Source labels openChecked July 26, 2026

Exponentials conjectures and theorems

Four exponentials conjecture* Let $x_0, x_1$ and $y_0, y_1$ be $\mathbb Q$ -linearly independent pairs of complex numbers, then some $e^{x_i y_j}$ is transcendental.

Special functions AMS 33

Mathematical statement

Four exponentials conjecture* Let $x_0, x_1$ and $y_0, y_1$ be $\mathbb Q$ -linearly independent pairs of complex numbers, then some $e^{x_i y_j}$ is transcendental.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

four_exponentials_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem four_exponentials_conjecture (x : Fin 2 → ℂ) (y : Fin 2 → ℂ)    (h1 : LinearIndependent ℚ x) (h2 : LinearIndependent ℚ y) :    ∃ i j : Fin 2, Transcendental ℚ (exp (x i * y j)) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipediabackground