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Paul Nelson has solved the subconvexity problem, bringing mathematicians one step closer to understanding the Riemann hypothesis and the distribution of prime numbers.
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.
New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.
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