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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24823 |
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Table of Contents:
- We formalize Hilbert's Seventh Problem and its solution, the Gelfond-Schneider theorem, in the Lean 4 proof assistant. The theorem states that if $α$ and $β$ are algebraic numbers with $α\neq 0,1$ and $β$ irrational, then $α^β$ 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.