A critique of Lean and the culture of formal mathematics communities
By
ibobev
A five-star bake. Worth schmearing, sharing, saving.
Summary
The article discusses the author's perspective on the modern formal mathematics community, particularly the pressure to justify not using the Lean proof assistant. The author acknowledges Lean's technical merits—great language, good tools, large library, and enthusiastic community with astounding recent accomplishments—but expresses discomfort with what they perceive as cultism, insularity, and conformity in the dependent-typed world. The piece draws on the author's 40-year history with formal mathematics, including work on AUTOMATH, LCF, HOL system, and HOL Light, to provide historical context and critique of current trends in the field.
Key quotes
· 3 pulledI have been told that when proposing to formalise mathematics these days, you have to explain why you are not using Lean.
And that reminds me why I left the dependent-typed world 40 years ago: its cultism, insularity and conformity.
Lean is a great language with good tools, a large library and a huge, enthusiastic user community that has lately accomplished astounding things.
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