December 19, 2025
Proofs, memes, and monads
From Zero to QED: An informal introduction to formality with Lean 4
Lean 4 tutorial lands: fans hype, nitpickers swarm, AI crowd crashes the party
TLDR: A new Lean 4 tutorial pairs real programming with machine-checked math, and the crowd is fired up. Fans love the practical start, nitpickers grill the monads page, and the AI crowd cites Terence Tao—turning a tutorial into a debate about how formal methods should meet AI.
Lean 4 just got the glow-up fans begged for: a beginner-friendly series that teaches both real programming and machine-checked math, backed by actual code in a GitHub repo. The community immediately split into camps: “finally, practical!” versus “show me the receipts on monads.” Oersted called the motivation “fresh and compelling,” pointing readers to the why page here, while IshKebab cheered that it starts with everyday coding before the brain-bending proof stuff—then promptly nitpicked the monads page for talking about “bind” without using it and glossing over arrow sugar. Cue the monad wars. Meanwhile, randomtoast brought the AI thunder, name-dropping mathematician Terence Tao and recent work on formal proofs, and even tossing in models like Sonnet and Opus 4.5 to compare code sprawl with proof discipline. The vibe: half classroom, half courtroom. Fans love that every example is machine-verified; skeptics are here for consistency and clarity. Jokes flew about graduating from “hello world” to “hello theorem,” plus memes warning that QED (the classic “we’re done” stamp) might now mean “Quit Every Day” if the monad page stays spicy. Verdict: hype, hope, and heated line edits—exactly the energy a proof-powered tutorial deserves.
Key Points
- •The tutorial series teaches Lean 4 from first principles to address gaps in learning resources.
- •It is a machine-verified Lean project: all code, proofs, and theorems are typechecked by the Lean compiler.
- •The first arc focuses on Lean as a programming language, covering syntax, types, control flow, polymorphism, monads, and IO.
- •The second arc focuses on Lean as a theorem prover, including proofs, type theory, dependent types, and tactics to prove classic results.
- •The article provides installation steps (git clone, lake build) and a References appendix; prior theorem prover experience is not required.