• The YouTube channel of the theoretical computer science group at Jagiellonian University (\(\mathbb{M}\)) has many interesting seminar talks, often in the direction of graph algorithms and computational geometry.

  • “A.I. is coming for mathematics, too” (\(\mathbb{M}\)), writes Siobhan Roberts in the New York Times, based on an IPAM workshop on machine-assisted proof.

  • 3Blue1Brown video on counting faces in arrangements of the diagonals of a convex polygon (\(\mathbb{M}\)) and on why the resulting sequence of numbers looks like the powers of two for quite a while until it doesn’t.

  • Visualization of the van Cittert–Zernike theorem: an incoherence source of radiation, seen from far away, will look like a spatially coherent point source.

  • In my SoCG 2023 talk on my paper “Non-crossing Hamiltonian paths and cycles in output-polynomial time”, I mentioned that I thought it would be possible to solve the Euclidean TSP, count non-crossing paths or cycles, or solve other related optimization problems in time fixed-parameter tractable in the parameter min(# points interior to the hull, # points whose deletion produces a collinear subset), the same parameter controlling the output size for my algorithm. I was planning to write this up as a separate paper but then I found the following reference (\(\mathbb{M}\)):

    Deĭneko, Vladimir G., Hoffmann, Michael, Okamoto, Yoshio, and Woeginger, Gerhard J. (2006), “The traveling salesman problem with few inner points”, Oper. Res. Lett. 34 (1): 106–110, doi:10.1016/j.orl.2005.01.002.

    It gives a parameterized algorithm with time singly exponential in the number of interior points. I think it’s possible to get singly-exponential dependence in linear space (maybe with a worse base of the exponential), and to bring in the collinear-subset parameter, but that doesn’t seem like a big enough improvement to write up as a new paper. See also the followup, “Euclidean TSP with few inner points in linear space”, by Gawrychowski and Rusak at ISAAC 2014, doi:10.1007/978-3-319-13075-0_55, arXiv:1406.2154, which however has worse-than-exponential time dependence on the parameter.

  • Henry Segerman and his brother fabricate a Peaucellier–Lipkin linkage. It can draw straight lines!

  • The title of “New discovery toward sugar origami” (\(\mathbb{M}\), via) is kind of misleading, and if you’re looking for something about sweet paper folding you’re likely to be disappointed. Instead, it’s about a phenomenon that both proteins and RNA exhibit: by controlling their sequences of subunits you can control the shape into which these polymers fold. The research described in the link shows that the same is true for polysaccharides, chains of sugar units.

  • LIPIcs: Affordable, high-quality and open-access proceedings of conferences in Computer Science (\(\mathbb{M}\)). Luca Aceto looks back on 15 years of this publication series.

  • Two recent preprints by David Wood and colleagues (\(\mathbb{M}\)) give product-theorem strengthenings of classical results in graph minor theory. “Tree-minor theorem revisited” shows that graphs with an excluded tree minor are subgraphs of a product of a clique with a bounded-pathwidth graph, where the clique product allows the pathwidth to be proportional to the radius of the tree rather than depending on its full size. And “Grid-minor theorem revisited” shows that graphs with an excluded planar graph minor are subgraphs of a product of a clique with a bounded-treewidth graph, where again the clique product allows the treewidth to be a function of the treedepth of the excluded minor rather than its size.

  • The Apple pizza slice emoji comes from a pizza that has been sliced into 7.4 pieces. Or at least that seems to be the implication of its 48.5° apex angle.

  • The University of California is reversing course on its data science admissions standard (\(\mathbb{M}\); paywalled, sorry). The issue is that, under a recent policy change, we were letting students count high school “data science” courses that were “more akin to data literacy” towards its requirement that new students have three years of high school mathematics. This replaced other high school mathematics courses that prepared the students to take calculus (either in high school or as freshman). The students who had been encouraged to do this were entering the university without enough mathematics to begin calculus, hindering them in any field where calculus is required (the sciences, engineering, computer science, mathematics, economics, etc). The short summary of the linked article is that a systemwide faculty committee, the Board of Admissions and Relations with Schools, voted unanimously last week to reverse this policy. Another vote is scheduled tomorrow by the California Board of Education, on its recommendations to the state’s high schools on how to teach mathematics, which “currently encourages high schools to consider offering data science” citing the now-reversed policy. For more background, see a post from April 2022, where I linked an open letter by California academics on the topic and several related blog posts.

  • A two-dimensional Cantor set whose projections onto the coordinate axes are full-dimensional intervals, but whose projections in any other direction have measure zero. Applying point-line duality (and taking the union with a 90° rotation of the result) produces a system of lines of all slopes whose union has area zero.

  • Chernoff turns 100 (\(\mathbb{M}\)). Chernoff bounds, so often used in theoretical computer science (credited by Chernoff to Herman Rubin) are over 70.

  • 19: The penultimate oscillator period to be discovered in Conway’s Game of Life (\(\mathbb{M}\)). The oscillator is called cribbage and is surprisingly simple: a honey-farm hassler stabilized by two eaters and two custom still lifes.

  • An open letter to the MAA concerning this year’s Florida Mathfest (\(\mathbb{M}\)). Or, how to mitigate the problems when you are stuck holding your conference in a state that has made itself inhospitable to basically everyone who is not white, male, and heterosexual? Unfortunately, the responses from MAA and Project NEXT have not “substantively addressed the outlined asks”.