Formalizing Principia Mathematica using Lean
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover. Throughout the formalization, I tried to rigorously follow Prof. Russell’s proof, with no or little added statements from my side, which were only necessary for the formalization but not the logical argument. Should you notice any inaccuracy (even if it does not necessarily falsify the proof), please let me know as I would like to proceed with the same spirit of rigour. Before starting this project, I had already found Prof. Elkind’s formalization of the Principia…
Formalizing Principia Mathematica using Lean launched on April 25, 2025 with 188 votes, #198 of 7,818 launches that month and more than 95% of that year's launches. The site was still online in September 2026, 1 year on.
In plain words
This project formalizes the first volume of Bertrand Russell's Principia Mathematica using the Lean theorem prover. It translates Russell's mathematical proofs into machine-verifiable code while adhering closely to the original arguments, adding minimal statements beyond those necessary for formalization. The work targets mathematicians and formal verification researchers interested in classical logic foundations and serves as an alternative formalization to existing versions in other proof assistants.
written from the facts on this page · September 2026
From the sources
Rewriting Principia Mathematica in Lean. Contribute to ndrwnaguib/principia development by creating an account on GitHub.
This project aims to formalize the first volume of Whitehead & Russell’s Principia Mathematica using the Lean theorem prover. The goal is to ensure that the formalization aligns clearly with the corresponding theorems in the book to avoid confusion (See Metaprogramming =Syll= ) Principia Mathematica ’s notation (Peano-Russell notation) is exceptionally known for its sophistication that it has a separate entry on the Stanford Encyclopedia of Philosophy (SEP) . Also, Prof. Landon Elkind’s Squaring the Circles: a Genealogy of Principia’s Dot Notation explains the notation skillfully. I would like to believe that after reading a few examples of how some formulas were formalized and contrasting…from github.com
In the maker’s words, at launch
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover. Throughout the formalization, I tried to rigorously follow Prof. Russell’s proof, with no or little added statements from my side, which were only necessary for the formalization but not…
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