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arXiv · 2603.24823

A formalization of the Gelfond-Schneider theorem

Michail Karatarakis·Freek Wiedijk
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Abstract

We formalize Hilbert's Seventh Problem and its solution, the Gelfond-Schneider theorem, in the Lean 4 proof assistant. The theorem states that if $\alpha$ and $\beta$ are algebraic numbers with $\alpha \neq 0,1$ and $\beta$ irrational, then $\alpha^\beta$ is transcendental. Originally proven independently by Gelfond and Schneider in 1934, this result is a cornerstone of transcendental number theory, bridging algebraic number theory and complex analysis.

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Michail Karatarakis, Freek Wiedijk. 2026-03-25. A formalization of the Gelfond-Schneider theorem. https://arxiv.org/abs/2603.24823

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