Solved: The Sum-Free Sets Conjecture
A seemingly simple mathematical problem—the sum-free sets conjecture—has baffled mathematicians for decades. The conjecture explores whether, within any set of integers, there exists a large subset where the sum of any two numbers in the subset is not also in the subset. In 1965, the renowned mathematician Paul Erdős posed the question, providing a lower bound. Despite many attempts to improve upon it, progress remained stagnant until February of this year, when Oxford graduate student Benjamin Bedert finally solved the problem, demonstrating that any set of integers contains a large sum-free subset, significantly larger than previously estimated. Bedert's proof cleverly combines techniques from diverse mathematical fields, offering new approaches to similar problems. This achievement is hailed as a major breakthrough in mathematics.