AI Disclosure: Draft was written fully by a human. Heavy use of AI for editing. In April 2026, Kevin Buzzard posed the following challenge for Lean AI autoformalization: can an AI system both define t...

AI Disclosure: Draft was written fully by a human. Heavy use of AI for editing. See On AI usage for more. At this point no one doubts that AI is a tremendous capability boost for all human intellectua...

YouTube video by Future of Mathematics Symposium

YouTube video by Antithesis

Recent advances in general models — ChatGPT and Claude — have started to autonomously solve open mathematical problems. For example, Erdős 1196, Tim Gowers’s PhD student problems, OpenAI’s Ramsey numb...

An new old approach to emulation.

Note: AI was used to edit this post. As a proof-of-human thought and input, I am also publishing the original draft which was written fully before asking AI to edit the post with me. This post is aime...

This post is aimed at a general programmer and no prior knowledge of math or CS is assumed. I got nerd-sniped to write this after reading Simon’s excellent post Code proven to work. As someone who wor...

Human Intuition, AI Formalization: A Real Analysis Case Study Disclaimer - I wrote the core ideas; Claude helped flesh out and polish the article. See appendix for more on this. This is a follow up to...

Preface: Why All Mathematicians Should Learn Lean LLMs can generate plausible-sounding proofs at unprecedented speed and scale. Some are correct, many are not, and LLMs themselves cannot reliably tell...

Leaning on AI It’s been five months since my last dedicated Lean post and as usual I have started to lose steam on Lean projects. After the thrill of discovering the world of formalized mathematics st...

Is this JS function pure? In 2019, as functional programming was making the last inroads dethroning OOP, I kept hearing the mantra of “just use pure functions” in JS. Something didn’t sit right with m...

Why formalize mathematics - more than catching errors I read a good post by one of the authors of the Isabelle theorem prover, that got me thinking. The author, Lawrence Paulson, observed that most ma...

It’s been 3 months since my previous post about learning Lean part 3, so it’s time to write another one. I have mostly continued to work through Tao’s Analysis book through his excellent companion - w...

Lean is a theorem prover and programming language that enables correct, maintainable, and formally verified code.

I am continuing to learn Lean (see part 1 and part 2). I lost some steam around March-April, but in the last two months I picked it up again. In a way it was a nice spaced repetition for relearning so...

I am continuing to learn Lean (see part 1) by going through Mathematics in Lean. These are my notes as I just finished chapters one through five. Mathematics in Lean The online book is well-paced and ...

Motivation I’ve been captivated by the recent movement to popularize mathematics formalization through the Lean theorem prover, and this year I’m diving deeper into learning it. For those unfamiliar w...

Ticket to Ride: First Journey simulation authored with AI After playing Ticket to Ride: First Journey with my family recently, I got the urge to analyze some statistical properties of the game. This s...

Puzzle games of 2024 As the year draws to a close, I want to share my favorite puzzle games from 2024. This isn’t meant to be an exhaustive review or ranking of all puzzle games released this year, bu...

Advent of Code 2024 Retro Advent of Code AoC is an annual programming competition that releases daily coding puzzles throughout December. For the past four years, I’ve tackled these challenges from th...