Graduate Student Solves Classic Problem About the Limits of Addition
1 min read
Summary
Mathematicians have long been fascinated by sum-free sets - sets of numbers which contain no two numbers whose sum is a third number in the set.
Sixty years ago, mathematician Paul Erdős asked how large a subset of a set of integers had to be sum-free.
While he was able to prove that any set must contain a subset of at least N/3 elements, he suspected that the actual number would be much larger.
This question, now known as the sum-free sets conjecture, remained open for decades, with no obvious way to make progress.
In February this year, graduate student Benjamin Bedert solved the problem, proving that any set of N integers must contain a sum-free subset of at least N/3 + log(log N) elements.
Bedert relied on a technique involving the Littlewood norm, a method that others had unsuccessfully tried to use to solve the conjecture.
“It’s a fantastic achievement,” mathematician Julian Sahasrabudhe told Quanta Magazine.
