New proof bounds π's irrationality exponent at 6.0446, fully formalized in Lean 4
Michael_D_Moor · x · 2026-10-07
A newly released 46-page paper (v4, Oct 6, 2026) on GitHub proves that the irrationality exponent of π is at most 6.0446, tightening how well π can be approximated by rationals.
Key points:
- The repo includes a complete Lean 4 / Mathlib formalization (Lake project MuPi: 20 files, 6,238 lines);
- The Lean proof is complete modulo the prime number theorem, which enters as an explicit hypothesis in the form θ(x) x;
- The paper has not yet been refereed; v3 (the first public version, Oct 3) remains available with changes documented.
The paired release of paper plus machine-checkable proof is a notable example of the formal-math workflow in the AI era.
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