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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.
Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.
For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.
Why do mathematicians enjoy proving the same results in different ways?
In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.
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