James Maynard recently co-authored a proof of the Duffin-Schaeffer Conjecture.
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More James Maynard on Numberphile: http://bit.ly/JamesMaynard

On the Duffin-Schaeffer conjecture - by Dimitris Koukoulopoulos and James Maynard - https://arxiv.org/abs/1907.04593

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Correction of typo: 355/113 is Pi approximation, not 133