• In a discussion on Wikipedia (\(\mathbb{M}\)), I asserted that it is typical to group the operations within mathematical formulas into meaningful chunks, analogously to the way we group sequences of sounds or letters into meaningful words. The example I was looking at concerned covering the edges of a random graph \(G(n,\tfrac12)\) by few cliques, for which the number of cliques needed turns out to be

    \[\Theta\left(\frac{n^2}{\log^2 n}\right).\]

    How I would expect such a formula to be read by someone knowledgeable about random graphs and the relevant notation is:

    • \(\Theta\): this is both an upper and a lower bound, and we are allowing ourselves to be sloppy about constant factors

    • \(n^2\): the number of edges in the graph

    • \(/\log^2 n\): smaller by a \(\log^2\) factor. But why \(\log^2\)? (After more thought, or looking a little farther into the source:) It’s the number of edges that can be covered by a single clique.

    It occurred to me to wonder: is this sort of chunking actually a typical way to read mathematical expressions? Where, if anywhere, do we teach beginning mathematicians to do this? Or is it just something they pick up along the way, maybe by example from seeing instructors talk about formulas, the way new language learners might pick up the ability to pick out and understand words from speech without ever being taught phonics?

  • A blatantly false statement: 3-edge-colored plane graphs have equally many vertices with each of the two cyclic orderings of incident edge colors. ChatGPT was confidently wrong in answering whether this was true until explicitly asked for a counterexample.

  • “More than a dozen faculty and staff unions and associations” from the University of California, not trusting their campus administration’s representation of their interests, sued in US courts to block government demands that the university “eliminate diversity programs and disavow recognition of transgender people” (\(\mathbb{M}\)). They have succeeded in an early milestone of their case, receiving a preliminary injunction blocking the government from imposing massive fines on the university.

  • Treewidth may have too many equivalent definitions, but there is another parameter in graph theory with too many names (\(\mathbb{M}\)). It is the intersection number, the edge clique cover number, the clique edge cover number, the clique cover number, or the R-content. The computational problem of finding this number has been called the intersection number problem, the intersection graph basis problem, covering by cliques, the edge clique cover problem, the clique edge cover problem and the keyword conflict problem.

    The problem can be expressed either as covering the edges of a graph with as few cliques as possible, or as representing the vertices of a graph by sets with as few total elements as possible so that adjacency corresponds to having a nonempty intersection. Its applications involve concisely representing conflicts between pairs of things, scheduling meetings so that all compatible pairs of participants meet and no incompatible participants meet, allocating bandwidth on fiber optic networks, generating compact letter displays that visualize the distinguishability of statistical variables, and analyzing biological food webs and protein interactions. Anyway, it is now a Good Article on Wikipedia.

  • The Miller–Rabin test provides a randomized polynomial time factorization algorithm for Carmichael numbers (\(\mathbb{M}\)). In the comments we find an earlier but very obscure mention of this: fgrieu, crypto stackexchange, 2012.

  • Apparently Wikipedia:Scam warning needs to be more widely known (\(\mathbb{M}\)). If there is a Wikipedia article about you and someone contacts you saying that there is a problem with it and they can fix it but you need to pay them, do not respond (and optionally forward the correspondence to paid-en-wp@wikipedia.org). They are scammers.

  • Incorrect citation association for articles in online-only Springer Nature journals (\(\mathbb{M}\)). We’ve known for a long time that citation counts are only a distorted proxy for scientific impact, but this preprint by Tamás Kriváchy finds a worse problem: the counts are not even accurate. Citations to many journals have been misattributed to the papers listed as article 1 of the same volume, causing those first articles to have anomalously higher citation counts than the rest.

  • A reminder that what you think may be standard arithmetic notation may actually mean something entirely different in nearby cultures (\(\mathbb{M}\)): an Italian resort sign using “÷” to indicate a range of room numbers.

  • Peter Cameron, as a retired professor still active in research, finds himself locked out of unfree-open-access publication (\(\mathbb{M}\)), because his university won’t use their publication-fee funding for emeriti despite continuing to count his publications towards its research productivity metrics:

  • There was a boosted post here but it got deleted and now I can’t trace my broken bookmark to recover whatever it was. A drawback of the Mastodon system?

  • It is graduate-school application season and that means filling out lots of web forms to submit recommendation letters to lots of schools (\(\mathbb{M}\)). One thing I am noticing is that a significant fraction of these forms require a phone number from the recommender. It has been years since my university automatically provided and paid for an office phone number for all faculty members; we could still have a number if we paid for it using our own funds but I do not. I am not going to put my personal cell phone number on these forms (fortunately they tend to allow any nonblank alphanumeric input) and if anyone I didn’t know called on it I would probably not answer. Nobody ever calls to verify graduate-school recommendation letters anyway. So what is the point?

  • ACM Transactions on Algorithms is looking for a new editor-in-chief (\(\mathbb{M}\)). The nomination deadline is December 31.

  • Mustard watches (\(\mathbb{M}\)), 1990 article by Y. J. Ringard (Jean-Yves Girard) spoofing the tendency of research papers to define “novel” concepts by glomming together two things that should stay separate. Like storing mustard in the mechanism of your watch, because “what is the point of knowing time if you cannot get mustard?”

  • It’s not a good time to be a program chair of a major conference. As reported in Nature (\(\mathbb{M}\), archived, via), analysis by Pangram found 21% of the peer reviews at ICLR (a major annual machine learning conference) to be entirely written by AI, and “more than half contained signs of AI use”. This appears to be in violation of ICLR’s terms of conduct, which “prohibited AI use that would have breached the confidentiality of manuscripts”. The ICLR chairs write that they are planning to penalize reviewers who did this by desk-rejecting the reviewers’ submissions but they say little about what they are doing for authors whose submissions received these reviews.

    Apparently unrelatedly, the reviewing system used by ICLR suffered a major privacy breach that allowed submission authors to connect their reviews with the full reviewer identities; in response, the conference reverted scores to what they were before the rebuttal phase and reassigned all papers to new area chairs.

  • A cute two-piece dissection puzzle from a pentagonal house with a traditional gable roof to a modern cubist architecture.