On May 14, 2025, DeepMind announced that AlphaEvolve, a large language model applied to a set of mathematical problems, had matched or exceeded the best known bounds on several problems. In the case of the sum and difference of sets problem, AlphaEvolve, using a set of 54265 integers, improved the known lower bound of θ=1.14465 to θ=1.1584. In this paper, we present an improved bound θ=1.173050 using an explicit construction of a U set that contains more than 1043546 elements. For fast integer and floating-point arithmetic, we used the (free) GMP library.
@article{arxiv.2505.16105,
title = {Sums and differences of sets (improvement over AlphaEvolve)},
author = {Robert Gerbicz},
journal= {arXiv preprint arXiv:2505.16105},
year = {2025}
}