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Diophantine approximations and [[transcendental number theory]] are very close areas that share many theorems and methods. Diophantine approximations also have important applications in the study of [[Diophantine equation]]s.
The 2022 [[Fields Medal]] was awarded to [[James Maynard (mathematician)|James Maynard]], in part for his work on Diophantine approximation.
== Best Diophantine approximations of a real number ==
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