o-craven-canto:Alternate timeline in which all Greek and Latin roots are swapped:catastrophe -> contraversecephalopod -> capitopedchlorophyll -> viridofoliademocracy -> populimperyhomicide -> anthropoctonyhomosexual -> equigamickilometer -> millimensureinterregnum -> mesarchymagnanimous -> megapsychicmanuscript -> chirographymotorcycle -> ergatorotemicroscope -> parvovisoroxygen -> acidofexpolyamory -> multierastytelevision -> remotoscopeuniverse -> monostrophe

One of the interesting things to contemplate is the scale of the internal combustion engine. It’s a very human scale device; pistons the size of fists, Valves about as wide as knuckles. It’s the kind of thing a man with normal sized machine tools can make. Most internal combustion engines in the world are on […]

Joel David Hamkins and Atticus Stonestrom, “The pattern of consistency strength for membership in a computably enumerable set,” preprint. arxiv:2610.24919. Abstract. Every computable preorder relation on the natural numbers is the order of consistency strength for the membership assertions “$n\in … Continue reading →

NASA/Goddard Space Flight Center Illustration of a binary neutron star merger just as the two stars make contact. All neutron stars have intense magnetic fields. The typical magnetic field of a neutron star is about 100,000 times stronger than the strongest magnetic fields we can create on Earth. But about 1% of neutron stars have even stronger magnetic fields. Known as magnetars, their magnetic fields can be 1,000 times stronger than a regular magnetic field. They are a likely cause for…

In the spirit of my recent “Math 2.0” talk on new ways to use AI assistance to enhance the human understanding of mathematics, rather than substitute for it, I am using this post to propose an experimental challenge, inspired by the recent activity around excluding Landau–Siegel zeroes, as discussed in this previous post. There is a well-known connection between Landau–Siegel zeroes and the tenth discriminant problem, which I will briefly recall here; an in-depth discussion on this problem can…

Mini billet, just pour avoir une note que les 19 et 20 octobre 2026, j’ai travaillé du balcon pendant une heure en après-midi. La catastrophe climatique est plaisante une fois de temps en temps.

Attention Conservation Notice: optimality in a one-dimensional parametric model is so 1960s. Wikipedia says “For practical statistics problems, it is important to determine the MVUE if one exists, since less-than-optimal procedures would naturally be avoided, other things being equal”, but they’re not using the word “practical” to mean what I would use it to mean In the Laplace (or double exponential) distribution, with density \[f(x;\theta) =\frac{1}{2} \exp(-|x-\theta|)\] the maximum…

By David Tuller, DrPH Olympic Sprinter Bedbound for 22 Hours a Day The BBC has profiled Beth Dobbin, a top-level sprinter who is, per the story’s headline, “now bedbound for 22 hours a day” with a severe case of myalgic encephalomyelitis (ME). In 2021, Dobbin, 32, represented Great Britain at the summer Olympics in Tokyo. […]

For a given prime , the Legendre symbol is defined as follows: if is a quadratic residue modulo , then ; if is a quadratic non-residue modulo , then ; and if divides , then . Let be an integer that is not a perfect square. (One could require to be a fundamental discriminant if desired, although it turns out to be immaterial for the arguments here.) By combining quadratic reciprocity with the prime number theorem in arithmetic progressions, one can show that the Legendre symbol is asymptotically…

The number of papers being submitted to the Open Journal of Astrophysics continues to rise, as demonstrated by the following graphic which shows the stats for new submissions for the last five years: It’s very clear that the thicket is getting thicker and thicker as times goes on! The increasing number of articles is of course very welcome indeed, but it is increasing the load on our Editorial Board and that includes me! I think it’s time once again to look for more volunteers to join the team,…

Splitting N! into N factors is trivial. It’s defined as the product of N integers, the integers 1 through N. Can you still split N! into N factors if you put a minimum size requirement on the factors? You can’t split 3! into three factors unless one of the factors is 1, but you can split 4! into factors ≥ 2: 4! = 24 = 2 × 2 × 2 × 3 Define t(N) as the largest number such that N! can be expressed as the product of integers greater than or equal to t(N). So based on the discussion above, t(N) ≥ 1…

Hailey Nelson/ Arizona State University Artist’s illustration of a supermassive black hole at the center of a radio galaxy launching powerful jets all the way into the galaxy’s circumgalactic medium. Supermassive black holes are powerful engines. They can rip stars apart and feed upon them. They blast jets of ionized gas at near-light speeds. On the other hand, these gravitational beasts are rather small. Though they can be millions or billions of solar masses, they are localized to within the…

as eleições brasileiras estão a todo vapor e com menos de uma semana para o segundo turno, eu acho que o coração de todos está na palma da mão. o que vai acontecer? (♫♪♬ vai dar pt, vai dar, vai dar pt vai dar ♫♪♬). eu sempre tive minha escolha muito às claras: sempre fui de esquerda. pra mim não existe outro caminho: ou a revolta é popular ou ela não é. sempre fui muito feminista. meus ídolos eram Raul e Engenheiros do Hawaii e Chico Buarque, em outras palavras, eram os cds que meus tios…

Before we begin, I’m thrilled to share that Astrolab is continuing to be a sponsor of my Moon Monday blog+newsletter for the third year in a row!California-based Astrolab is developing large multi-purpose rovers called FLIP and FLEX for advanced exploration of our Moon this decade and next. The first FLIP rover is slated to fly on Astrobotic’s upcoming Griffin lunar lander. And NASA has selected a FLEX rover as one of its two Artemis crew-capable Lunar Terrain Vehicles, which will be more…

I just finished preparing my undergraduate lecture on the Debye model for solids. Here are my slides. The course is a third-year course on statistical mechanics. In the previous lecture, they learned about blackbody radiation and derived the Planck spectrum.(Note. The derivations are not included, as I sketch them by hand on a document viewer. This slows down the pace of the lecture and engages the students as they detect mistakes I make. :) ) A few things I find interesting about the lecture…

France Statistiques Projections macroéconomiques de la Banque de France - Publication trimestrielle Cette projection partage une prévision à deux ans des indicateurs suivants : croissance du PIB annuel inflation taux de chômage évolution du pouvoir d’achat des ménages croissance de l’investissement des entreprises taux de marge des entreprises non financières Panorama des prêts à l’habitat des ménages de la Banque de France - Statistiques et observations mensuelles Je m’attarde uniquement sur :…

BOUNAN, Michel. Original autograph manuscript for the preface (“Mise en garde”) to the new edition of Incitation à l’autodéfense. n.p. [Paris]: n.p., n.d. [September 2004]. Three loose leaves of white paper; written in blue ink on the rectos only; 21 x 29.7 cm. Heavily corrected with numerous cross-outs, marginal substitutions. Unique; from the author’s working papers. This manuscript represents the complete, raw drafting process for the warning preface added to the 2005 Éditions Allia edition…

Je suis allé au Mans ce weekend pour manifester en soutien du mouvement lycéen. Voilà quelques photos. Mention spéciale pour la pancarte Porco Rosso. Si vous pouvez, sortez, soutenez, manifestez. N'abandonnons pas les plus jeunes générations comme celles avant nous. #france #lemans #movementLyceen #protest #mouvementetudiant #polFR #politique #giletsjaunes #bloquonsTout #leftism #anticapitalism #anticapitalisme #bloqus #17octobre #ghibli #intergenerationalSolidarity #solidarity

Welcome to my 203rd gems post. This is where I share some of the latest news, ideas and resources for maths teachers. 1. Diagram BuilderI absolutely love this game changing diagram builder! mathfigures.com is the best I've seen. Thank you to @harryzafar for drawing it to my attention. It's incredibly easy to use. If you want to make a diagram for a lesson, resource or assessment,

It’s Saturday again, so it’s time for another update of activity at the Open Journal of Astrophysics. Since the last update we have published a further eight papers, bringing the number in Volume 9 (2026) to 245 and the total so far published by OJAp up to 693. There was no arXiv update on Monday 12th October owing to a US holiday, and I was on strike on Wednesday 14th October, so there were no papers published on either 13th or 14th October. I continue to include the posts made on our Mastodon…

Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz have written a blog post over on Kevin Buzzard’s blog entitled “How to Formalize All of Mathematics”, regarding recent proposals to automatically formalize the entirety of the mathematical literature. The issues regarding formal mathematics are parallel to those regarding informal mathematics, in particular the tradeoff between speed, scale, and understanding when one prioritizes the production…

This post began as a thread on X last night. I’ve edited the thread to turn it into a blog post, making some additions and corrections. I’m watching 2010: The Year We Make Contact. The movie opens saying the monolith is located at the Lagrange point between Jupiter and Io. I got nerd sniped and wondered where that was. There are five Lagrange points, but presumably the movie refers to L1 or L2 because these are near Io. Lagrange points L3, L4, and L5 are essentially in the orbit of Io, but 60,…

Para uma pessoa que não é muito dada a viajar, eu até que viajo muito. Fiz um mapeamento de todas as minhas viagens nos últimos 15 meses, desde julho de 2025, e pedi pra um chatbot de inteligência artificial calcular pra mim quantos quilômetros eu viajei no total. Inclusive, acho que esse é um belo uso de IA, e vou tentar fazer isso para todas as viagens das quais me recordo. Se você acha que é glamuroso viajar tanto assim, meu nervo ciático tem uma boa opinião sobre isso. Talvez seja massa se…

arXiv imposes a new limit of two submissions per submitter per month (\(\mathbb{M}\)). Book of Shapes: A collection of minimal, generative and customizable SVG-patterns (\(\mathbb{M}\), via). Sham scientific societies are misleading star researchers, according to Nature (\(\mathbb{M}\), via). The \(13\times 13\) zebra graph is untraceable (\(\mathbb{M}\)). A zebra is a fairy chess piece that jumps like a longer knight, two steps in one direction and three in another. Almost a proof without…

I just read a powerful article about AI in mathematics, “The Enshittification of Mathematics”, by Fenner Tanswell, from the Mathematical Intelligencer. You can find it here. This is why we need philosophers of mathematics!

In the OpenAI Math Drop some papers have Lean proofs, others don't, including L = RL = BPL. Why is it hard to formalize results on complexity classes? Let's consider an example, Lautemann's proof that BPP is in \(\Sigma^p_2\). It's a beautiful proof because it comes down to a single formula. I gave the full proof in a 2025 post, but to remind you, here is the setup. Let \(B\) be in BPP, accepted by a probabilistic polynomial-time Turing machine \(M\) with error bounded by \(2^{-n}\). Let…

NASA Hubble Hubble image of the El Gordo supercluster with the estimated dark matter highlighted in blue. Seven billion light-years from Earth, there is an unexpected cluster of galaxies. It has two regions in the process of colliding with each other with a combined mass of more than two quadrillion solar masses. Given its mass, the distant cluster has been nicknamed El Gordo, the Fat One. What makes it unusual is that it’s extraordinarily large for that period of the Universe. How did such a…

In February this year I went to the AAA108 conference in Vienna. This was the 108th meeting of the Arbeitstagung Allgemeine Algebra. I was obviously going to talk about graphs on groups, but I thought I should take the time to see how the ideas would transfer to arbitrary algebras (in the sense of universal algebra). Some constructions obviously don’t; for example, the commuting graph is only available if the algebra has a distinguished binary operation. But a surprising amount of stuff works…