Finding meaning in error terms

Four decades ago, Mikio Sato and John Tate predicted the shape of probability distributions to which certain “error terms” in number theory conform. Their prediction—known as the Sato-Tate Conjecture—has been verified for an important class of cases, thanks to the recent work of Laurent Clozel, Michael Harris, and Richard Taylor [3], and of Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor [16], combined with Richard Taylor’s most recent [50] which establishes this advance in our understanding.

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