March 3, 2026
Sharks, proofs, and cheap thrills
130k Lines of Formal Topology: Simple and Cheap Autoformalization for Everyone?
AI cranks 130k lines of math for $100 — cheers, side-eye, and ELI5 requests
TLDR: An AI teamed with a proof checker to formalize 130k lines of a topology textbook for about $100. Fans call it the future, skeptics worry the machine might “prove” the wrong thing, and developers ask how to borrow these methods to make software testing stronger.
An AI plus a fast “proof checker” just speed-ran a big chunk of a classic math textbook, spitting out 130k lines in two weeks for about $100. The setup sounds simple: a chatbot (think ChatGPT/Claude) loops with a checker called Megalodon until the math sticks. The project claims famous topology theorems were formalized — the kind of brain-benders that usually take humans months. Cue the crowd: one commenter pleaded, “can somebody explain like I’m five?” while others fired up shark memes about Megalodon swallowing math.
The hype camp (like timmg) is thrilled: “finally turning AI loose on formal math,” already daydreaming about auto-formalizing everything. The pragmatic camp (esafak) wants receipts for software: if math can be nailed down with machine-checked proofs, can we bring those tricks to everyday code instead of flaky unit tests? And then there’s the trust police (bmenrigh) asking the awkward question: did the system really prove what we think it did, or are we rubber-stamping misunderstandings? That tension — speed and scale vs. assurance and human review — is the drama. Bonus spice: this wasn’t done in the popular Lean tool, but an obscure checker, promising a 2026 tool war. It’s part breakthrough, part “who watches the watchers” showdown, and the comments are loving the chaos.
Key Points
- •Project started on November 21, 2025 and reached 160k lines of formalized topology by January 4, 2026.
- •About 130k lines were generated between December 22 and January 4 for approximately $100 in LLM subscription costs.
- •Formalized results include Urysohn’s lemma (3k lines), Urysohn’s Metrization theorem (2k lines), and the Tietze extension theorem (10k+ lines).
- •Workflow uses a feedback loop between an LLM (ChatGPT 5.2 or Claude Sonnet 4.5) and the Megalodon proof checker, with a core set-theory library.
- •Authors believe autoformalization could become easy and ubiquitous in 2026 across proof assistants due to this simple, low-cost setup.