"Can be used as a weapon" applies to nearly everything, and ceases to have any meaning. Even on a tank, they aren't considered a weapon, only the whole take together is the weapon, or the cannon alone.
isn't blitzscaling essentially the same thing, except for when American companies do it (not always within their own country, e.g. spotify, netflix, or amazon)
the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture, looking under the hood is often a field of horrors.
I won't take a side in things, but OpenAI stated the model they used here started training August 28th. Note that "training" here might mean "post-training with RLHF an Astra base model" or something. but training had only started a little over a week earlier.
worth mentioning there's some indication the 240k peak was massively inflated by bot accounts. but by all means there are many fewer bot accounts this year, and it's still ~150k concurrents frequently. so it's still doing very well, but the numbers are a little different.
they're using a new model trained since the prompts happened. They are not denying the other group's solution may have been in their model weights, despite it being unreleased.
it's very possible they only had to use the massive compute budget because they were trying to plagiarize his work before he published it though, e.g. autonomously do things in ~7 days what he had likely been thinking about for ~1 year.
Of course you do if you're a) only given a partial solution b) racing against someone else using a competing AI.
The open question was whether their LLM got the nudge in the right direction because it got access to the chat somehow (e.g. automated training that scraped his chat logs) or just a high level "Navier stokes can be solved through LLM". It sounds like the former may have happened although right now we just have an accusation and a weak denial.
wasn't it reported elsewhere that they used the equivalent of $22M (street) in Astra tokens? obviously it's not the same when you own the machinery but still.
I guess I don't understand the issue you're raising. If you want to formalize a non-constructive proof, it remains non-constructive, even if you have a computer check the proof vs a human.
As a trivial example, in lean you can work with probability theory/measure theory. This has oodles of non-constructive parts, but we can ignore that for now. As part of this, you can use the probabilistic method. For example, if you want to prove that codes with optimal parameters exist, for many noise models it is known that sampling a code randomly from an appropriate (and often naive) distribution will yield a code with optimal parameters.
You should be able to prove this in lean (or any other theorem prover). But you cannot construct these codes. While you can sample a code randomly, verifying a code has good parameters is typically NP-hard (e.g. it is an instance of the minimum distance problem). So, you cannot (efficiently) "construct" a good code in lean4, despite being able to prove one exists.
This seems analogous to me that you could validate that a non-constructive proof is correct in lean4. Sure, it would be nice if the proof was constructive. But it isn't, and encoding it into a computer shouldn't give you that (non-trivial) property for free.
this isn't really true anymore. First, a number of the big results are constructions, not counterexamples. For example the existence of a non-sofic group. It was widely believed that non-sofic groups existed (so it wasn't a "counterexample" to a widely believed conjecture), but no constructions were known.
There are other examples though. For example, NP hardness of n^{1/400}-approx CVP. Like any NP hardness proof, this shows you can faithfully encode a hard problem (3SAT here iirc) in terms of another candidate hard problem. Not really a counterexample at all.
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