Isn't it immediately obvious that solving something that humans have been unable to do for decades or more is the most tangible proof of ASI, or at the very least pretty good AGI?
Is this something humans have been unable to do? There’s only so many people with the necessary skills to solve this. And you need these humans to choose to spend their time solving this, and not something else.
>Is this something humans have been unable to do?
It's a famous open problem so yeah
>There’s only so many people with the necessary skills to solve this. And you need these humans to choose to spend their time solving this, and not something else.
Sure, but that doesn't mean a lot of very skilled people hadn't attempted and failed to solve this.
> rejected any notion of utility. It would be fundamentally wrong for you to ask what's the value of solving the Erdős–Hajnal conjecture; the value is that it's solved. I disagree. Mathematicians care about the utility of a result. It is just that they regard mathematical understanding as a valid type of utility, and that can be arbitrarily far removed from practical utility. But a proof that doesn't help anyone unde…
It seems in mathematics that the utility of a problem is directly correlated with how difficult it is to solve, for some odd reason. If I defined some pointless construction and it turned out to be very difficult to prove, it would automatically over time become considered a "high utility" mathematics problem (again, for some odd reason). Mathematics is largely just smart people working on pointless puzzles, and only…
Most fields, in the aggregate, produce a lot of pointless work, but if you judge mathematics by its best examples, as judged by the field itself, and also by the outside intellectual community, it is a coherent body of work (& brilliantly creative). It is not pointless puzzles at all. William Thurston's geometrization theorem, Klein's erlangen program, Witten's work in physics-inspired mathematics, Langlands program, the Grothendieck school of Algebraic Geometry are deep and abiding intellectual achievements of true understanding. If you don't understand the meaning behind this work, it speaks to your ignorance, not to their significance. The "obvious practical problems" are not solved. Fluid Dynamics is wide open. Non-perturbative quantum theories are wide open. Heck, there are open mathematical problems in General Relativity. Dynamical systems are very poorly understood. Go read a book or something.
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
"every novel result is broadly perceived as a big deal" is not at all true. AI companies hype any novel result as proof that AI is good for mathematics, but professional mathematicians write tens of thousands of papers every year, and for 99.99% of them, nobody cares or writes it up. Mathematicians certainly don't go around saying each and every novel proof in their papers are a big deal. Do you have any evidence supporting your statement that it is "broadly perceived" (by whom?) as a big deal?
If all checks out this is a huge milestone. AI has now solved one of the most famous open problems in graph theory, using an off the shelf model, in one hour. It might be a better mathematician than most humans at this point. Kind of like when chess software started beating everyone except grandmasters. What’s left? Proposing and building out entirely new theories and frameworks? Then better than any human? Then alie…
It's hard for me not to think what's the point. I am a very average, even below average person in times of intelligence. What is even my value or reason to be if I know anything I can do, LLMs can do better? What is even my value both on job market and as a human?
There are smarter and better humans at just about everything you or I could want to do, that's just life. Most of life isn't about comparative advantages, it's about enjoying life with people we like.
Assuming all 64 subagents were running for a full hour (the tweet states just under an hour): Throughput Output tokens Output cost ---------------------------- ------------- ----------- 40 tok/s (5.5 low) ~9.2M ~$275 55 tok/s (5.5 base) ~12.7M ~$380 70 tok/s (5.5 high) ~16.1M ~$485 750 tok/s (Sol Fast, $75/M) ~172.8M ~$13,000 Claude estimates that tool use / input tokens might add 10-15% on top of that depending on e…
Sol fast isn't the Cerebras 750 tok/s version, it's just 1.5x speed at 2.5x price I assume they didn't use the Cerebras version for this since it's probably very supply-constrained right now
But Sol is running on Cerebras. That’s the whole point of this. That’s how they get 750 tokens per second. There is no other way.
This is not a remark about AI, but there's something funny about mathematics in that every novel result is broadly perceived as a big deal. We attach basically zero value to writing a new program that hasn't existed before, or a piece of text that hasn't existed before. It's boring, or even a net negative, unless you can show that the result benefits the world in some way. We'd find it weird if OpenAI put out a relea…
> there's something funny about mathematics in that every novel result is broadly perceived as a big deal.
Is this true? Or is it just that mathematics is an isolated enough field that only the results that are a big deal get broadcast widely to the public.
I know little of the inner workings of the field of mathematics, but my naive assumption would be that there's probably lots of novel but boring results being discovered/proven all the time and we don't hear about them because no-one outside of the person doing the work and a handful of their colleagues is really that interested in it. Likely a lot aren't published in any way, because they're just stepping stones towards the goal of the actual area/paper/whatever being worked on.
> a human mathematician would aspire to Some do. But there's also the notion that a clever trick is a bad explanation.
Hmmm... seems to me that if you can find a solution without creating the desired explanation - then that's a problem with the original question - not the solution itself. And discovering a bad question leads to the correct question. No?
> then that's a problem with the original question - not the solution itself
I think there's a good counterexample to this:
Atiyah/MacDonald proove the Nullstellensatz ultimately by using some trick involving determinants.
They give a very nice theoretical treatment of the content and context of the theorem. But the proof at one crucial point uses techniques that live conceptually outside of this context: While its possible to see that the argument is sound, it does not give a good explanation of _why_ it's true within the context of the theorem.
(You could of course argue that they did not give enough context
... but that's exactly my point: the trick makes the proof work but hides the explanation)
To be able to propose interesting conjectures you need to walk the walk of trying to prove things yourself. That's not great for future generations.
It is the same with anything technical; you need taste and wisdom, which are borne of experience. I think society will want to subsidize this learning lest it deskills en masse.
It would be nice, but I don't have much hope as it doesn't help next quarter's profits.
It seems like a solid set of criteria for how easily a task can be automated by AI agents is:
- extent to which correctness of solution be easily specified and checked
- extent to which new potential solutions can be implemented as text
- extent to which prior art exists online
This basically maps to software engineering and math. I think a fair bit of AI hype comes from the fact that the very architects of AI are the people whose jobs are most easily automated by AI. They think, “if my job receives this much of a boost from AI, surely every job will be the same”. Ironically it couldn’t be further from the truth… and likewise the predictions of widespread labor obsolescence