Editing Roth's theorem (section)

{{Short description|Algebraic numbers are not near many rationals}}
{{for|Roth's theorem on arithmetic progressions|Roth's theorem on arithmetic progressions}}
In [[mathematics]], '''Roth's theorem''' or '''Thue–Siegel–Roth theorem''' is a fundamental result in [[diophantine approximation]] to [[algebraic number]]s. It is of a qualitative type, stating that algebraic numbers cannot have many [[rational number|rational]] 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 {{harvs|txt|first=Axel|last= Thue|authorlink=Axel Thue|year=1909}},  {{harvs|txt|authorlink=Carl Ludwig Siegel|first=Carl Ludwig |last=Siegel|year=1921}}, {{harvs|txt|authorlink=Freeman Dyson|first=Freeman|last=Dyson|year=1947}}, and {{harvs|txt|authorlink=Klaus Roth|first=Klaus|last= Roth|year=1955}}.