Linkage

Biomedical papers with fabricated references blew up by more than a factor of ten from 2023 to 2026 (\(\mathbb{M}\), via). Relatedly, arXiv has added a new policy banning author of papers with hallucinated citations or other artifacts of unchecked LLM use for a year (and after that permanently requiring publication prior to allowing a preprint, kind of problematic for publication in journals whose submission process depends on having an arXiv preprint. Unfortunately I can’t find a direct reference to this in the actual posted arXiv policies and I’m not going to link to X/twitter where Tom Dietterich posted the only semi-official communication I can find on it.

Fish curve drawn as an epicycle. See also “Wheels on wheels on wheels” by Frank Farris in Math. Mag. on symmetric doily patterns drawn using epicycles.

I recently learned that the cubic and quartic cases of Fermat’s last theorem (the impossibility of integer solution of \(x^3+y^3=z^3\) and \(x^4+y^4=z^4\)) go back farther than Fermat (\(\mathbb{M}\)), to medieval Islamic mathematics. Abu-Mahmud Khujandi tried to prove the impossibility of the cubic case (but the proof was faulty) and later Ibn al-Khawwām included both cases in a list of open problems.

The age of an open problem is not a good proxy for its difficulty or importance, notes Lance Fortnow.

Another day, another journal editorial board mass resignation (\(\mathbb{M}\), via) this time from Springer’s Natural Language Semantics, over publisher demands to increase article publication charge revenue by increasing their number of acceptances. Instead the same editors are launching a new diamond open-access journal, Semantics of Natural Languages, through the Open Library of Humanities.

The American Diabetes Association has ejected from its annual meeting the editor-in-chief of its journal Diabetes Care, its former president, and three other scientists (\(\mathbb{M}\)), for handing out reprints of an editorial published in the journal and critical of the US government’s attacks on science. According to video evidence the ejected scientists “were not disruptive or disorderly in their conduct”. Nevertheless, the ADA claims that this behavior constituted a violation of the association’s code of conduct.

On circle packing with more than one size of circle.

Jeremy Kun (1) enjoys a rambly substack post on software developer bros who don’t even know how to find the center of a triangle, and how this somehow portends the obsolescence of software development (2) excuses the bros from their ignorance on the basis that there are “at least 26 different definitions of a triangle’s center”, (3) discovers that the Encyclopedia of Triangle Centers has “actually over 71 thousand definitions”, (4) realizes that his own ignorance has made him become the software bro he was enjoying the substack diss of, and (5) describes the whole saga, as if waking from a dream.

Terry Tao clearly explains why proposed new US funding rules requiring conference travel to be planned years ahead of time as part of grant proposals do not work for the time scales of mathematics research (\(\mathbb{M}\)). These rules would be even more disastrous for computer science, where conference publication is essential for making one’s research known and where one cannot know which conferences the research will appear in until the conference acceptance and rejections come in, only a few weeks or months before the conference itself.

How to wrap a hat tiling around a cylinder such as, say, a coffee mug, if you had a manufacturing process for them that didn’t involve leaving a seam in the design.

New preprint: “Existence of a periodic orbit for billiards in polygons (\(\mathbb{M}\)), Giovanni Forni. I think the title is self-explanatory; this claims to solve a major open problem in geometric dynamical systems. (I have too little expertise in this topic to evaluate its correctness.)

My 2024 paper “Non-crossing Hamiltonian paths and cycles in output-polynomial time](https://ics.uci.edu/~eppstein/pubs/p-noncross.html)” has been given the inaugural 2025 Algorithmica Best Paper Award (\(\mathbb{M}\)) as the most impactful paper in the journal Algorithmica from the past three years. The paper shows that one can list all of the traveling salesperson tours through a set of points in the plane in an amount of time polynomial in the number of tours. This number can be exponential, but the harder part of the problem is finding the tours quickly when there are fewer than exponentially many of them.

Dissident Russian mathematician Mikhail Verbitsky, traveling from Brazil to an award ceremony in Armenia, was arrested there at the request of the Russian government (\(\mathbb{M}\)). The linked article, in French, is from the French Mathematical Society, which strongly protests this action. As of posting he is said to be freed on a technicality but forbidden from leaving Armenia.

Seventeen camels and where they can take you (\(\mathbb{M}\)). Jim Propp on how “six seemingly unrelated brain-teasers” including the 17-camel inheritance problem as well as exercises on counting edges in forests can be solved by the same trick for dealing with linear equations with constant offsets.