Lean on PostDoc Problems

Math Arena AI

Sat, 26 Apr 2025 22:41:39 +0000

I was doing some research for a talk and came across this website for recording AI results on math problems: https://matharena.ai/

LLMs have been getting better and better at solving math problems but there is a worry that all they do is regurgitate what they already know. So, if an AI has seen a problem before you can expect it to solve it but if it hasn’t then all bets are off. Many of the progress claims are in fact reporting these memorized solutions.

Rubik's Cube in Lean

Wed, 06 Nov 2024 21:28:19 +0000

This Github repo contains the proof that there are $2^{12} \times 3^{8} \times 8! \times 11!$ Rubik’s cubes:

https://github.com/vihdzp/rubik-lean4

What! This is the most amazing thing I’ve read in a long time. What is the reason of this number? And it’s verified in Lean!!!

Terrence Tao - Lean

Wed, 01 Nov 2023 13:21:33 +0000

Terry Tao posted on Mastodon that he found a bug in a proof in one of his papers thanks to trying to formalize it in Lean. This is an excellent use case of Lean and tbh the only one that I think is going to be taken seriously for a while.

PaperProof

Wed, 01 Nov 2023 13:18:16 +0000

This looks like a really cool tool for visualizing proofs in Lean:

https://github.com/Paper-Proof/paperproof

https://lakesare.brick.do/lean-coq-isabel-and-their-proof-trees-yjnd2O2RgxwV

This will probably get unweildy very fast for even moderately-sized proofs. But I suspect that it’ll be of great help for beginners.

llmstep and LeanInfer

Sat, 09 Sep 2023 22:37:41 +0000

I came across two LLM based tactics for Lean

They both use [LeanDojo](2023-09-04 leandojo.qmd) somehow and I don’t understand the difference between the two. Unfortunately, I do not know enough about LLM and AI to tell if this is actually good or just hot gas.

LeanDojo

Mon, 04 Sep 2023 16:22:19 +0000

This was posted a while back on the Lean Zulip:

LeanDojo

LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

According to their description, LeanDojo is an open-source Lean playground consisting of toolkits, data, models, and benchmarks. Plus they also provide an LLM-based prover and a chatGPT plugin. All of this looks amazing and something worth learning more about.

Short tactics tutorial

Thu, 31 Aug 2023 21:13:45 +0000

I have always wanted to learn tactics writing in Lean. But for whatever reason, none of the tutorials that exist online have been helpful. I suspect that the best way to learn to write tactics to play around and modify the existing ones. I came across this short, 4-page tactics tutorial that looks promising. I’ll give it a go when I get some time.

Loogle!

Thu, 31 Aug 2023 16:37:51 +0000

An improved search engine for Lean:

I haven’t used it yet but it looks promising. I personally don’t like the search on mathlib4_docs and find it very glitchy, slow, and cumbersome. Normally, I just use grep in VSCode instead, which is better but still very cumbersome and requires a lot of regex jujitsu. Hopefully this search is better and more useful. Looking forward to trying it out.