-turned-coder tries “robot proofs,” comments go nuclear over AI and “Prop”
TLDR: A math PhD turned coder is learning Lean to formalize proofs and spotlight human intuition, hinting at AI-assisted math. Comments erupted over AI’s role, nitpicks about “Prop” vs. decidability, and a “Rocq” typo, revealing a split between purists and pragmatists on how math should be done in the future.
A former math PhD turned software engineer just kicked off a public journey into Lean, the tool that turns proofs into code so a computer can double-check every step. Their pitch: formalization lets humans write about the ideas and intuition, while the machine handles the tedious checking—perfect fuel for training smarter AI. Cue the comment section. One reader cheered the unusual résumé: “SWE meets math brain—let’s go.” Another dove straight into the weeds, warning that “non-computational” isn’t the same as “non-computable,” and that Lean’s logic quirks matter more than you think. A long post comparing Lean to “Rocq” (yes, autocorrect, we see you) set off lighthearted snark and debates about when you can just write “rfl” versus doing a full proof. Then the real drama: a late-night commenter asked if large language models (the ChatGPT-style AIs) can code Lean or Coq, and the thread lit up. Purists fretted about outsourcing thinking; pragmatists dreamed of AI as strategy coach, Lean as referee. The vibe? Curious, nerdy, and occasionally spicy—exactly the kind of internet energy that makes Kevin Buzzard’s talks trend among math fans. Everyone agrees on one thing: the future of math might be part story, part GitHub repo, and all receipts.
Key Points
- •The author is learning the Lean theorem prover to engage with the formalization of mathematics.
- •Formalization improves proof reliability and reduces the need for trust among collaborators by mechanical verification.
- •Formal proofs allow written exposition to focus on intuition and key insights, separating narrative from technical details.
- •The author envisions a two-tier workflow using conversational AI for strategy and Lean for formal proof construction, with proofs hosted on GitHub.
- •The author has a math PhD and software engineering background but notes gaps in type theory and foundations, citing Curry–Howard and dependent type theory as key areas.