December 27, 2025
When math goes meme, comments go feral
Some Junk Theorems in Lean
Silly math proofs spark a brawl: scary bug or nerdy joke
TLDR: A GitHub repo showcases “junk theorems” in Lean, a proof-checking tool, highlighting how sloppy definitions can yield silly but valid proofs. Commenters split between alarm over partial functions and AI auto-provers, and veterans saying it’s harmless and fixable—spotlighting how formal math can mislead without careful design.
Lean is a tool that checks math proofs. A cheeky GitHub repo, junk-theorems-in-lean, shows how you can “prove” ridiculous things when your definitions are sloppy. The crowd? Split. One newcomer gasped “TIL junk theorems are real,” linking a friendly primer, while another was baffled by a line like “Theorem 6… The binary expansion of 7,” turning it into the meme of the day.
Anxious voices piled on. “This would make mathematicians angry,” warned one commenter, arguing basic subtraction should come in a safe flavor and a “danger, it explodes” flavor. Another was spooked by partial functions—like a square root that spits out 0 for negatives—and worried that AI auto‑provers will happily stack nonsense on top of nonsense.
Then came the cool-headed pushback. Veterans shrugged: the point of formal systems is to prove useful stuff; junk is a side effect. One logician cheekily jabbed the philosophy wars: set theory can say absurd things like “1 is in 2,” and type theory fans shouldn’t get too smug—every camp has quirks. The vibe: equal parts panic, pedantry, and punchlines, with the community debating whether this is a teachable moment, a tooling fix, or just nerd comedy.
Key Points
- •Public GitHub repository collecting formally verified “junk theorems.”
- •Implemented using Lean4 and Mathlib, as stated in the description.
- •Licensed under Apache-2.0.
- •Contains core source file JunkTheorems.lean and supporting build/config files (lakefile.toml, lake-manifest.json, lean-toolchain).
- •Repository metadata lists 39 stars, 1 fork, and a history of 137 commits.