novel approach to classical problems in Diophantine approximation. Among its notable successes are the proof of the decades-old Oppenheim conjecture by Margulis, with later extensions by Dani and Margulis and Eskin–Margulis–Mozes, and the proof of Baker and Sprindzhuk conjectures in the Diophantine approximations on manifolds by Kleinbock and Margulis. Various generalizations of the above results of Aleksandr Khinchin in metric Diophantine approximation have also been obtained within this framework. See also Davenport–Schmidt theorem Duffin–Schaeffer conjecture Heilbronn set Low-discrepancy sequence Notes References External links Diophantine Approximation: historical survey. From Introduction to Diophantine methods'' course by Michel Waldschmidt.