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 with this revolution, I highly recommend watching Kevin Buzzard’s talks on YouTube for an overview of why formal mathematics is generating such excitement in the mathematical community.
The immediate benefits of formalization are well-documented: it helps catch errors in proofs and reduces the need for trust between collaborators since every step is mechanically verified. However, I believe there’s another compelling advantage that’s less frequently discussed: formalization enables a better separation of concerns in mathematical writing.

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A software engineer with a math PhD background shares personal learning notes from diving into the Lean 4 theorem prover. The post covers initial stumbling blocks for someone coming from mainstream programming languages: the three-level type hierarchy (terms, types, universes), the disorienting homoiconicity of dependent types vs. the clean type/value separation in TypeScript, optional argument names in type signatures, numeric literals resolved via type classes, and the practical separation of Prop vs. Type despite Curry-Howard equivalence. The author also lists open questions around definitional equality, Prop vs. Decidable, #eval vs. #reduce, and the power of simp relative to CAS tools.

Learning Lean: Part 1

Syntactic separation of the three kinds of objects