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Graduate Student Solves Classic Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
In his 1965 paper, Erdős showed — in a proof that was just a few lines long, and hailed as brilliant by other mathematicians — that any set of N integers has a sum-free subset of at least N/3 elements. “The longer it went without people being able to improve on that simple bound, the more cachet this problem acquired,” said Ben Green, Bedert’s doctoral adviser at Oxford. “I certainly tried to prove the sum-free conjecture using [Bourgain’s] ideas,” Green said, but “we still don’t understand much about the structure of sets with small Littlewood norm.
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