One of the numerical exponents that was improved via Deepmind's AlphaEvolve (AE) tool (as part of a collaboration I am involved in) has just been improved: https://arxiv.org/abs/2505.16105

The question concerns the best exponent θ for which one can construct large sets of integers A,B with |A+B| = O(|A|) and |A-B| >> |A|^θ. The previous best construction, due to Gyamarti, Hennecart, and Ruzsa in 2007, gave a lower bound of 1.14465; our group was able to use AlphaEvolve to obtain the improvement 1.1584; and this new paper obtains 1.173050. (The best known upper bound is 4/3.)

All constructions proceed by first locating an auxiliary finite set U of integers with good properties. The original construction of Gyamarti et al. was a set of cardinality 30000 or so, constructed according to a specific recipe; AE did an unconstrained search and found an example of cardinality 54265 that gave the better bound; and the new paper returns to (a modification) of the original construction but with much larger parameters to find (with computer assistance) a set with more than 10^43546 elements.

It is tempting to simplify this to a zero-sum narrative of "winners" and "losers", but I think it is great that different approaches can complement each other here to make mathematical progress. The advantages of an AE-type approach are more in the direction of breadth rather than depth; one can use AE to scan large ranges of problems to identify places where the literature could be improved, and human experts (perhaps also assisted by computers) can then focus attention on these problems to make further progress.