The Gelfond-Schneider Theorem states that if a and b are algebraic numbers, a is not equal to zero or one, and b is irrational, then a raised to the power b is transcendental. Proved independently by Aleksandr Gelfond and Theodor Schneider in 1934, it resolved Hilbert's seventh problem and gives a general method for proving numbers such as two raised to the power of the square root of two are transcendental.
Facts
StatementThe Gelfond-Schneider theorem establishes the transcendence of a large class of numbers: if a and b are algebraic numbers with a not equal to 0 or 1 and b irrational, then any value of a^b is transcendental. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Gelfond-Schneider Theorem (Wikipedia)
Wikimedia FoundationLead paragraph
In mathematics, the Gelfond-Schneider theorem establishes the transcendence of a large class of numbers.
History section
It was originally proved independently in 1934 by Aleksandr Gelfond and Theodor Schneider.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.