It may not be the worst aspect of the US invasion of Venezuela, but the fact that Trump cites Venezuela's failure to pump enough oil out of the ground as one of his reasons for invading is nevertheless deeply depressing.

This, but adding 1. My main non-plane trips in 2025 were one train journey to Venice, one to Leiden, and one to Saint Jean de Luz in the south west corner of France. All three went smoothly -- as last year my main gripe is that it is quite a bit more expensive to go by train than to fly.

Four degrees of separation: "Countries meeting in Brazil for two weeks could manage only a voluntary agreement to begin discussions on a roadmap to an eventual phase-out of fossil fuels ..." www.theguardian.com/environment/...

This comment has a strong guns-don't-kill-people vibe.

Around ten years ago Marijn Heule, Oliver Kullmann and Victor Marek proved that if you 2-colour the positive integers from 1 to 7825, then you must be able to find x, y and z all of the same colour with x^2+y^2=z^2 -- that is, a monochromatic Pythagorean triple. 1/

I crossed an interesting threshold yesterday, which I think many other mathematicians have been crossing recently as well. In the middle of trying to prove a result, I identified a statement that looked true and that would, if true, be useful to me. 1/3

Quel sera l’impact de l’IA sur les mathématiques dans les prochaines années ? par @wtgowers.bsky.social @college-de-france.fr www.youtube.com/watch?v=bcTW...

I can just about cope with the idea that the amount of CO2 in the atmosphere has hit a new record -- it's what one would expect even if we were rapidly decarbonizing. But that the *rate of increase* has hit a new record is unbelievably depressing. www.theguardian.com/environment/...

Gatwick expansion blows another huge hole in the UK Government's already perforated climate commitments. New article on Gatwick expansion with my @tyndallcentre.bsky.social colleague Dr Lois Pennington @loispennington.bsky.social climateuncensored.com/gatwick-expa...

Many thanks to the sender of an email that includes the heartwarming sentence, "I have long admired your contributions to mathematics, particularly [insert their field or specific result you respect]."

Happy to be able to say that my automatic theorem proving group in Cambridge submitted a successful bid to the AI for Math Fund, launched this year by Renaissance Philanthropy and XTX Markets. Here is the fund website, which contains descriptions of all the 29 projects to be funded.

The UK's terrorism problem has just got a whole lot worse.

Around a year ago my mother, my two sisters and I attended an event of a kind we would never normally go to: a celebration for fans of a TV series, who came from all over the world. The series in question was Granada TV's version of Sherlock Holmes, starring Jeremy Brett. 1/2

This article points out that of the three people in the infamous photo of Prince Andrew, Virginia Giuffre, and Ghislaine Maxwell, Andrew is the only one who isn't either dead or in prison. In other news, I am the only one out of me, Keir Starmer and Bukayo Saka who isn't either a PM or a footballer.

I have now added a third video to this IMO2025 series, in which I solve Question 5 (in about an hour and a half).

I have added a second video to this IMO2025 series, in which I solve Question 4. (I decided to skip Q2 as it was geometry and Q3 for now as it would normally be harder than Q4 and I want to work up.) It's pretty long -- an hour and 46 minutes -- but you can always watch at double speed.

From time to time I like to video myself solving maths problems in real time. Since the IMO has just happened, I plan to try a few of this year's questions. Here I get through Question 1. More to come at some point. www.youtube.com/watch?v=1G1n...

I've started a second blog, in which I will discuss in as systematic a way as I can topics about which people (including me) have strong feelings. I explain more about its nature and purpose in an introductory post. First up after that: a long post about the war in Gaza.

My friends Tony and Estelle (and Gilles) showed that Lipschitz-free Banach spaces can be more diverse than previously thought and at same time that opposition to authoritarian policies can be more diverse than previously thought. Be like them!

"We’re at a new point in human history,” Wagner says. Up until the last decade, “the major drivers of biodiversity losses around the planet were really land degradation and land loss, habitat loss. But I think now that climate change is by far exceeding that"

Hmm, who to go for? www.theguardian.com/world/2025/m...

I wonder what the "Why don't you go and protest in China?" brigade will make of this news. www.carbonbrief.org/analysis-cle...

Wow, looking forward to this!

Suppose we accept the premise that it is important for our care workers to be home grown. There are two steps: to solve the problem that it is very difficult to recruit home-grown care workers, and to stop recruiting care workers from abroad. Who in their right mind thinks step 2 comes first?

I'm reluctantly in favour of these experiments. I hope we never need to resort to geoengineering, but if, as seems a distinct possibility, we end up with a choice between geoengineering and catastrophe, then I'd rather we knew as much as possible about geoengineering before going ahead.

Today I have received by email: one disproof of the Riemann hypothesis, one proof that P =/= NP, one proof of the Riemann hypothesis, and one proof that Peano arithmetic is inconsistent (which follows from the two Riemann hypothesis papers, but this was an independent discovery).

I'm sorry fellow Arsenal supporters, but this would not have happened without City winning two of the last three titles and Liverpool one of them. So all the pain has been for a good cause. (Also, I want Arsenal to win their first title under Arteta after a certain player has moved on.)

Latest Truss idea: to launch a social network that by definition won't catch on. “... what I am doing is establishing a new free speech network, which will be uncensored and uncancellable, to actually talk about the issues people don’t want to talk about.” www.theguardian.com/politics/202...

"Labour sources said that the promise of thousands of additional jobs had outweighed environmental considerations." www.theguardian.com/business/202...

An interesting metaphor in today's Guardian.

Yesterday I touched my toes (with straight legs) for the first time for decades -- probably since I was a teenager. However much I was told that it's possible to improve one's flexibility, it somehow took actually doing it, via a nightly stretching exercise for about three months, to believe it.

Glad to see that the main thing I missed from Twitter -- trending topics -- is now present on Bluesky. (The fact that it is still somewhat rudimentary is, if anything, an advantage.)

Just got an email from the Fulbright Association. As of right now, funding has been cut off to 12,500 US citizens currently abroad and and more than 7,400 foreigner scholars and students in the United States

It's tempting to record instances where language models are bad at maths. In the interests of fairness, here's a case where I've used one to help me find references to an open problem I heard about a long time ago and have wanted to find for many years.

This is deeply depressing (not what @steveclimate.bsky.social writes, but what he is writing about). There are many ways to discourage flying besides shaming, not least of which are (i) acknowledging that we need as a society to fly less, and (ii) not building new runways.

An exciting result has just appeared on arXiv, concerning the following simple-seeming problem: if A is a set of n positive integers, then how large a sum-free subset B must it contain? That means that if x, y and z belong to B, then x + y should not equal z. 🧵

Elon Musk is not the only billionaire taking over the federal government. He's just the loudest. The quieter ones are equally as dangerous. heated.world/p/you-alread...

I've just tried out o3-mini-high on the following question. I'm wondering if you can help me with the following maths problem. I'd like to find a property of pairs of distinct primes such that if X is any infinite set of primes, then one can find a pair of distinct primes in X ... 🧵

The death toll from Israel’s war on Gaza has been revised to more than 61,700 people according to government officials, after reclassifying thousands of people who had been missing in the rubble.

I wrote to my (Labour) MP about this in late 2023 and got a reply that did its best to make me feel that he was on my side, while also not actually agreeing to do anything at all. ("I do not support revoking licences already handed out.") Thank goodness for the courts.

Delighted to be able to say that just under a fortnight ago William Eric Gowers, my first grandchild, was born, and everything seems to be going well. I've been looking forward to this since before I even became a parent, and now it's finally happened.

Now that it's 2025, I can celebrate having got through 2024 without flying. To do this I had to turn down a number of interesting invitations, and I also made three trips by train (two to the south of France and one to Berlin) that would have been cheaper and quicker to do by plane.

It seems that OpenAI's latest model, o3, can solve 25% of problems on a database called FrontierMath, created by EpochAI, where previous LLMs could only solve 2%. On Twitter I am quoted as saying, "Getting even one question right would be well beyond what we can do now, let alone saturating them."

AIMO, the Artificial Intelligence Mathematical Olympiad, is in its second year, with a new and harder set of problems. It has just awarded a prize of $20,000 to Md Boktiar Mahbub Murad for being the first person to write a program that solves 20/50 of the problems and make it freely available.

If you celebrate Christmas and are struggling to think of what to give someone, and if you have a few million pounds to spare, then here's a suggestion. www.christies.com/en/stories/j...

A few days ago Lawrence Hollom posted a preprint that solves a problem about posets, informally known as the fishbone conjecture, which I am told was extremely central in the area. 🧵 arxiv.org/abs/2411.16844

I've just received a message from Eton to ask whether I would consider helping them with, among other things, a building project to provide suitable sports facilities for the foreseeable future. Can any effective altruists advise me whether this would optimize the benefit of my charitable giving?

Just a little example of what fellows of the Royal Society are getting up to these days.

The Royal Society could not continue with both Elon Musk and Dorothy Bishop as fellows. I wonder what they decided.

I’ve just attended a Bourbaki seminar for the first time, given by Michael Harris. Full marks to him for starting with “un moment de silence pour les enfants de Gaza”. The reason I’m here is that later Yuval Wigderson will be talking about last year’s big breakthrough on Ramsey’s theorem.