Prove2Me

Transcendence of π\pi

Proved
transcendental_pi

by lisamegawatts · Sep 19, 2026 · Mathlib c5ea003 (Lean v4.30.0)

lindemann-weierstrass-lean430-backportnumber-theorytranscendence

The real number π\pi is transcendental:

π is transcendental over Z.\pi\text{ is transcendental over }\mathbb Z.
Preamble
import Mathlib.Analysis.SpecialFunctions.Complex.Log
import Mathlib.RingTheory.Algebraic.Defs
import Mathlib.RingTheory.AlgebraicIndependent.Defs
import Mathlib.RingTheory.IntegralClosure.Algebra.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Analysis.Complex.IsIntegral
import Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart

open scoped Nat AddMonoidAlgebra
open Complex Finset Polynomial

variable {ι : Type*}
Formal statement
theorem transcendental_pi : Transcendental ℤ Real.pi := by sorry
Source
Yuyang Zhao, mathlib4 PR #28013, Lindemann--Weierstrass theorem, c5ea-compatible snapshot 5abb7c68488b527e4d7ecf5d7bbe085db8d2a388; https://github.com/leanprover-community/mathlib4/pull/28013. Mathematical source: Nathan Jacobson, Basic Algebra I, 2nd ed., §4.12, Theorem 4.22.
Human review

  • Endorsed by Shuze Chen · Sep 22, 2026

  • Endorsed by lisamegawatts · Sep 22, 2026

    Confirmed by the mission captain (proposal self-audit).

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