skybrian's recent activity
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Comment on Why socialists should embrace luxury apartments in ~society
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Comment on Human mathematicians are being outcounterexampled in ~science
skybrian LinkFrom the article: [...] [...] [...]From the article:
It is now 9 years since I had a mid-life crisis, realised I no longer trusted many human mathematicians when it comes to technical details, discovered Lean, and started to argue that interactive theorem provers should play an important role in the future of mathematics. So of course my first question was “is the counterexample formalized in Lean”. The answer was “no”.
But under a week later (26th May 2026), I got an email from Fields Medallist Mike Freedman. Mike is now the Chief Science Officer for Logical Intelligence, a company cofounded by Turing Award winner and “godfather of AI” Yan LeCun. Mike informed me that their system had autoformalized the entire ChatGPT-generated paper in Lean and could I take a look. I looked, and my post-doc Thomas Browning looked too. And indeed this was what Logical Intelligence had done: they had formalized precisely the statement that the profound theorem of number theory implied the Erdős counterexample. Breakthrough LLM-generated mathematics being formalized in real time. Interesting data point.
Of course there is an elephant in the room here though, the profound theorem of number theory which takes 100+ pages to prove (it needs huge chunks of global class field theory, a theory developed at the beginning of the 20th century and for which there are still no short proofs; it is proving difficult to compress). In 2025 I had run a Clay Summer School with Richard Hill on the formalization of class field theory, and one year later we have nearly done the local case (it is the current PhD project of my student Edison Xie); the global case remained open, and indeed in 2025 formalizing global class field theory seemed like a fantasy.
One month later, on June 26th 2026, my perception of what was possible again changed. Boris Alexeev announced on the Lean Zulip that he had steered ChatGPT to a complete formalization of the Erdős counterexample, assuming nothing beyond the axioms of mathematics. Boris works at OpenAI and had used their new model Sol to do the autoformalization. Boris made the code public and it did not take long for me to realise that somewhere within all this AI-generated (and sometimes horrible, although sometimes decent) code was indeed a proof of some really hard theorems in global class field theory. Also of interest to me was that Sol had generated 1.2 million lines of Lean code in the three weeks that it had worked on the project. Lean’s fantastic (declaration of conflict of interest: I am a maintainer) mathematics library mathlib is only 2.3 million lines of code, and took nine years to write. Perhaps it was at this point that the penny really dropped for me — large AI-generated developments of mathematics are inevitable. One cannot trust AI-generated code so I ran it in a sandbox on my machine (malicious Lean code can run arbitrary commands on your computer — Lean is a programming language, after all). Indeed, it was proving nontrivial theorems about the cohomology of number fields. Wow.
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I was not sure how good Logos’ tool was going to be, but I wanted a development of the theory of finite flat group schemes in Lean for my ongoing proof of Fermat’s Last Theorem, so I put uploaded some classic papers in the area to Fable and ChatGPT, and got them together to write down an exposition of the theory in natural language. I passed this pdf document over to Logos the day before the workshop, and on the first day of the workshop they said that one of the claims in the pdf was false and they had found an explicit counterexample. Another counterexample! I took a look and indeed the LLM-generated pdf was simply wrong at some point when describing a standard construction; false alarm. I had missed this myself though when reading through the pdf. Interesting how AI had again found a counterexample. I fixed the pdf. I thought it was interesting that the AI didn’t just say “I don’t quite follow this argument”, it instead said “here is a proof that this argument is simply wrong”, a much more powerful statement.
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The day after the workshop finished, on Saturday 11th July, I got a DM from Akhil telling me that Sol had found a counterexample. He sent me a 12 page pdf. I immediately replied saying that I was not reading AI-generated informal mathematics and could he please formalize the entire thing in Lean. Four hours later he replied again, saying that Fable had autoformalized the entire thing. I scanned over the 1076-line Lean file, checking that the code did not delete all the files on my hard drive (Lean is a programming language, so it can do this). Convinced that it was only theorems, I then compiled it on my laptop and it took me under 5 minutes in total to check that (a) the statement of the claimed theorem used only concepts in mathlib (and thus things like HopfAlgebra can be trusted to mean what mathematicians think of as Hopf algebras) (b) the statement of the claimed theorem was that there was a counterexample and (c) the proof compiled. At this point I knew that we had a counterexample — a group scheme of order 4 which was not killed by 4. I suggested to Akhil that he make a PR to mathlib with the counterexample — which he did. I would have also suggested to him that he draft a press release saying that a machine had solved a 60-year-old question of Grothendieck in algebraic geometry, but somehow by this point I was almost becoming immune to all of this. It wasn’t clear to me that the media would even be able to distinguish between “machine resolves question due to Erdős” and “machine resolves question due to Grothendieck” even though I personally found the latter far more interesting. Of course the Grothendieck counterexample was far far easier than the Erdős one (a thousand lines, not a million), all I’m saying is that it’s an area of mathematics that I personally find more interesting. I pointed out to Akhil that machines seemed to be getting very good at finding counterexamples and suggested that he try the Hodge conjecture next.
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I think it’s worth stepping back at this point and surveying what the attitudes of human experts to these sorts of things are. On Tuesday (14th July) I went to work at Imperial and the Grothendieck counterexample was the talk of lunch. A member of the faculty (who I won’t name) said to me that the fact that the counterexample was so easy to find just indicated that humans had not spent enough time thinking about the problem, implying that a 60-year-old question of Grothendieck was not actually that interesting to work on. I didn’t tell him that at some point earlier in my career I had spent a week working hard on the problem. In my mind my colleague is just going through the five stages of grief; right now they seem to be in the denial phase.
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Human mathematicians are being outcounterexampled
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Comment on China wants to use 115,000 banned Nvidia chips to fulfil its AI ambitions in ~tech
skybrian LinkHere's a Hacker News comment from someone who says there's already a lot of network traffic coming from Xinjiang. Or at least there was for a while.Here's a Hacker News comment from someone who says there's already a lot of network traffic coming from Xinjiang. Or at least there was for a while.
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Comment on China wants to use 115,000 banned Nvidia chips to fulfil its AI ambitions in ~tech
skybrian Linkhttps://archive.is/nZSst From the article: [...] [...] [...]From the article:
A Bloomberg News analysis of investment approvals, tender documents and company filings shows that Chinese firms aim to install more than 115,000 Nvidia Corp. AI chips in some three dozen data centers across the country’s western deserts. Operators in Xinjiang intend to house the lion’s share of those processors in a single compound — which, if they can pull it off, could be used to train foundational large-language models like those of Chinese AI startup DeepSeek.
The complex as envisioned would still be dwarfed by the scale of AI infrastructure in the US, but it would significantly boost China’s computing prowess as President Xi Jinping pushes for technological breakthroughs. Such a project also would raise serious concerns for officials in Washington, who restricted leading-edge Nvidia chip sales to China in 2022 over worries that advanced AI could give Beijing a military edge.
Yet the Chinese documents contain no explanation of how companies plan to acquire the chips, which cannot be legally purchased without licenses from the US government, permits that haven’t been given. The companies listed in the filings, state officials and central government representatives in Beijing declined to comment when asked to explain.
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None of those familiar with the US probes said they previously knew of the data center buildout in Xinjiang. All said that while they believe there are indeed banned chips in China, they’re not aware of an illicit trade network sophisticated enough to procure more than 100,000 such processors and direct that hardware to a centralized location.
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To be sure, Bloomberg News has not found evidence that China has amassed, or can amass, 115,000 banned Nvidia chips — nor evidence that smaller volumes of restricted semiconductors that US officials believe are in the country have been directed to centralized locations.
And yet in Yiwu, the construction goes on.
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The authorities in Xinjiang are particularly suspicious of foreigners due to Western allegations of human-rights abuses against ethnic Uyghurs. Interview requests sent to eight data center operators in Yiwu were ignored, rejected or agreed to and then cancelled at short notice. The Xinjiang government and Ministry of Industry and Information Technology (MIIT), the central government ministry overseeing data center development, didn’t reply to Bloomberg requests for comment.
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China wants to use 115,000 banned Nvidia chips to fulfil its AI ambitions
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Comment on US President Donald Trump says he will impose fifty percent tariffs on Canadian goods in thirty days in ~society
skybrian LinkFrom the article: [...]From the article:
The move comes one day after Trump threatened to impose tariffs in retaliation for wildfires in Ontario that sent thick smoke pouring into the United States late last week. After watching Sunday’s World Cup final alongside Canadian Prime Minister Mark Carney, Trump told reporters that the subject had come up.
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On Monday, however, a senior administration official said the president’s latest tariff action was unrelated to his irritation over the wildfires. Instead, the official said, the president was acting in response to Canada’s retaliation for emergency tariffs Trump imposed in April 2025, when U.S. alcohol was removed from Canadian store shelves. The administration has also complained about Canadian limits on auto imports and dairy products.
Monday’s action relies on a never-before-used provision of a 1930 trade law, which provides for tariffs of up to 50 percent against countries that discriminate against U.S. goods. The 30-day delay provides time for the two nations to resolve the dispute before tariffs take effect.
If the tariffs do take effect, they will apply to most Canadian goods, including those that qualify for duty-free treatment under the United States-Mexico-Canada Agreement that Trump negotiated during his first term. Energy, potash fertilizer, critical minerals, fish and products covered by existing national security tariffs will be exempt, said the administration official, who briefed reporters under ground rules that did not allow them to be identified.
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US President Donald Trump says he will impose fifty percent tariffs on Canadian goods in thirty days
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Comment on MTA says G train shutdown worth it to finally modernize Brooklyn-Queens subway line in ~transport
skybrian LinkFrom the article: [...] [...] [...] [...]From the article:
After planned signal upgrades meant a 10-week shutdown of the line in 2024 — and continued work on the signaling system meant scattered outages weeknight and weekend outages last year as well — riders in Greenpoint were angered to learn this spring that there would be yet more weekends with no G train service this summer.
MTA officials said they’d discovered a leak in the tunnel under the Newtown Creek — and that repairing it alongside the ongoing upgrades meant taking the trains out of service for multiple weekends between the Bedford-Nostrand and Court Sq. stations.
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“We are making a massive investment in the modernization of this line,” Torres-Springer said. “It will only be the fourth line across the 22 lines that will be fully re-signaled.”
“We’ve enabled cell service across the entire G line as part of this work,” he added. “Five more stations [will] become A.D.A. accessible.”
Torres-Springer also noted the MTA’s decision last year to swap out all the line’s older subway cars for the state-of-the-art R211.
But the primary reason for the work — the cause of the shutdowns that began in 2024 — is the first one: the installation of modern computerized signaling, known as communication-based train control, or CBTC.
The system — which is already in place on the L train, the No. 7 train, portions of the E, F, M and R trains — will allow the MTA to precisely track trains in the tunnels, letting them safely run more closely together. The upgrade will also streamline dispatching, allowing trains to be routed from the MTA’s Midtown rail control center.
To install the new system means putting in brand new switches and new traffic lights. It means adding small wireless transponders at regular intervals along the tracks, along with 5G radios to let them communicate. And it means wiring all of those devices up to a computer that can control them while talking to dispatchers.
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MTA officials expect to conduct more than a year of testing, troubleshooting, and software tweaks before turning the new system on. A large keyed switch in the newly-minted Train Control Room up the tracks at Court Square was marked “LEG[ACY]” for the existing signal system and “CBTC” for the new one. Workers can flip it back and forth for upcoming tests.
But MTA officials say it will be late 2027 or early 2028 before that switch is flipped for good. And all along the track-side, new signal lights were covered in black plastic, so as not to confuse train operators before the new system comes online.
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Torres-Springer said the damage could be traced back to repairs done in 2015 after 2012’s Hurricane Sandy.
That’s when “the old MTA,” as he put it, “made some repairs, but left the leaks to be remediated by somebody in the future.”
“We’re not doing that,” he said. “We went in and we saw that the leaks were extensive, and we’re repairing them.”
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MTA spokeswoman Sophie Deixel told The News that work crews had managed to drill along 1,000 feet of the tunnel that weekend — 100 sets of holes — and pump grout along 450 feet of tunnel.
Each tube of the 95-year-old tunnel is 3,200 feet long. The MTA estimates it will take until the year’s end to seal them both.
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MTA says G train shutdown worth it to finally modernize Brooklyn-Queens subway line
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Comment on Linus Torvalds says Linux is not "anti-AI", tells haters to 'fork it' and 'just walk away' in ~tech
skybrian Link ParentI'm skeptical of that sort of rhetoric because online arguments often seem important at the time, and yet we've forgotten them in a week. I think it's largely a way of making our recreational...I'm skeptical of that sort of rhetoric because online arguments often seem important at the time, and yet we've forgotten them in a week. I think it's largely a way of making our recreational typing seem dramatic.
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Comment on How much energy do data centers and artificial intelligence use? in ~enviro
skybrian Link ParentAnother way to frame it is that AI companies have deep pockets and would probably would be quite willing to pay for lots of expensive electricity infrastructure upgrades, for themselves and...Another way to frame it is that AI companies have deep pockets and would probably would be quite willing to pay for lots of expensive electricity infrastructure upgrades, for themselves and everyone else, if deals can be negotiated. That's an opportunity for the communities where data centers are built. It seems better to somehow get big tech to pay for things to fund everything off residential rate payers or taxpayers?
Also, if the resources being consumed are mostly sunlight and wind, it's not so bad to use more. That could probably be negotiated too if communities are smart about it.
Also, though they don't create that many jobs, data centers should be paying taxes that can fund other things like schools.
It all depends on what kind of deals communities can negotiate for themselves.
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Comment on Why socialists should embrace luxury apartments in ~society
skybrian Link ParentSure, sometimes they or the management company they hire do a bad job in a specific case and deserve criticism. On the other hand, everywhere you look in a city, there are buildings that someone...Sure, sometimes they or the management company they hire do a bad job in a specific case and deserve criticism. On the other hand, everywhere you look in a city, there are buildings that someone needs to maintain. Buildings are expensive and don't build and maintain themselves. Someone has to arrange for the work to be done, and the workers aren't going to do it just because someone asks them nicely. Nor should they! They expect to be paid.
How many people, poor or otherwise, do you provide shelter for? It seems like we shouldn't disparage all the people who are doing that work, as a class, because some of them do it badly? It's like criticizing all doctors or all teachers.
Though, there may be better systems; I'm not going to say public housing can't work when in some places it does seem to work, or so I've read.
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Comment on Why socialists should embrace luxury apartments in ~society
skybrian Link ParentIt's taking something ordinary and spinning it as inherently sinister. We all do things for money and I wouldn't expect anyone to work unpaid. Whether it's good deal or a bad one depends on...It's taking something ordinary and spinning it as inherently sinister. We all do things for money and I wouldn't expect anyone to work unpaid. Whether it's good deal or a bad one depends on circumstances.
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Comment on A skeptical overview of AI and consciousness in ~humanities
skybrian Link ParentMaybe it would happen because it's learning from people or animals somehow? LLM's learn a lot of different ways of writing from what people have written.Maybe it would happen because it's learning from people or animals somehow? LLM's learn a lot of different ways of writing from what people have written.
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Comment on Why socialists should embrace luxury apartments in ~society
skybrian Link ParentYes, houses are for living in, and renting housing to people is providing people with a place to live. They're not sitting vacant, and that's important. And then you spin it as "harvesting money...Yes, houses are for living in, and renting housing to people is providing people with a place to live. They're not sitting vacant, and that's important.
And then you spin it as "harvesting money from the poor." You oughta be ashamed to repeat such nonsense.
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Comment on Why socialists should embrace luxury apartments in ~society
skybrian Link ParentThough it's a bit fragmented, SF has quite a bit of public transit, and I think there's still room for more density along major transit lines? For example, along Geary.Though it's a bit fragmented, SF has quite a bit of public transit, and I think there's still room for more density along major transit lines? For example, along Geary.
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Comment on How much energy do data centers and artificial intelligence use? in ~enviro
skybrian LinkFrom the article: [...] [...] [...] [...] [...] [...]From the article:
We can look at this question on two levels. The first is the total amount of electricity AI uses. The second is about individual impact, or how much electricity each query consumes.
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Non-AI data centers consumed two-thirds of the total, and AI-focused ones, the remaining third. Based on this data from the International Energy Agency, I estimate that AI consumed around 0.5% of the world’s electricity in 2025.4
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Given how quickly demand for AI has been increasing, it might be surprising that AI-focused data centers consume less, on aggregate, than non-AI ones. Projections expect this gap to close quickly. In the chart, I’ve also included the IEA’s base-case projection of data center demand in 2030.
These projections are highly uncertain, and some have argued that the IEA is among the most conservative in its assessment of AI demand growth. Even so, most of the growth in data center demand will come from AI-focused facilities. In this scenario, data centers grow to 3% of global electricity in 2030, and AI centers then use about the same amount as non-AI ones.
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1.5% of the world’s electricity might not seem like much. But in some places, that share is far higher. This is really the key challenge with growing data center demand: it’s geographically concentrated, meaning the world’s demand is served by a small number of electricity grids.
In the chart, you can see the share of electricity used for data centers in different regions. 5% of electricity in the United States is used to power data centers. For AI-focused ones specifically, it’s probably around 2%.
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But in fact, this demand is even more locally concentrated. Beneath Europe’s 1.6% figure, we have Ireland, where data centers account for more than 20% of electricity consumption. Beneath the 5% US figure, there are states where data centers make up more than 10% of demand.6 In states such as Virginia, it’s more than one-quarter.
This, combined with the rapid pace of AI growth, could put pressure on local grids, even if total electricity demand is not overwhelming for the world as a whole.
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For longer queries or requests that rely on AI agents or reasoning, the footprint is higher. Epoch AI estimated that a long query (7,500 words of input) could consume about 2.5 Wh, and a very long one (75,000 words) could consume 40 Wh. Those are far higher than the simple text query.
There are fewer estimates for other types of requests. In its 2026 report, the IEA provides estimates of GPU electricity consumption for agentic tasks with reasoning.7 A standard request to an AI agent — such as Claude — is estimated to consume around 1.1 Wh. An agentic request with reasoning, around 50 Wh. This is similar to the estimates for maximum-length text queries.
However, all of these are still relatively small compared to the average person’s daily electricity consumption, especially in high-income countries.
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While we don’t know how much AI energy demand will grow in the future, the key points we learn from the data today are likely to hold true. For an individual worried about their own use of AI, the energy use of individual chatbot queries is small. For the world as a whole, data centers make up a relatively small share of total electricity consumption, and that won’t change in the coming years. The issue is that supply is so geographically concentrated: whether grids can meet this surge in demand while keeping emissions and local prices under control is the real test.
A final point that’s worth keeping in mind is that the figures we’ve looked at measure electricity consumption, not carbon emissions. For those worried about the climate impacts of data centers and AI, how that electricity is generated arguably matters more than how much it uses. A query served by a data center on a coal-dominated grid will have a much larger impact than one running on a renewables- or nuclear-heavy one. How the growth of AI affects emissions depends not just on its energy efficiency and demand, but also on how clean the grids are that supply it.
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How much energy do data centers and artificial intelligence use?
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Comment on Why socialists should embrace luxury apartments in ~society
skybrian Link ParentThe results would likely vary based on the competence of particular local governments. What if local governments gave it a go and then we’ll see if they can do better?The results would likely vary based on the competence of particular local governments. What if local governments gave it a go and then we’ll see if they can do better?
Apology accepted! I do agree that the rents (and house prices) are too damn high. I suspect a lot of people are quietly getting by with the family helping them out, if they're lucky enough to have someone who can help.
I think the way out, or at least to keep things from getting worse, is more housing, through any means. And, perhaps making it more viable to move to cheaper locations. And UBI would be nice.