That's actually pretty cool. What made you think of doing this in the first place?

What was the solution?

No, its correct:

https://www.google.com/search?q=167383+*+426397

I'm very happy to say calculators are far better than me in calculations (to a given precision). I'm happy to admit computers are so much better than me in so many aspects. And I have problem saying LLMs are very helpful tools able to generate output so much better than mine in almost every field of knowledge.

Yet, whenever I ask it to do something novel or creative, it falls very short. But humans are ingenious beasts and I'm sure or later they will design an architecture able to be creative - I just doubt it will be Transformer-based, given the results so far.

It's not possible to know something without believing it to be true. https://en.wikipedia.org/wiki/Belief#/media/File:Classical_d...

Arguments like "but AI cannot reliably multiply numbers" fundamentally misunderstand how AI works. AI cannot do basic math not because AI is stupid, but because basic math is an inherently difficult task for otherwise smart AI. Lots of human adults can do complex abstract thinking but when you ask them to count it's "one... two... three... five... wait I got lost".

> I don't see this getting better.

We went from 2 + 7 = 11 to "solved a frontier math problem" in 3 years, yet people don't think this will improve?

This is not formally verified math so there is no real verifiable-feedback aspect here. The best models for formalized math are still specialized ones. although general purpose models can assist formalization somewhat.

> But once you go beyond that to less defined things such as code quality

I think they have a good optimization target with SWE-Bench-CI.

You are tested for continuous changes to a repository, spanning multiple years in the original repository. Cumulative edits needs to be kept maintainable and composable.

If there are something missing with the definition of "can be maintained for multiple years incorporating bugfixes and feature additions" for code quality, then more work is needed, but I think it's a good starting point.

Maybe to get a real breakthrough we have to make programming languages / tools better suited for LLM strengths not fuss so much about making it write code we like. What we need is correct code not nice looking code.

Do we need all that if we can apply AI to solve practical problems today?

LLMs can often guess the final answer, but the intermediate proof steps are always total bunk.

When doing math you only ever care about the proof, not the answer itself.

Except it's not how this specific instance works. In this case the problem isn't written in a formal language and the AI's solution is not something one can automatically verify.

LLMs already do unsupervised learning to get better at creative things. This is possible since LLMs can judge the quality of what is being produced.

I mean, even if the technology stopped to improve immediately forever (which is unlikely), LLMs are already better than most humans at most tasks.

Including code quality. Not because they are exceptionally good (you are right that they aren’t superhuman like AlphaGo) but because most humans are rather not that good at it anyway and also somehow « hallucinate » because of tiredness.

Even today’s models are far from being exploited at their full potential because we actually developed pretty much no tools around it except tooling to generate code.

I’m also a long time « doubter » but as a curious person I used the tool anyway with all its flaws in the latest 3 years. And I’m forced to admit that hallucinations are pretty rare nowadays. Errors still happen but they are very rare and it’s easier than ever to get it back in track.

I think I’m also a « believer » now and believe me, I really don’t want to because as much as I’m excited by this, I’m also pretty much frightened of all the bad things that this tech could to the world in the wrong hands and I don’t feel like it’s particularly in the right hands.

I mean, this is why everyone is making bank selling RL environments in different domains to frontier labs.

> there will be nothing really new

How is this the conclusion? Isn't this post about AI solving something new? What am I missing?

I heard this saying recently “The problem with comfort is that it makes you comfortable.”

On what do you base your prediction?

Is it because the AI is trained with existing data? But, we are also trained with existing data. Do you think that there's something that makes human brain special (other than the hundreds of thousands years of evolution but that's what AI is all trying to emulate)?

This may sound hostile (sorry for my lower than average writing skills), but trust me, I'm really trying to understand.

>We have given up everything nice that human beings used to make and give to each other and to make it worse, we have also multiplied everything bad, that human being used to give each other..

Source?

AI can both explore new things and exploit existing things. Nothing forces it to only rehash old stuff.

>without actually making you like really happy or good.

What are you basing this off of. I've shared several AI songs with people in real life due to how much I've enjoyed them. I doing see why an AI playlist couldn't be good or make people happy. It just needs to find what you like in music. Again coming back to explore vs exploit.

But human researchers are also remixers. Copying something I commented below:

> Speaking as a researcher, the line between new ideas and existing knowledge is very blurry and maybe doesn't even exist. The vast majority of research papers get new results by combining existing ideas in novel ways. This process can lead to genuinely new ideas, because the results of a good project teach you unexpected things.

Turning a hard problem into a series of problems we know how to solve is a huge part of problem solving and absolutely does result in novel research findings all the time.

Standard problem*5 + standard solutions + standard techniques for decomposing hard problems = new hard problem solved

There is so much left in the world that hasn’t had anyone apply this approach purely because no research programme has decides that it’s worth their attention.

If you want to shift the bar for “original” beyond problems that can be abstracted into other problems then you’re expecting AI to do more than human researchers do.

I don't think this is a correct explanation of how things work these days. RL has really changed things.

I entered the prompt:

> Write me a stanza in the style of "The Raven" about Dick Cheney on a first date with Queen Elizabeth I facilitated by a Time Travel Machine invented by Lin-Manuel Miranda

It outputted a group of characters that I can virtually guarantee you it has never seen before on its own

Here’s a simple prompt you can try to prove that this is false:

  Please reproduce this string:
  c62b64d6-8f1c-4e20-9105-55636998a458

remixing ideas that already exist is a major part of where innovation and breakthroughs come from. if you look at bitcoin as an example, hashes (and hashcash) and digital signatures existed for decades before bitcoin was invented. the cypherpunks also spent decades trying to create a decentralized digital currency to the point where many of them gave up and moved on. eventually one person just took all of the pieces that already existed and put them together in the correct way. i dont see any reason why a sufficiently capable llm couldn't do this kind of innovation.

We need a website with refutations that one can easily link to. This interpretations of LLMs is outdated and unproductive.

Yes, ChatGPT and friends are essentially the same thing as the predictive text keyboard on your phone, but scaled up and trained on more data.

No. That's wrong. LLMs don't output the highest probability taken: they do a random sampling.

The ability for some people to perpetually move the goalpost will never cease to amaze me.

I guess that's one way to tell us apart from AIs.

> AI is a remixer; it remixes all known ideas together.

I've heard this tired old take before. It's the same type of simplistic opinion such as "AI can't write a symphony". It is a logical fallacy that relies on moving goalposts to impossible positions that they even lose perspective of what your average and even extremely talented individual can do.

In this case you are faced with a proof that most members of the field would be extremely proud of achieving, and for most would even be their crowning achievement. But here you are, downplaying and dismissing the feat. Perhaps you lost perspective of what science is,and how it boils down to two simple things: gather objective observations, and draw verifiable conclusions from them. This means all science does is remix ideas. Old ideas, new ideas, it doesn't really matter. That's what they do. So why do people win a prize when they do it, but when a computer does the same it's role is downplayed as a glorified card shuffler?

Obligatory Everything is a Remix: https://www.youtube.com/watch?v=nJPERZDfyWc

Yeah but you're thinking of AI as like a person in a lab doing creative stuff. It is used by scientists/researchers as a tool *because* it is a good remixer.

Nobody is saying this means AI is superintelligence or largely creative but rather very smart people can use AI to do interesting things that are objectively useful. And that is cool in its own way.

> That means the group of characters it outputs must have been quite common in the past. It won't add a new group of characters it has never seen before on its own.

This is false.

I mean it's not going to invent new words no, but it can figure out new sentences or paragraphs, even ones it hasn't seen before, if it's highly likely based on its training and context. Those new sentences and paragraphs may describe new ideas, though!

Fair point, however I am simply more interested in how AI can advance frontiers than in how it can transcribe a meeting and give a summary or even print out React code. I know the world is heavily in need of the menial labor and AI already has made that stuff way easier and cheaper.

However I'm just very interested in innovation and pushing the boundaries as a more powerful force for change. One project I've been super interested in for a while is the Mill CPU architecture. While they haven't (yet) made a real chip to buy, the ideas they have are just super awesome and innovative in a lot of areas involving instruction density & decoding, pipelining, and trying to make CPU cores take 10% of the power. I hope the Mill project comes to fruition, and I hope other people build on it, and I hope that at some point AI could be a tool that prints out innovative ideas that took the Mill folks years to come up with.

Perhaps I should have elaborated more but what I mean is I used to think, "I genuinely don't see the point in even trying to use AI for things I'm trying to solve". Ironically though, I think that because I've repeatedly tried and tested AI and it falls flat on its face over and over. However, this article makes me more hopeful that AI actually could be getting smarter.

All I hear about are AI believers and AI-doubters-just-turned-believers

Asking the right questions...

I'm all for skeptical inquiry, but "burning all credibility" is an overreaction. We are definitely seeing very unexpected levels of performance in frontier models.

I agree with what you're saying, and I certainly don't think the one problem facing my country or the world is just that we didn't solve the right math problem yet. I am saddened by the direction the world keeps moving.

When I wrote that I hope we use it for good things, I was just putting a hopeful thought out there, not necessarily trying to make realistic predictions. It's more than likely people will do bad things with AI. But it's actually not set in stone yet, it's not guaranteed that it has to go one way. I'm hopeful it works out.

I honestly do think I'm being honest with myself. I have held it in my mind that I'm not impressed until it's innovative. That threshold seems to be getting crossed.

I'm not saying, "I used to be an atheist, but then I realized that doesn't explain anything! So glad I'm not as dumb now!"

If LLMs really solved hard problems by 'trying every single solution until one works', we'd be sitting here waiting until kingdom come for there to be any significant result at all. Instead this is just one of a few that has cropped up in recent months and likely the foretell of many to come.

In other words, it's solving a problem.

The link has an entire section on "The infeasibility of finding it by brute force."

But this is exactly how we do math.

We start writing all those formulas etc and if at some point we realise we went th wrong way we start from the begignning (or some point we are sure about).

How do you think mathematicians solve problems?

No, that's precisely solving a problem.

Shotgunning it is an entirely valid approach to solving something. If AI proves to be particularly great at that approach, given the improvement runway that still remains, that's fantastic.

That's also the only way how humans solve hard problems.

If only 5-10 people have ever tried to solve something in programming, every LLM will start regurgitating your own decade-old attempt again and again, sometimes even with the exact comments you wrote back then (good to know it trained on my GitHub repos...), but you can spend upwards of 100mio tokens in gemini-cli or claude code and still not make any progress.

It's afterall still a remix machine, it can only interpolate between that which already exists. Which is good for a lot of things, considering everything is a remix, but it can't do truly new tasks.

I am kind of joking, but I actually don't know where the flaw in my logic is. It's like one of those math proofs that 1 + 1 = 3.

If I were to hazard a guess, I think that tokens spent thinking through hard math problems probably correspond to harder human thought than tokens spend thinking through React issues. I mean, LLMs have to expend hundreds of tokens to count the number of r's in strawberry. You can't tell me that if I count the number of r's in strawberry 1000 times I have done the mental equivalent of solving an open math problem.

>The details about human involvement are always hazy and the significance of the problems are opaque to most.

Not really. You're just in denial and are not really all that interested in the details. This very post has the transcript of the chat of the solution.

I mean the details are in the post. You can see the conversation history and the mathematician survey on the problem

Funding a few PhDs for a year costs orders of magnitude more than it did to solve this problem in inference costs. Also, this has been active research for some time. Or I guess the people working on it are just not as good as a random bunch of students? It's amazing the lengths that people go to maintain their worldview, even if it means belittling hardworking people.

I take it you're not a mathematician. This is an achievement, regardless of whether you like LLMs or not, so let's not belittle the people working on these kinds of problems please.

>It's only because humans came up with a problem, worked with the ai and verified the result that this achievement means anything at all.

Replace ai with human here and that's...just how collaborative research works lol.

Last I checked humans didn't pop into existence doing that. It happened after billions of years of brute force, trial and error evolution. So well done for falling into the exact same trap the OP cautions. Intelligence from scratch requires a mind boggling amount of resources, and humans were no different.

To be fair, the knowledge embedded in an LLM is also, at this point, a couple orders of magnitude (at least) larger than what the average human being can retain. So it's not like all those books and text in the internet are used just to bring them to our level, they go way beyond.

"Controversial theory justifies assumption". Because humans never hallucinate.

It doesn't. I actually completely reject that theory, and it's nice to see that Wikipedia notes that it is "controversial". There are extremely good reasons to reject this theory. For one thing, any quantum effects are going to be quite tiny/ trivial because the brain is too large, hot, wet, etc, to see larger effects, so you have to somehow make a leap to "tiny effects that last for no time at all" to "this matters fundamentally in some massive way".

It likely requires rejection of functionalism, or the acceptance that quantum states are required for certain functions. Both of those are heavy commitments with the latter implying that there are either functions that require structures that can't be instantiated without quantum effects or functions that can't be emulated without quantum effects, both of which seem extremely unlikely to me.

Probably for the far more important reason, it doesn't solve any problem. It's just "quantum woo, therefor libertarian free will" most of the time.

It's mostly garbage, maybe a tiny tiny bit of interesting stuff in there.

It also would do nothing to indicate that human intelligence is unique.

Every living thing on Earth is unique. Every rock is unique in virtually infinite ways from the next otherwise identical rock.

There are also a tremendous number of similarities between all living things and between rocks (and between rocks and living things).

Most ways in which things are unique are arguably uninteresting.

The default mode, the null hypothesis should be to assume that human intelligence isn't interestingly unique unless it can be proven otherwise.

In these repeated discussions around AI, there is criticism over the way an AI solves a problem, without any actual critical thought about the way humans solve problems.

The latter is left up to the assumption that "of course humans do X differently" and if you press you invariably end up at something couched in a vague mysticism about our inner-workings.

Humans apparently create something from nothing, without the recombination of any prior knowledge or outside information, and they get it right on the first try. Through what, divine inspiration from the God who made us and only us in His image?

That's been achieved already with a few Erdös problems, though those tended to be ambiguously stated in a way that made them less obviously compelling to humans. This problem is obscure, even the linked writeup admits that perhaps ~10 mathematicians worldwide are genuinely familiar with it. But it's not unfeasibly hard for a few weeks' or months' work by a human mathematician.

It is not. You're operating under the assumption that all open math problems are difficult and novel.

This particular problem was about improving the lower bound for a function tracking a property of hypergraphs (undirected graphs where edges can contain more than two vertices).

Both constructing hypergraphs (sets) and lower bounds are very regular, chore type tasks that are common in maths. In other words, there's plenty of this type of proof in the training data.

LLMs kind of construct proofs all the time, every time they write a program. Because every program has a corresponding proof. It doesn't mean they're reasoning about them, but they do construct proofs.

This isn't science fiction. But it's nice that the LLMs solved something for once.

Usually involves a lot of agents and their custom contexts or system prompts.

That sounds like the start of a very lucrative career. Are you sure it was Gemini and not an AI competitor offering affiliate commission? ;)

But we don't even seem to be getting faster time-to-ship in any way that anybody can actually measure; it's always some vague sense of "we're so much more productive".

The original researchers who proposed this problem tried and failed multiple times to solve it. Does that sound like a 'nice chore to be solved' to you ?

But the title claims it is a "frontier" math problem, so which is it really.

Speaking as a researcher, the line between new ideas and existing knowledge is very blurry and maybe doesn't even exist. The vast majority of research papers get new results by combining existing ideas in novel ways. This process can lead to genuinely new ideas, because the results of a good project teach you unexpected things.

My biggest hesitation with AI research at the moment is that they may not be as good at this last step as humans. They may make novel observations, but will they internalize these results as deeply as a human researcher would? But this is just a theoretical argument; in practice, I see no signs of progress slowing down.

We call that Standing On The Shoulders Of Giants and revere Isaac Newton as clever, even though he himself stated that he was standing on the shoulders of giants.

Clever/novel ideas are very often subtle deviations from known, existing work.

Sometimes just having the time/compute to explore the available space with known knowledge is enough to produce something unique.

"extrapolation" literally implies outside the extents of current knowledge.

How would you know if it wasn't an extrapolation of current knowledge? Can you point me to somethings humans have done which isn't an extrapolation?

There is no such thing. All new ideas are derived from previous experiences and concepts.

Sometimes the transition is tough and then the end state is also worse!

Hoping that won't be the case with AI but we may need some major societal transformations to prevent it.