Linux is not a relevant comparison, because the fundamental capabilities of an OS do not grow exponentially with time or investment.
If building full sovereign ownership of the production chain for frontier-level AI were so easy, there wouldn't only be two countries on the entire planet that have that right now. If distillation worked in the way you seem to imagine it does, nearly every country in the world would have a full sovereign frontier AI stack.
The keyword in your sentence is "access". The rest of the world would have cheap access to AI, but no ownership of anything at the frontier. If the US joined the rest of the world, declined to develop frontier AI, and allowed itself to become dependent on cheap Chinese AI, once that dependency was fully realized it would eventually translate into a lack of access to the frontier. That doesn't matter until, suddenly, it becomes the single most important thing to the entire country's future.
China is making a simple bet: that the US will offshore AI in favor of cheap tokens, just like the US previously offshored manufacturing in favor of cheap goods. They're doing this because they know that if they alone possess frontier manufacturing and AI capabilities, then they alone can build the world's most powerful technologies in the future which combine the two (e.g., robotics that will revolutionize all their industries, domestic life, and military far beyond any other country).
You're not seeing it because you're thinking in terms of internal US economics, but this is a question about international economics and geopolitical leverage in the distant future.
The reason to consider the ban is because it might be the only way to preserve a fully autonomous and independent American frontier AI stack and the long-term strategic value of possessing such a stack could vastly outweigh the cost of giving up true free market competition on AI. If giving US startups and other companies access to cheaper Chinese AI means sacrificing the US's ability to own its own frontier AI stack, is that a rational trade, or would it severely and irrecoverably sacrifice the country's technological autonomy and leverage for decades to come in exchange for cheaper tokens for a little bit early on?
If the US not only gives up most of its manufacturing capability to China, but also allows itself to give up its own AI stack and become almost entirely dependent on foreign AI, then it's conceivable the combination of the two sacrifices will deal a permanent deathblow to the country in exchange for what will turn out to have been a couple decades of cheap goods and AI tokens.
Let's suppose it's true that not acting and allowing widespread usage of Chinese open-source AI models would in fact make both OpenAI and Anthropic non-viable as companies. I'm not actually fully convinced of that premise, but let us suppose it as an axiom. That would result in the wipeout and failure of the US's primary AI labs, and the country would become fully dependent on Chinese AI. That kind of hard dependency would have vast ramifications for the future. It could mean China could simply change their mind one day and decide that open-source AI isn't as important as they thought. It could mean that China gains sole control over the intelligence used by tens or hundreds of millions of Americans daily to understand world politics, decide who to vote for, etc. It would mean, in the event of any kind of geopolitical or military conflict, the US could end up being at a severe and unrecoverable disadvantage to China.
I'm not necessarily taking a position on this yet, because candidly I haven't made up my own mind yet. But, if preventing that kind of strategically losing position also happens to protect VCs and eliminate some free market competition, that seems like a relatively low price to pay. Again, this is predicated on the assumption that OpenAI and Anthropic really cannot survive as companies if they have to compete fully on merit with Chinese AI labs.
And this is exactly why I haven't switched. While it may not seem like a big deal, there's no value add for me personally in spending time trying to figure out when I should use a better US model vs. go with a Chinese model.
Perfect -- that's great to see. The proof strategy in Lean appears essentially identical to the natural language strategy (as much as is reasonably possible). I think this settles it!
We're talking past each other for some reason. I'm not "unhappy" with anything. I just pointed out that (1) a result like this requires peer review by a professional human mathematician, which fundamentally bottlenecks progress in a pretty severe way; (2) such review would not be necessary if it were accompanied by a formal Lean artifact; (3) you can have both a formal proof and an informal proof together (one does not rule out the other); (4) searching for proofs formally first, then translating successful auto-verified proofs into natural language, is the most scalable approach in the near future for AI mathematics; (5) AI conjecturers would likely benefit from the results of (4) for making large leaps and connections, which can then scale into formal proofs for verification, which then feed back into the same loop ...; (6) humans guide this process through taste, judgment, and their own intuition, likely often intervening to ensure that the loop is aligned and producing a body of conceptual informal mathematics that is valuable to humanity.
You are assuming that the latter, once autonomously discovered and verified at scale, could not simply be translated into the former, also perhaps autonomously at scale (or otherwise selectively as determined by human interest, taste, and relevance).
I disagree. It's the only way to scale AI mathematics far beyond human mathematics. Any interesting verified result would, obviously, be rewritten back into natural language for human understanding and consumption (as well as potentially for the benefit of AI conjecturers too). You are falsely assuming that advances in formal mathematics would not feed back into similar (potentially massive) advances into informal mathematics, and I think that's simply wrong. We're just at the very, very beginning of that curve.
I think this is, in fact, inevitable. It's the exact same RL loop that allowed AlphaGo to vastly exceed the world's top human players. You can theoretically RL formal proof techniques vastly beyond human capability by removing the need for any human review for correctness. It is completely reasonable to assume that "informalization" will become a real sub-field of mathematics in the near future.
Nah, if it produced the proof in Lean which is automatically verified to be correct, you could then just write a natural language version of the proof to accompany it (often using AI to do that part too). That's becoming the standard for AI math these days. Generating purely informal natural language proofs via AI is fundamentally bottlenecked by requiring rare professional mathematician review on every single candidate output proof.
Formal methods post-AI are completely different than formal methods pre-AI. There are multiple companies (Axiom, Harmonic, Logical Intelligence, etc.) developing neural theorem provers that do exactly what the commenter above mentioned, and it works.
> At no point did anyone think to explain that we were measuring the areas under curves, or their rates of change
That's odd. Odd enough that I'm not sure I even believe you. It might be more likely that you weren't interested at that time and didn't really digest what you were being taught. I don't think I've ever heard of high school students being taught calculus with zero mention of areas under curves or rates of change.
Since this isn't in Lean and it's extremely easy for something like this to contain a subtle mistake, I think I'd prefer this be announced by a professional mathematician. The proof appears relatively short and elementary (not to be confused with easy -- just not using any advanced or modern machinery) so it shouldn't take long for the mathematics community to do a peer review. Without that, you could easily crank out hundreds or thousands of PDFs like this that all look plausible and are beyond the ability of a gifted amateur to review.
You were certainly not switching back-and-forth between Fable (a model available to the public generally only since July 1) and Codex for the last several months.
Hard-to-predict memory performance over time is enough of a reason to never seriously use Haskell in production. These days, if you really like the type system, just use Rust: most of the type system benefits, vastly easier to predict its performance and memory usage. Space leaks in Haskell are no joke.
That said, I'm convinced that language choice is pretty much irrelevant, outside of avoiding particularly horrible languages for production, of which Haskell is one of the biggest examples.
This is not what I was expecting, and there's no way this design lasts very long.
It needs to just have one mode that can do anything. That's it. The only choice to make, really, is whether agentic tasks run locally on your machine or in a VM on a shared cloud.
Codex has arguably been better than Claude Code for months now, but it's flown under the radar because it just didn't capture the same viral marketing effect and OpenAI in general has had more optics / PR issues than Anthropic amongst the online developer crowd. I use the word "better" not in the sense that the underlying GPT models are fundamentally smarter or more intelligent, but rather that as a product Codex is just simpler, cheaper, and abundantly reliable and low-drama.
There's a lot of really important software out there where being able to easily verify effect-free core logic would certainly be very useful. An e-commerce web app is not a good example. Anything safety-critical -- aerospace, defense, medical devices, power generation, industrial machines -- already requires a certification process. Auto-generating proof evidence as part of the cert process (which generally requires a rigorous spec anyway) in the near future seems like a no brainer.
If building full sovereign ownership of the production chain for frontier-level AI were so easy, there wouldn't only be two countries on the entire planet that have that right now. If distillation worked in the way you seem to imagine it does, nearly every country in the world would have a full sovereign frontier AI stack.