Linkage
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ACM considers allowing LLMs to read its digital library (\(\mathbb{M}\)) and requests feedback on this choice.
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Daedalus’ labyrinth (\(\mathbb{M}\)), a puzzle game dual to loopy/slitherlink.
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Voronoi go (\(\mathbb{M}\)), a variant of go where you can play anywhere on the board (not just intersections).
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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.
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3-boundary surfaces for 3-component links (\(\mathbb{M}\)) with crochet, 3d-printed, and vector graphics illustrations.
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zbMATH digitizes 50 years of its old reviews (\(\mathbb{M}\)).
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Three new Wikipedia articles about mathematics books (\(\mathbb{M}\)), posted by Samuel Adrian Antz: Characteristic Classes (1974) by John Milnor and Jim Stasheff, Instantons and Four-Manifolds (1984) by Dan Freed and Karen Uhlenbeck, and The Geometry of Four-Manifolds (1990) by Simon Donaldson and Peter Kronheimer.
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AI in scientific publishing: Slower, worse, and more expensive (\(\mathbb{M}\), via). H. Holden Thorp notes that the rapid increase in AI-generated research is increasing rather than decreasing the need for human effort, in checking the research, and likens the resulting effects on human workers to those in the industrial revolution’s shift from craftspeople to factory workers.
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The existence of designs (\(\mathbb{M}\)), posted to arXiv in 2014 by Peeter Keevash, has finally been accepted for publication in the Annals of Mathematics, 12.5 years later.
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Three recent algorithms preprints on arXiv make some strong and interesting claims (\(\mathbb{M}\)):
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“Bellman–Ford in almost-linear time”, by Hair, Li, Li, and Zhang, arXiv:2607.19346, computes single-source shortest paths in a directed graph with real weights, allowed to be negative but with no negative cycles, in time \(O(m^{1+o(1)})\), building on recent subquadratic breakthroughs by overlapping authors.
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“Splay trees are almost dynamically optimal”, by Chmel, Haeupler, Hladík, Koucký, Roeyskoe, Rozhoň, Sladký, and Tarjan, arXiv:2607.18498, proves a competitive ratio of \(O(\log\log n(\log\log\log n)^3)\), the first nontrivial competitiveness for splay trees. Tango trees have a slightly better proven bound but unlike splay trees cannot be \(O(1)\)-competitive.
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“Shortest paths with linear edge weights”, by Chillara, Gajjar, and Raja, arXiv:2607.21055, considers shortest -paths in a directed graph whose weights vary linearly as a function of one or more parameters. Different parameter settings give different paths, but how many? The answer was known to be \(n^{\Theta(\log n)}\) for a single parameter, with weaker bounds for more. The new preprint proves a bound of the same form for any fixed number of parameters.
You might have thought that such old and well-established topics in algorithms research as shortest paths and balanced binary search trees would be very stable, but instead things are still changing rapidly.
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Wikimedia refuses to recognize a union for its employees (\(\mathbb{M}\)) after a supermajority of workers signed union cards requesting it.
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A long thread about variants of Kőnig’s infinity lemma in relation to computability theory.
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On using computational hardness to resolve a mathematical conjecture (\(\mathbb{M}\)). Noam Zeilberger points to “A system of interaction and structure III: The complexity of BV and pomset logic” (Lê Thành Dũng Nguyên and Lutz Straßburger, doi:10.46298/lmcs-19(4:25)2023) where an incompatibility of complexity classes for provability in two conjecturally-equal logics led to a counterexample to their equality.
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I don’t know why it took me so long to realize it (\(\mathbb{M}\)), but my phone’s HP 16C programmer’s calculator app turns out to be surprisingly useful for mixing hex-coded html/svg colors.