David Pollard has a new draft, "Probability tools, tricks, and miracles" (last updated June 2006). Lots of good things in there, from a quick skim! And, if nothing else, worth reading for the quality of the writing and the exposition choices and notes. www.stat.yale.edu/~pollard/Boo...
sorry for accidentally inventing a swarm of cybersecurity demons, but now that it exists, the only way to stop a bad swarm of cybersecurity demons is a good swarm of cybersecurity demons
People used to be able to impress and intimidate reviewers with complicated proofs. This will change. In the age of AI inscrutable proofs are cheap. It is understandable proofs that are valuable. Opaque complexity is now it is a sign of laziness or lack of insight.
Super interesting. “The point is that there are so many ways in which a result can be strengthened that it is hard to know in advance in which direction you should go. With the benefit of hindsight, it could have been done [by a human mathematician].”
It is not correct, that mathematicians have not weighed in. Here's for example an interview with Francesco Fournier-Facio (Cambridge) on the non-sofic groups. share.google/skdtcxZutEYd...
why would I ever again share a well formulated open research question in an open problems session of a conference?
This paper prompted Jack Clark, one of the co-founders of Anthropic to post this to their news letter: "the singularity could be delayed" (as a reminder: always be wary of statements from people who work in corporate AI labs--their livelihood depends on certain outcomes and beliefs)
Don't forget (a) heavy subsectioning; (b - i; ii) overly emphatic adjectives and adverbs; (c) referencing expressions with (...); (d) insane use of display math; or (e) introductions written in the stylistic equivalent to the colour grey. Every day seeing this state of affairs worsen makes me sad.
AI-generated paper starter pack: include your prefered! Starting with a classic. AI-hallucinated references! arxiv.org/pdf/2607.07808
Some initial thoughts, and a complicated mix of feelings. Wow. I mean, Erdos problems are cool (I genuinely mean that), I didn't know about the Jacobian conjecture before it got disproved. But this newest batch from OpenAI hits home in a way the previous announcements did not.
“Zusammenfassung: Die Europäer haben auf eine Bedrohung von außen nicht gemeinsam reagiert, sondern sind übereinander hergefallen. Der gestrige Tag war ein schwarzer Tag für Europa und ein Fest für seine Feinde.” www.zeit.de/politik/2026...
Ceuta: Ein Fest für die Feinde Europas
Die Reaktionen auf den Ausnahmezustand in Ceuta? Teils faktenfreies Spanien-Bashing. Man muss festhalten: Friedrich Merz fiel hier beinahe positiv auf.
zeit.de
-67%. Still up close to 100% ytd lol.
So what do we think the actual July mark for Sit Awareness will be?
FT scoop: Citadel buys Situational Awareness equity holdings after steep AI losses www.ft.com/content/5fb4...
Citadel buys Situational Awareness equity holdings after steep AI losses
Deal comes after Leopold Aschenbrenner’s investment firm held overnight crunch talks with investors
ft.com
There’s a lovely video of Hong Wang from IHES, which is much happier than the one I saw at the #ICM2026 Fields medallists ceremony 📽️ youtu.be/3s35qhi_inU?...
Hong Wang, professeure permanente en mathématiques à l'IHES
YouTube video by Institut des Hautes Etudes Scientifiques (IHES)
youtu.be
This is (selfishly) a worry of mine. Doing things is now trivial and understanding is what enables valuable contributions. In this regime having had 20 years to develop intuition about a subject is an enormous advantage
This is very important to resolve adequately, especially for young students. Their work could be in danger of being scooped by quick AI prompting from more experienced researchers, who know more context about given problem, and who have access to more compute/tokens. 4/n
Professor Hong Wang, a Fields Medalist, the highest honor in mathematics, has taken on an unexpected new role: fashion influencer.
I’ve just discovered this super interesting exchange between Daniel Litt and Jacob Tsimerman xcancel.com/littmath/sta...
“In fact during the workshop I learnt from Harvard PhD student Bryan Wang that Harvard were already giving free Fable access to all PhD students, post-docs and faculty at Harvard.”
I don't want to work for an AI company, but I'm extremely interested in what's going on, because we're seeing a battle for the future of mathematics. Another data point: Kevin Buzzard says any PhD student who is not paying $200 per month for an AI subscription is crazy. (Are they all so rich? 😕)
A really good mathematician told me Anthropic is paying people like him $250/hour to improve Fable by throwing hard math problems at it. They also get a separate account where they can use Fable for their own purposes. They can do it for 5 months maximum.
I’m a sucker for these videos presenting the medalists
2026 Fields Medal: Hong Wang
YouTube video by Simons Foundation
youtube.com
An unorthodox solution to a major math problem came from an unorthodox place: a teenager who, after finding homeschooling confining, found her way to research mathematics.
How a High School Student Overturned a Famous Conjecture
When Hannah Cairo was a 17-year-old high school student, she did something mathematicians had been unable to do for four decades: she overturned the Mizohata-Takeuchi conjecture, a famous prediction…
youtube.com
TMLR has been facing an significant uptick in the number of submissions since the start of 2026. This is placing an extreme burden on our amazing team of reviewers & action editors. To ease this burden, TMLR will be implementing submission quotas, effective July 1. 1/n medium.com/@TmlrOrg/ann...
When the ARR time series has to be put on a logarithmic scale. I still find it baffling
SpaceX's business model is currently less "data centers in space" and more "space in data centers" www.cnbc.com/2026/06/22/s....
How (not) to call English place names in French. fr.wikipedia.org/wiki/Liste_d... I am now referring to the University of Oxford as «l'Université d'Osenefort», and I regret there is no «Camepont» on the list for Cambridge because that would be even better.
Liste des noms français de toponymes du Royaume-Uni — Wikipédia
fr.wikipedia.org
J'adore cette page (notamment Ouestmoutiers et Clocestre)
On m'a demandé de regarder cette vidéo www.youtube.com/watch?v=AYPQ... de @monsieurphi.bsky.social sur les progrès des LLM en maths et de donner mon avis. Attention, ça va être très long!, parce que forcément j'ai beaucoup à raconter. 🧵⤵️ •1/59
Nouvelle vidéo ! On parle des progrès récents et fulgurant dans la recherche en maths par IA. Ça va très très vite. youtu.be/AYPQIntoJeE
@3blue1brown.com is doing a series on information theory!
Reinventing Entropy | Compression & Intelligence Part 1
YouTube video by 3Blue1Brown
youtube.com