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Congratulations, Dr. Liu!
Oct 27, 2026 · original
Another UC Irvine doctoral student, Songyu (Alfred) Liu, successfully passed his doctoral defense this week, co-advised by Mike Goodrich and me. Alfred came to UCI in 2020, initially working with cognitive scientist Mark Steyvers, who has a joint appointment in computer science. Their work eventually turned into a 2024 publication, “ Combining Human and AI Strengths in Object Counting under Information Asymmetry ”, in the 12th AAAI Conference on Human Computation and Crowdsourcing (2024), but in the meantime Alfred decided that he preferred topics that were more directly computational, and switched to working with Mike Goodrich (and eventually me). The three topics of his doctoral dissertation are reconstructing graphs from shortest path queries (the sort of information you might obtain from the Unix ping command), connections between different graph width parameters, and graph drawing,
Linkage
Oct 15, 2026 · original
arXiv imposes a new limit of two submissions per submitter per month ( \(\mathbb{M}\) ). Book of Shapes: A collection of minimal, generative and customizable SVG-patterns ( \(\mathbb{M}\) , via ). Sham scientific societies are misleading star researchers , according to Nature ( \(\mathbb{M}\) , via ). The \(13\times 13\) zebra graph is untraceable ( \(\mathbb{M}\) ). A zebra is a fairy chess piece that jumps like a longer knight, two steps in one direction and three in another. Almost a proof without words that the graph of its moves on a \(13\times 13\) chessboard has no Hamiltonian path. The Harvard/Smithsonian Astrophysics Data System , a large bibliographic database for astronomy, astrophysics, and related fields, has been transitioning for the last year or so to become SciX with expanded areas of coverage “across space, Earth, and planetary sciences”, and is scheduled to complete th
Linkage
Sep 30, 2026 · original
The 3D Heesch Hemiobelisk: a nonzero-Dehn-invariant hexahedron with a complete corona ( \(\mathbb{M}\) ). The Immerman–Szelepcsényi theorem formalized in Lean as part of the LAX Lean archive ( \(\mathbb{M}\) ), a form of literate programming for Lean proofs that includes definitions for computational complexity theory. This year’s STOC call for papers has made significant changes, in the face of an onslaught of AI-generated submissions ( \(\mathbb{M}\) , via ). Submissions must list authors, all of whom must be human, no author can be on more than five submissions, all submissions must be posted in identical form to arXiv prior to submission, AI use is allowed but must be disclosed, AI reviewing is also allowed subject to author consent, and (perhaps the biggest change) authors must also prepare and submit a 20-30 minute explanatory video. Recognizing penny graphs is \(\exists\mathbb{R}\
Linkage
Sep 15, 2026 · original
Brick territories experiment ( \(\mathbb{M}\) ). What shapes do you get when \(n\) simultaneous breakout games compete against each other for pixels? Lillian Oppenheimer , 1898–1992 ( \(\mathbb{M}\) ), early and significant promoter of origami in the US, founder of the organization that became OrigamiUSA, mother of notable mathematicians William Kruskal, Martin David Kruskal, and Joseph Kruskal, and grandmother of computer scientist Clyde Kruskal. Now a Good Article on Wikipedia (not one that I wrote or edited; I merely reviewed it). Python sets and dictionaries can have quadratic-time performance ( \(\mathbb{M}\) ), for adversarially-chosen data. Terry Tao on what can be learned from studying problems rather than on what their solutions happen to be . Ig Nobel Prize goes to a study showing that rich people are more likely than others to steal candy from children ( \(\mathbb{M}\) ). The
Periodic coloring of infinite planar graphs
Sep 14, 2026 · original
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. So for any reasonable definition of an infinite planar graph, the 4-color theorem for finite planar graphs implies that every infinite planar graph is also 4-colorable. One way to construct infinite planar graphs is to make them periodic: start with any periodic tiling of the plane, decorate a single prototile by vertices and edges that may wrap from one tile to the next, and form an infinite graph from the copies of these decorations on all the tiles of the tiling. One possibility is to simply use one vertex in each tile, with edges that connect that vertex to its copies in each adjacent tile, in which case coloring the graph is the same as coloring the tiles of the tiling. For instance, here are two periodic colorings of the f
Linkage with two research problems
Aug 31, 2026 · original
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. Because I haven’t solved them, they are not very precisely formulated, and I don’t know how difficult or interesting they are nor even whether someone else might have already considered them; that’s often the way at the start of research. I think maybe I need to start bringing my DSLR along again when I go to the beach ( \(\mathbb{M}\) ) rather than relying on my cell phone camera (Pixel 6 Pro, yes I know it’s getting old now). Here’s what it thinks a crashing wave looks like, without additional processing except for a bit of a crop. To me it more resembles the kind of molded privacy glass that one uses for a bathroom window. Amazon buys rare books to destructively scan them for AI training ( \(\mathb
Fractional rings of tangent spheres
Aug 17, 2026 · original
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. If you keep one ring fixed, you can rotate the other ring continuously, possibly changing the sizes of some of the spheres as they rotate but keeping the pattern of tangencies unchanged. Here’s a nice animation I found on Wikipedia, where the ring of six spheres rotates continuously while the other ring of three spheres (the central blue one and the two green planes, considered as degenerate spheres tangent at infinity) stays fixed. The larger red sphere is not part of this configuration and I don’t know why the author of this animation included it. We can describe the graph of tangencies of these nine spheres by using the join operation o
Linkage
Aug 15, 2026 · original
A permutation generation algorithm in the work of 13th-century Kabbalist Abraham Abulafia ( \(\mathbb{M}\) , via ). The resulting permutation sequence is the one you get by reversing suffixes whose lengths form the sequence \((((2, 3)^2, 2, 4)^3, 2, 5)^4, \dots\) but that’s not the generation rule. Instead the rule is: to generate the permutations of \(1, 2, 3,\dots, n,\) form its \(n\) cyclically rotated permutations (starting with \(1, 2, 3,\dots, n,\)) and for each one in order, recursively generate the permutations of its length-\((n-1)\) suffix. The link claims that this is the first method for systematically listing permutations (long before the discovery of the Steinhaus–Johnson–Trotter algorithm for generating a different ordering, by 17th-century bell ringers). However, I’m not entirely convinced: it’s not the same as an enumeration algorithm, but factorials and lists of permuta
Non-coplanar unit distances
Aug 2, 2026 · original
Reports that LLMs have killed the Erdős unit distance problem turn out to be greatly exaggerated. There is still plenty not yet understood about the problem. The problem asks, for \(n\) points in the Euclidean plane, how many pairs can be at unit distance from each other? When Paul Erdős posed the problem in 1946 , he observed that the graph of unit distances cannot contain a subgraph of the form \(K_{2,3}\), a complete bipartite subgraph with two vertices on one side and three on the other. One way to see this is to draw unit circles through the two vertices on one side of a supposed \(K_{2,3}\) subgraph. These cross each other at most twice, and their two crossing points are the only points that can be vertices on the other side of the subgraph. Through reasoning later generalized as the Kővári–Sós–Turán theorem , Erdős observed that this forbidden subgraph implies an \(O(n^{3/2})\) up
Linkage
Jul 31, 2026 · original
ACM considers allowing LLMs to read its digital library ( \(\mathbb{M}\) ) and requests feedback on this choice . Daedalus’ labyrinth ( \(\mathbb{M}\) ), a puzzle game dual to loopy/slitherlink. Voronoi go ( \(\mathbb{M}\) ), a variant of go where you can play anywhere on the board (not just intersections). Human mathematicians are being outcounterexampled ( \(\mathbb{M}\) ). Kevin Buzzard of the Xena Lean formalization project on recent counterexamples to the unit distance problem and Jacobian conjecture. 3-boundary surfaces for 3-component links ( \(\mathbb{M}\) ) with crochet, 3d-printed, and vector graphics illustrations. Innovations in Graph Theory added to DOAJ ( \(\mathbb{M}\) ). zbMATH digitizes 50 years of its old reviews ( \(\mathbb{M}\) ). Three new Wikipedia articles about mathematics books ( \(\mathbb{M}\) ), posted by Samuel Adrian Antz: Characteristic Classes (1974) by Joh

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