A taste of Lean.

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Universal Pairs for Diophantine Equations in the Archive of Formal Proofs

We tell the story of how schemes were formalized in three different ways in the Lean theorem prover.

The readings shared in Bluesky on 28 July 2025 are Gödel's first incompleteness theorem (in Lean4). #FormalVerification #ProofAssistant #LeanProver #Logic #Math Formalized formal logic (in Lean4). #F

Mathematicians learning Lean by doing.

The readings shared in Bluesky on 1 August 2025 are Unconstrained optimization (in Isabelle/HOL). ~ Dustin Bryant. #ITP #IsabelleHOL #Math Seed-Prover: Deep and broad reasoning for automated theorem

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

The readings shared in Bluesky on 29 July 2025 are Algorithmic conversion with surjective pairing: A syntactic and untyped approach. ~ Yiyun Liu, Stephanie Weirich. #FormalVerification #ProofAssistan

There are probably several different ways to prove Pelletier’s Problem 24, so we will just investigate one way. Informal Roadmap for the Proof The first thing to do, whenever formalizing anyt…

Church’s simple type theory is often deemed too simple for elaborate mathematical constructions. In particular, doubts were raised whether schemes could be formalized in this setting and a challenge was issued. Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. In this article we report on a successful formalization of schemes in the simple type theory of the proof assistant Isabelle/HOL, and we discuss the design choices which make this work possible. We show in the particular case of schemes how the powerful dependent types of Coq or Lean can be traded for a minimalist apparatus called locales.

We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erdős and Straus, Hančl, and Hančl and Rucki. Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization and discuss what this reveals about the use and potential of Isabelle/HOL in formalizing modern mathematical research, particularly in these parts of number theory and analysis.

The readings shared in Bluesky on 31 July 2025 are The math is haunted. ~ Dan Abramov. #ProofAssistant #LeanProver #Math #Exercitium: Problemas de programación con Haskell (julio de 2018). #Haskell #