I don’t really see how torrents solved this problem as so many seeders for any file could simply disappear. Not to mention, the significantly higher bandwidth costs of higher resolution video nowadays.
I’m less familiar with bilibili, but afaik it doesn’t do many of the revenue-sharing programs that YouTube does, so might have trouble attracting the same creators. They also have so far been pretty regional and so I’m not sure if we can use them as a sign of success yet.
Yes, as I mentioned to another commenter, I'm talking about the original formulation because that's what the article talks about. We have more options now, although (as you seem to be suggesting) they do all necessarily model position. They have to—there is no other way to do things like recover the subject in an English sentence without positional information.
I don't think this is how preferred suppliers have typically worked through the supply chain risk considering the US has definitely had preferred suppliers before and has not historically used this against a US company that was not on the list and the power of such a designation extends far past the military into all parts of the government. I'm pretty sure this has more traditionally been relegated to simple requirements or specifications.
I think this was discussed ad nauseum last time so I am wondering if somehow this has changed but the biggest part of the issue last time was the retaliation. You seem to suggest that this was due to the government not wanting restrictions on their actions. I feel this severely downplays how unusual this designation is considering, like Anthropic says, this has not been applied to domestic companies.
Why couldn't excluding Anthropic be done a different mechanism than a supply chain risk. Why wouldn't this be a standard part of an agreement or a request and simply refuse to renew or cancel a contract rather than being designated a supply chain risk. If some third party contractor for an unrelated non military reason wanted to use Claude as part of their process, it seems perfectly allowable.
If this was a remotely standard way of operation, why did a fair amount of corporate America sign briefs concerned with the retaliatory aspect.
Parts of the action seemed wholly retaliatory as well since Pentagon officials certainly used it as a threat. Why can't a US company have views contrary to the policies of the US government? Certainly the US government is free to not do business with them, but this designation affects everybody doing any kind of indirect business with the US government which is a rather long chain. If this becomes a legitimate mechanism, how might we distinguish caring about a secure supply chain and simply wiping out a company that disagreed with a pro war attitude? If a machining shop had a policy against manufacturing weapons at all, could they be blocked from making server racks for Microsoft or perhaps light fixtures for the Department of Labor? There are plenty of areas that are, again, non military? I don't think it's credible to claim that Anthropic will deliberately sabotage operations.
Is it not possible that this would change the risk profile of depending on them. It makes sense to work with people who support you than oppose you for things which are critical.
My point is did everyone know all of those principals and how committed Anthropic was to them from the beginning or did new information come in and now they need to adjust. Just because something is a term in a contract that doesn't mean it's necessarily strongly held belief that will never change.
Who runs the government changes every 2 to 4 years… are you suggesting we completely swap every vendor in the US government to align with whatever political party is in office?
There’s nothing indicating Anthropic was not keeping their end of the contract. If they had, there would have been other recourse.
I think the Navier Stokes problem kind of illustrates what he’s highlighting. I think most people even before AI expected that this would resolve in the negative and that you could get finite time blow up. There wasn’t really ever going to be a situation where the resolution to this question, or really any of the other Millenium Prize problems as far as I know, gives some kind of immediate massive practical feedback.
The hope with many of these problems in math is that in trying to prove that, we get some additional insight into why it blew up that could be applied elsewhere to more general PDEs that cannot be easily controlled.
I think the observation from Tao and many others is that when humans solved these problems, the additional insights into intuition and theory building came for free since humans can give expository on what they found hard or what was their own intuition. This is much more difficult or tedious to extract from an AI model. Even when people did have access to the chain of thought, it wasn’t always very helpful to figure out what was the exact thing that made it all click. This is even more difficult how that the CoT are hidden but I would think the sort of difficulty of extracting the key ideas for a human might be worse now with more advanced models.
There’s a long term aspect to this too where we have historically used these problems as markers for the other parts of mathematics but if AI can solve it all, then suddenly this signal is not very meaningful.
Maybe to bring it closer to home. If an oracle just gave you P \neq NP, then this would be generally uninteresting since this was already expected. There’s a deeper question of why that needs to be answered. However, one would hope that creating such a separation would give us tools that allow us to create lower bounds on a lot more problems we do care about and perhaps some bigger insight onto what makes a problem intrinsically hard or easy. These long term considerations are helpful but are definitely more vague. The remarkable part is that AI is separating the part about proving theorems and the “free” insight you get.
To be quite clear, the solution to the _Navier Stokes problem_ is one in which you get a finite time blow up (i.e. infinite pressure). This is more meant to suggest that Navier Stokes is unphysical in some way which is not necessarily unexpected.
There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can also drive pressure in other ways.
The proof of finite-time singularity may impact both fluid dynamics models (CFD) and AI reasoning models. Under specific conditions, Navier–Stokes equations allow velocity to grow infinitely, causing the continuum fluid assumption to break down. Knowing the exact mathematical breakdown mechanisms helps developers improve adaptive mesh refinement and sub-grid scale models around high-vorticity regions (like vortex stretching and turbulent shear layers). While aerodynamic simulations for vehicles operate far from singularity thresholds, their stability at extreme boundaries could improve?
Proving out the combination of scaling inference-time compute and agent collaboration to solve previously intractable mathematical problems is WOW. By pairing creative candidate generation with automated proof checkers (like Lean) we are leaning into a repeatable framework for AI-driven scientific discovery.
> Knowing the exact mathematical breakdown mechanisms helps developers improve adaptive mesh refinement and sub-grid scale models around high-vorticity regions (like vortex stretching and turbulent shear layers).
This is 100% wrong and reads like copy paste of AI slop.
Any simulation which uses sub-grid scale models is already solving a different PDE than the actual Navier-Stokes considered in the Millenium problem, and that PDE is guaranteed to have different properties. Full stop.
And to claim this is somehow connected to AMR methods is an example of the kind of pseudoscientific statement Wolfgang Pauli would have called "not even wrong".
I'm curious what regulatory pressure there is on EU AI companies that wouldn't apply to many of the US firms. The AI Act and GDPR still apply to the tech giants since they operate in the EU (e.g. Anthropic watermarking). There are labor laws that are definitely more strict but many of the US firms have operating presence in the EU as well. I imagine that being directly in the EU probably does increase regulatory oversight but I'm curious how this would manifest in Mistral in particular.
Regarding local models, Gemma, GPT-OSS, Nemotron, and Inkling (maybe upcoming Muse series as well) all are fairly decent options at a variety of hardware costs.
These laws apply to US companies in a more limited way because if we fine them too much they complain to US government that other countries have laws they have to follow. And then the US government intervenes to protect their money and data/intelligence extraction machinery (big tech companies). Usually with at least partial success.
This is rather weird framing since usually an additional citizenship (especially one in a country like the US) is considered a valuable thing to have for your child. Usually people claiming birthright citizenship are weird are doing it because they also see it as valuable. It’s also woven into the traditions of New World countries.
Regarding your concerns, I don’t see why it is unreasonable to simply renounce citizenship later or just simply double check your travel itinerary during the late stages of a pregnancy. This seems like at best an unfounded concern.
I’m just trying to evaluate whether born-within-the-borders citizenship makes sense by imagining myself in that situation. I don’t really see citizenship in another country as a positive, because I only hold loyalty to one nation. Even if I wanted my kid to be a citizen of some other country… like… if I want to play 3rd base for the New York Yankees, I would expect that any team worth joining would have to let me join. I would never imagine that there’d be loophole that allow me buy a ticket and then sneak into the dugout and take the field. If folks are collecting citizenships like Pokémon cards for specific benefits related to each one, I’d be concerned that they don’t really hold loyalty to any one of them… and thus shouldn’t have citizenship in the US. After all, you’d never be allowed to play on the Yankees and the Red Socks at the same time.
US citizenship is a liability, because it comes with being taxed in every country. About half the financial institutions in the world will refuse to do business with you if you're a US citizen, because they don't want to file taxes with the US for their customers. It also provides a good excuse for the US to extradite you for anything you do that's illegal in the US, such as installing software on your computing device.
I agree that you can "just renounce" although notice that this won't necessarily work (it will for the US assuming you follow the procedure properly)
However being a dual citizen isn't necessarily all upside. Citizenship comes with requirements, particularly in some countries military service is mandatory and so if you're a citizen - even though you are a permanent resident of somewhere else, you must either go do your service or maybe pay a fine depending on the country.
You also get treated differently if things go wrong. Foreigners are entitled in most cases to diplomatic assistance from the representatives of their country. Your country can't necessarily do much for you, but typically you will get that phone call home to let loved ones know what happened, they can find a lawyer who speaks your language (but you'll need to find a way to pay them), if there's some paperwork snafu they might be able to help (often for a fee). It's at least nice, if you're jailed or in hospital after surprise food poisoning or whatever, to hear somebody who speaks your language.
None of this applies to dual citizens. You're "home" from their point of view, so no need to contact your diplomatic representative, maybe you have never been there since the day you were born and can't speak a word of the language but too bad.
> You also get treated differently if things go wrong.
Not treated differently. Treated the same.
You are required by law to enter your country of citizenship using that country's passport (this is true for every country). Not doing so can result in fines or jail time. This is precisely to stop idiots from playing the "foreigner" card to try to, for example get out of paying a speeding ticket or parking fines.
You are spreading false information. I routinely enter my other country with a combination of US passport and national ID card. I haven't renewed my passport for that country in almost 20 years, more than half of which I was living there for.
I’m less familiar with bilibili, but afaik it doesn’t do many of the revenue-sharing programs that YouTube does, so might have trouble attracting the same creators. They also have so far been pretty regional and so I’m not sure if we can use them as a sign of success yet.
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