New Book-Sorting Algorithm Almost Reaches Perfection: https://www.quantamagazine.org/new-book-sorting-algorithm-almost-reaches-perfection-20250124/
Quanta on the list labeling problem, based on "Nearly Optimal List Labeling" (https://arxiv.org/abs/2405.00807) by Bender, Conway, Farach-Colton, Komlós, Koucký, Kuszmaul, and Saks, from FOCS 2024.
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Scott Aaronson on the ongoing situation at the NSF (https://scottaaronson.blog/?p=8609) or, as he calls it, "the American science funding catastrophe". He writes that, despite the executive order freezing all operations supposedly being rescinded, grant funding is still frozen and operations at a standstill.
If you thought you saw me boost a different post going into more detail about the same thing, you did, but it was taken down, presumably out of fear of consequences for making truth public. Let this be a sign to keep locally any information you want kept rather than relying on others to keep it for you.
Edit: The post I linked to earlier is now back up in a modified form: https://blog.computationalcomplexity.org/2025/01/the-situation-at-nsf.html
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Grid bracing: https://en.wikipedia.org/wiki/Grid_bracing
This is a mathematical abstraction of problems of making a grid-like structure rigid by adding cross-bracing, of a type that should be familiar to anyone who has played with building blocks, built houses of cards, or tried to assemble a backless bookshelf. It forms a bridge between combinatorics and structural engineering in providing a solution to these problems based purely on graph connectivity analysis rather than numerical simulation.
Now a Good Article on Wikipedia.
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My paper "What is...treewidth" has appeared in the Notices of the AMS for its February issue: https://www.ams.org/journals/notices/202502/rnoti-p172.pdf
It is a very high-level survey of the subject, necessarily limited by the format to have not much technical depth and not many references. If you already know what treewidth is and use it in your work, you might not learn much of use from it. My focus instead was on explaining to mathematicians (and computer scientists) in related fields why they might want to learn it. If you work in sparse numerical linear algebra, Bayesian inference, control theory, game theory, low dimensional topology, network science, or algebraic geometry, then this paper overviews applications of treewidth in your area, and if you don't work in those areas then you might still learn something from it about those applications.
And if you're still wondering "what is treewidth" after reading this post, then the survey does also cover the (many) ways of defining it and using it in graph structure theory and graph algorithms. But for this post, I'll try to do it in a single sentence: it's a way of describing arbitrary graphs as "thickened trees" and a measure of how much thickening is needed.
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What do all those different squiggly equal signs mean?
A Wikipedia discussion on the symbol (\simeq) (called "asymptotically equal to" by the Unicode consortium, unicode U+2243) led me to https://math.stackexchange.com/questions/864606/difference-between-%E2%89%88-%E2%89%83-and-%E2%89%85 where I learn that it is commonly used for homotopy equivalence or maybe equivalence of categories. In my experience the more common symbol for asymptotic equivalence is (\sim). It's unfortunate that Unicode named these by a specific (and in this case dubious) choice of semantics than by a name that could convey a wider meaning. I guess the LaTeX name "simeq" also conveys the idea of a meaning "similar or equal" but "similar" can mean a lot of things.
The stackexchange link also discusses several other such symbols.
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Why is zero plural? https://ell.stackexchange.com/questions/352455/why-is-zero-plural via https://news.ycombinator.com/item?id=42787651
Sadly, the answers describe that zero is grammatically plural (that is, that in English, one uses singular only when there is exactly one of something and plural when the number is different than one, including zero) without pointing to any historical linguistics scholarship on why that came to be.
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On faith, religion, conjectures and Schubert calculus: https://igorpak.wordpress.com/2024/12/29/on-faith-religion-conjectures-and-schubert-calculus/, Igor Pak. This blog post is related to Pak's new preprint "Positivity of Schubert Coefficients" with Colleen Robichaux, https://arxiv.org/abs/2412.18984 . The preprint combines an unproved assumption from mathematical analysis (GRH) with one from complexity theory (the Miltersen–Vinodchandran Assumption on the non-existence of subexponential circuits for nondeterministic exponential time problems from https://doi.org/10.1007/s00037-005-0197-7) to prove that, under those assumptions, the positivity of Schubert coefficients can be verified in NP. The blog post explains how Pak went from a position of disbelieving in derandomization (lacking the faith in P=BPP that many complexity theorists hold) to a position where it is reasonable to make an assumption that implies the ability to derandomize interactive proofs (NP=AM).
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New arXiv preprint, "Computational geometry with probabilistically noisy primitive operations", https://arxiv.org/abs/2501.07707, and new explanatory blog post, "Twenty questions with a random liar", https://11011110.github.io/blog/2025/01/16/twenty-questions-random.html
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New Calculator template brings interactivity to Wikipedia articles: https://en.wikipedia.org/wiki/Wikipedia:Wikipedia_Signpost/2025-01-15/Technology_report
The template basically allows the creation of small forms that allow readers to specify some numbers as input and use a formula to generate an output. It's even possible to simulate some simple algorithms step-by-step and expand the form after each step: see for instance an example of this at https://en.wikipedia.org/wiki/Euclidean_algorithm#Procedure
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Claire Voisin: Mathematics as a private space – from the unveiling of conjectures to worldwide recognition, https://euromathsoc.org/magazine/articles/206
Interesting interview with Voisin in the European Mathematical Society magazine, more about her life and philosophy than her mathematics.
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New photo-essay on my blog: Linus Pauling Commemorative Ceramic Mural, https://11011110.github.io/blog/2025/01/11/linus-pauling-commemorative.html, documenting a public artwork in Palo Alto where Pauling once had a research office.
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Quanta on recent irrationality proofs for specific values of L-series, along the lines of Apéry's proof that (\zeta(3)) is irrational: https://www.quantamagazine.org/rational-or-not-this-basic-math-question-took-decades-to-answer-20250108/
Relatedly, @QuantaMagazine hasn't posted since June 2023, and @quanta_bot hasn't posted since November 2022. Is Quanta actually federated anywhere currently?
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Recent encounters with atom-thin salami slicing (https://reeserichardson.blog/2024/12/30/recent-encounters-with-atom-thin-salami-slicing/), several case studies in bad-to-dishonest academic publishing by Reese Richardson, via https://retractionwatch.com/2025/01/04/weekend-reads-honest-overachievers-the-unpublished-lucy-letby-paper-atom-thin-salami-slicing/
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Buddha cat dreams of Escher birds
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A beautiful day on the northern California coast today, after a much stormier day yesterday.
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Buried in a story about yet another Elsevier journal editorial board resigning en masse (Journal of Human Evolution, https://retractionwatch.com/2024/12/27/evolution-journal-editors-resign-en-masse-to-protest-elsevier-changes/), there is an alarming new development in Elsevier's publication practices:
"In fall of 2023, for example, without consulting or informing the editors, Elsevier initiated the use of AI during production, creating article proofs devoid of capitalization of all proper nouns (e.g., formally recognized epochs, site names, countries, cities, genera, etc.) as well italics for genera and species. These AI changes reversed the accepted versions of papers that had already been properly formatted by the handling editors. This was highly embarrassing for the journal and resolution took six months and was achieved only through the persistent efforts of the editors. AI processing continues to be used and regularly reformats submitted manuscripts to change meaning and formatting and require extensive author and editor oversight during proof stage."
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Nice new/updated 3blue1brown video on the square peg problem, with some broader discussion on what topology is and what it might be good for: https://www.youtube.com/watch?v=IQqtsm-bBRU
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Women's biographies on the English Wikipedia have reached a milestone number, 20% of all biographies: https://en.wikipedia.org/wiki/Wikipedia:WikiProject_Women_in_Red/Metrics/20%25_milestone
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I promised myself months ago, when we started to get warnings like https://arstechnica.com/gadgets/2024/08/chromes-manifest-v3-and-its-changes-for-ad-blocking-are-coming-real-soon/ that Google's plans to lobotomize ad-blockers were serious, that the day an ad got through on Chrome (+ uBlock Origin) was the day I would give up on Chrome, give up on running with two browsers open, and switch to Firefox for everything. That day has arrived.
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I have a new paper Princ-wiki-a Mathematica: Wikipedia Editing and Mathematics, https://www.ams.org/journals/notices/202501/noti3096/noti3096.html, in the January Notices of the AMS, and a new blog post, Pseudonymity in academic publishing, https://11011110.github.io/blog/2024/12/19/pseudonymity-academic-publishing.html
The Notices paper is on editing mathematics on Wikipedia, and I hope it encourages more to do so. The blog post is on the fact that the AMS would not let us list our pseudonymous coauthor as an author. Pseudonymity is important and highly protected on Wikipedia, in part because Wikipedia editing can sometimes put its editors into serious danger, but in this case it clashed with academic publishing standards, or at least the AMS's publishing policies, and I wanted to explore that.
Some of the other material in this issue also looked interesting to me, especially @tao's article on machine-assisted proof (https://www.ams.org/cgi-bin/notices/nxgnotices.pl?next=202501) and Nick Trefethen's on rational approximation (https://www.ams.org/journals/notices/202501/noti3066/noti3066.html). See https://www.ams.org/cgi-bin/notices/nxgnotices.pl?next=202501 for the whole issue.
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