Not to mention, it's still very much up in the air whether the model derived the answer of its own accord or sniped the important details from the researchers it was spying on.
>> isn't a counterpoint
Where do we disagree?
> How can I afford?
Mostly not my money, tech makes one fabulously wealthy, I care more about math than fast cars or whatever (even as a pizza driver you can afford a fancy car if that's your primary motive), etc.
> Already solved
That's a very interesting insight into mathematics. It's absolutely just as interesting to prove that certain proof techniques are or aren't possible as it is to actually prove the main result, sometimes moreso, especially if they have any chance of improving attacks at other problems.
To be fair, I think it's still an open question about how far it might surpass human capabilities.
I think it's clear that its speed of development will be significantly faster, but it's technically not proven that the frontier and problems don't themselves become increasingly difficult faster than any acceleration in intelligence past the point of human training, data and existing knowledge.
Should this be the case, we would see a rapid broadening of development, and a slow advance in the frontier in such a way that might surpass the collective capabilities of people, but not by very far.
Proving something in the affirmative often requires the creation of an entire new sub-field of math, or new tools. Think of Fermat's Last Theorem or something like that.
These results, while impressive, are clever constructions using existing techniques. It isn't clear that AIs can build new machinery like this. But if/when they can, yeah it is probably game over.
When you read the detail the compute they are throwing at it is incredible, tens of thousands of agents with different groups competing.
It's not like a single Gauss as you imply, "just" many, many mathematicians working tirelessly in a completely ego-less way, guided by other agents and ultimately humans, built - allegedly - on recent human insights.
Stunning, undoubtedly, but this is a "brilliant autistic herd" result, not that of a singular mind.
I slightly disagree. A single LLM is equally 'mindless' as a herd of them. As anyone will tell you they "simply predict the most likely next token," yet, complex solutions to difficult problems arise from them.
Many people have said that the architecture of LLMs will need to change for true ASI. I think that the herd of tens of thousands of agents can be seen as one such potential architectural extension. Whether or not a herd or a single LLM is used for a result like this is irrelevant.
To be clear, I think the orchestration of thousands of LLMs in their current form, even with ever increasing intelligence, is not the form ASI will take. There is still a major architectural breakthrough to come, in my limited, ignorant opinion.
[Edit: my only point here is that the prize is probably not driving human effort to the limit.]
Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement.
To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah ChatGPT proved X with 5 years of 24/7 work with 10x Terrence Tao level geniuses" it really doesn't cut it.
Or why's there's no new branch of mathematics invented by AI? That'd be indubitably _novel_ and _creative_. But to my knowledge (and I'm eager to be educated) there's nothing like that. What are the HARD examples of novelty, creativity and genius you claim? For how people like you talk about AI I'd expect idk, a unified theory on fundamental physics, or a novel engineering solution for material science and nuclear fusion, or at least improve itself to not need a bazillion GPUs to emulate a 20 watts wetware. Sure it would infinitely easier to make OpenAI literally print money with any of the thousand problems easier to solve with such amazing intelligence than the NSE problem right? Honest question
I think the counterpoint here is simply to look at what was being achieved with LLMs one year ago versus today, and extrapolate that trend. Sure, there may not be examples of what you've asked for yet, but Astra is literally a couple of months old, the model that solved Navier-Stokes is less than two weeks old. It appears that we're seeing the hockey stick that only the most bullish thought was possible.
Also there are proofs where the only human steering was "keep going".
Any result of such kind from an AI alone would be enough to refute my argument, yet you don't present any.
>Also there are proofs where the only human steering was "keep going".
Which ones?
>Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”).2 This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress.
> Drawing on extensive prior research by mathematicians over the past decades, it
> [Claude] has increased this bound [for the fraction of zeros of the Riemann zeta
> function that satisfy the Riemann hypothesis] from 41.6% to 67.2%. Claude also
> produced a formally verifiable proof of its result.