Terence Tao: Sidon set bounds refine a method—and expose its apparent limit

Terence Tao: Sidon set bounds refine a method—and expose its apparent limit

Terence Tao describes a paper by Daniel Carter, Kevin O’Bryant, and himself that refines an upper bound on the size of Sidon sets. The work grew from a blog discussion of using AlphaEvolve to improve the then state of the art. The authors obtained further refinements, but progress stalled after several months, and they released their preprint. Tao says the paper focuses on the method rather than the specific numerical constant. It uses weighted inequalities and optimization, then improves the bound by considering random choices and taking expectations. Tao calls the calculations “highly computer-assisted.” He says the method also extends to the more general class of Golomb rulers, where a given non-zero difference is permitted to appear up to a specified number of times. Tao says the method appears to be reaching its current limit, while noting that a different method obtained a slightly sharper bound. The supplied text’s mathematical expressions are missing, so the precise bounds and details needed to assess or reproduce the derivation cannot be determined from this reading. How much further can this method refine the bound before a different approach is needed?

Publication: 5752478a-5440-478e-8930-b59cdf484f67

attribution — pass: The reading correctly attributes the post to Terence Tao and the paper to Daniel Carter, Kevin O’Bryant and Tao. The method, the stalled progress, and the reported limit all stay framed as Tao's statements.

Daniel Carter, Kevin O’Bryant, and I have uploaded to the arXiv our paper On the diameter and distribution of Sidon sets.

summary — uncertain: Three central terms are never explained, so a non-specialist cannot follow the development. Smallest repair: add a plain gloss for each. A Sidon set is a set of integers whose pairwise sums are all distinct. AlphaEvolve is the AI tool behind the original improvement. Golomb rulers also need a gloss. The draft also says progress 'stalled after several months'; the source says it stalled and they released after several months of no progress. Tao's aside that they did not use 2026-level AI tools is relevant to the AI angle but omitted. The question is also duplicated inside the summary.

Recall that a Sidon set is a set of integers with the property that all the sums with and are distinct.

date — pass: originalPublished is 2026-10-29T04:05:18Z, based on the publisher page, and matches the feed entry. The 2026/10/28 date in the URL is consistent with a local-time evening post. No conflicting earlier date appears in the evidence.

support — pass: The claims are grounded in the source: the blog origin with AlphaEvolve, the stalled refinements, the random choices with expectations, the highly computer-assisted calculations, the extension to Golomb rulers, the apparent limit, and the sharper bound found by a different method. The limitation about missing mathematical expressions is accurate. The closing question follows from Tao's statement about reaching the method's limit and is not leading.

but we appear to be reaching the limit of our current method. Very recently, a slightly sharper bound of 0.942809522 was obtained by a different method

media — pass: The selected media is the verified direct link to Tao's original blog post. It matches the source URL and is the most direct access to the source.