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arXiv imposes a new limit of two submissions per submitter per month (\(\mathbb{M}\)).

The 3D Heesch Hemiobelisk: a nonzero-Dehn-invariant hexahedron with a complete corona (\(\mathbb{M}\)).

Brick territories experiment (\(\mathbb{M}\)).

The de Bruijn–Erdős theorem states that the number of colors needed to color an infinite graph is the same as the maximum number needed for its finite subgraphs.

In case you’ve been worrying that the recent publicity blitz of LLM solutions to open mathematics problems is causing us to run short, there are two more mixed in among my usual links here.

Soddy’s hexlet consists of a ring of six spheres, tangent to each other consecutively around the ring, and another ring of three consecutively-tangent spheres, so that all the spheres in the first ring are tangent to all the spheres in the second ring.

A permutation generation algorithm in the work of 13th-century Kabbalist Abraham Abulafia (\(\mathbb{M}\), via).

Reports that LLMs have killed the Erdős unit distance problem turn out to be greatly exaggerated.

ACM considers allowing LLMs to read its digital library (\(\mathbb{M}\)) and requests feedback on this choice.

The integer complexity of a number \(n\) is the minimum number of ones needed to express \(n\) as a parenthesized combination of sums and products of ones.

Another mathematics journal leaving its commercial publisher (\(\mathbb{M}\)), but with a twist: usually this is accomplished by a mass resignation of the editorial board.

I have another new preprint, the result of a research project with UC Irvine undergraduate Cindy Zhang: “Sudoku grids that require many clues” (arXiv:2607.05728, to appear at JCDCG3 2026).

On the scale of stupid things the US government is doing this is pretty small, but they appear to be banning the census bureau from any effective methods of privacy-preserving information release, and in particular from adding noise to their data to help…

I’ve been hesitating in writing up a blog post about my latest preprint, “Minimum-weight Steiner triangulation of convex polygons requires interior Steiner points” (with my student Zahra Hadizadeh, arXiv:2606.25302, to appear at CCCG) because, despite bei…