Communications of the ACM
Mathematicians Outwit Hidden Number Conspiracy
A conspiracy between adjacent integers would also imply conspiracies between all pairs of their multiples.
Credit: Eric Nyquist / Quanta Magazine
A new proof has debunked a conspiracy that mathematicians feared might haunt the number line. In doing so, it has given them another set of tools for understanding arithmetic's fundamental building blocks, the prime numbers.
In a paper posted last March, Harald Helfgott of the University of Göttingen in Germany and Maksym Radziwiłł of the California Institute of Technology presented an improved solution to a particular formulation of the Chowla conjecture, a question about the relationships between integers.
Their solution, which pushes techniques from graph theory squarely into the heart of number theory, has reignited hope that the Chowla conjecture will deliver on its promise — ultimately leading mathematicians to the ideas they'll need to confront some of their most elusive questions.
From Quanta Magazine
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