High Quality Content by WIKIPEDIA articles! In mathematics, the Thue–Siegel–Roth theorem, also known simply as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that a given algebraic number ? may not have too many rational number approximations, that are 'very good'. Over half a century, the meaning of very good here was refined by a number of mathematicians, starting with Axel Thue, and continuing with work of Carl Ludwig Siegel. Klaus Roth's theorem dates from 1955.

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