Graduate Student Solves Classic Problem About the Limits of Addition
a year ago
- #Mathematics
- #Sum-Free Sets
- #Number Theory
- Graduate student Benjamin Bedert solved a long-standing problem about sum-free sets in mathematics.
- Sum-free sets are sets of numbers where no two numbers add up to another number in the set.
- Paul Erdős initially posed the problem in 1965, showing any set of N integers has a sum-free subset of at least N/3 elements.
- Bedert's proof shows that the largest sum-free subset in any set of N integers is at least N/3 + log(log N), settling the sum-free sets conjecture.
- The proof uses advanced mathematical techniques, including the Littlewood norm and Fourier analysis.
- Bedert's work provides new insights into the structure of sets with small Littlewood norms.
- Despite the breakthrough, there remains a gap in understanding the exact growth rate of the deviation from N/3.