page_title: Roth's theorem
hierarchical_section_title: Roth's theorem
caption_attribution_description: Freeman Dyson Photo from Long Now Seminar, San Francisco, October 05, 2005
context_page_description: In mathematics, Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have 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 Joseph Liouville in 1844 and continuing with work of Axel Thue, Carl Ludwig Siegel, Freeman Dyson, and Klaus Roth.
context_section_description: In mathematics, Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have 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 Joseph Liouville in 1844 and continuing with work of Axel Thue (1909),  Carl Ludwig Siegel (1921), Freeman Dyson (1947), and Klaus Roth (1955).
caption: Freeman Dyson in 2005
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