Baker's Theorem gives an effective lower bound on the absolute value of a nonzero linear combination of logarithms of algebraic numbers, with algebraic coefficients, showing such a combination cannot be arbitrarily close to zero and quantifying how close it can come. Named for Alan Baker, it extended the Gelfond-Schneider Theorem to combinations of more than two logarithms and has been used to give effective bounds on the solutions of many classes of Diophantine equations.
Facts
StatementBaker's theorem gives a lower bound on the size of any nonzero combination of logarithms of algebraic numbers with algebraic coefficients, a result used to prove many numbers transcendental and to solve the class number problem for imaginary quadratic fields. 2 Classification
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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.
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Source Baker's Theorem (Wikipedia)
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1. Wikipedia: Baker's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers.
2. Baker's Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers.
lead paragraph, second sentence naming Baker's 1966 papers
The result, proved by Alan Baker (1966, 1967a, 1967b), subsumed many earlier results in transcendental number theory.
In Branch: Number Theory, Lead sentence
In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear c
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