Epoch confirms GPT5.4 Pro solved a frontier math open problem • Hacker News Board

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#641

Post by int_19h » Wed, Mar 25, 2026, 2:43 AM UTC

suddenlybananas wrote: post #506

famouswaffles wrote: post #485

Earlier quoted context omitted.

Yeah. What else would it be ? A brain capable of doing that was clearly the result of evolutionary pressures.

But there is no evolutionary pressure for the Poincaré conjecture, we were never optimized for that in particular, unlike these kinds of LLMs.

We were optimized to rapidly adapt to changing environments by solving the problems that arise through tool-making and cooperation in complex multi-stage tasks (like say hunting that mammoth to make clothing out of it). It turns out that the cheapest evolutionary pathway to get there has some interesting emergent phenomena.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#642

Post by int_19h » Wed, Mar 25, 2026, 2:45 AM UTC

gf000 wrote: post #507

virgildotcodes wrote: post #453

Earlier quoted context omitted.

We have a tremendous amount of raw information flowing through our brains 24/7 from before we are born, from the external world through all our senses and from within our minds as it attempts to make sense of that information, make predictions, generally reason about our existence, hallucinate alternative realities, etc. etc. If you were able to somehow capture all that information in full detail as you've had access…

Humans are "multi-modal". Sure we get plenty of non-textual information, but LLMs were trained on basically every human-written world ever. They definitely see many orders of magnitude more language than any human has ever seen. And yet humans get fluent based after 3+ years.

If you treat the human brain as a model, and account for the full complexity of neurons (one neuron != one parameter!) it has several orders of magnitude more parameters than any LLM we've made to date, so it shouldn't come as a surprise.

What is surprising is that our brain, as complex as it is, can train so fast on such a meager energy budget.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#643

Post by eru » Wed, Mar 25, 2026, 2:49 AM UTC

hnfong wrote: post #635

eru wrote: post #599

Earlier quoted context omitted.

That's a bit too pessimistic. Often times you can productively find some measurable proxy for the thing you care about but can't measure. Turing's test is a famous example, of that. Sometimes you only have a one-sided proxy. Eg I can't tell you whether Claude has a soul, but I'm fairly sure my dishwasher ain't.

> Turing's test is a famous example Ironically, the Turing test is the OG functionalist approach. The GP's comment basically sums up with the Turing test was designed for.

Yes, but I interpret Turing's paper not as saying "souls don't matter", but as "here's a good proxy that we can actually measure".

(I don't know what Turing's opinion on souls is, and it doesn't matter for that paper!)

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#644

Post by int_19h » Wed, Mar 25, 2026, 2:49 AM UTC

slopinthebag wrote: post #91

virgildotcodes wrote: post #69

Earlier quoted context omitted.

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 intere…

I doubt you can even define intelligence sufficiently to argue this point. Since that's an ongoing debate without a resolution thus far. But you claimed that humans aren't unique. I think it's pretty obvious we are on many dimensions including what you might classify as "intelligence". You don't even necessarily have to believe in a "soul" or something like that, although many people do. The capabilities of a human f…

It's very telling that you put "materialist" and "anti-human" in the same bucket.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#645

Post by int_19h » Wed, Mar 25, 2026, 2:54 AM UTC

slopinthebag wrote: post #162

famouswaffles wrote: post #151

Earlier quoted context omitted.

>The capabilities of a human far surpass every single AI to date What does this mean ? Are you saying every human could have achieved this result ? Or this ? https://openai.com/index/new-result-theoretical-physics/ because well, you'd be wrong. >, and much more efficiently as well. That we are able to brute-force a simulacrum of intelligence in a few narrow domains is incredible, but we should not denigrate humans wh…

> The capabilities of a human far surpass every single AI to date Meaning however you (reasonably) define intelligence, if you compare humans to any AI system humans are overwhelmingly more capable. Defining "intelligence" as "solving a math equation" is not a reasonable definition of intelligence. Or else we'd be talking about how my calculator is intelligent. Of course computers can compute faster than we can, that…

> But my point is that LLM's essentially arrive at answers by brute force through search.

If "brute force" worked for this, we wouldn't have needed LLMs; a bunch of nested for-loops can brute force anything.

The reason why LLMs are clearly "magic" in ways similar to our own intelligence (which we very much don't understand either) is precisely because it can actually arrive at an answer without brute force, which is computationally prohibitive for most non-trivial problems anyway. Even if the LLM takes several hours spinning in a reasoning loop, those millions tokens still represent a minuscule part of the total possible solution space.

And yes, we're obviously more efficient and smarter. The smarter part should come as no surprise given that our brains have vastly more "parameters". The efficient part is definitely remarkable, but completely orthogonal to the question of whether the phenomenon exhibited is fundamentally the same or not.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#646

Post by bananamogul » Wed, Mar 25, 2026, 2:55 AM UTC

energy123 wrote: post #456

qnleigh wrote: post #288

I am kind of amazed at how many commenters respond to this result by confidently asserting that LLMs will never generate 'truly novel' ideas or problem solutions. > AI is a remixer; it remixes all known ideas together. It won't come up with new ideas > it's not because the model is figuring out something new > LLMs will NEVER be able to do that, because it doesn't exist It's not enough to say 'it will never be able t…

> 67,383 * 426,397 = 71,371,609,051 ... You need to say why it can do some novel tasks but could never do others. Model interpretability gives us the answers. The reason LLMs can (almost) do new multiplication tasks is because it saw many multiplication problems in its training data, and it was cheaper to learn the compressed/abstract multiplication strategies and encode them as circuits in the network, rather than m…

Why are we reducing AIs to LLMs?

Claude, OpenAI, etc.'s AIs are not just LLMs. If you ask it to multiply something, it's going to call a math library. Go feed it a thousand arithmetic problems and it'll get them 100% right.

The major AIs are a lot more than just LLMs. They have access to all sorts of systems they can call on. They can write code and execute it to get answers. Etc.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#647

Post by bananamogul » Wed, Mar 25, 2026, 2:59 AM UTC

veltas wrote: post #350

qnleigh wrote: post #288

I am kind of amazed at how many commenters respond to this result by confidently asserting that LLMs will never generate 'truly novel' ideas or problem solutions. > AI is a remixer; it remixes all known ideas together. It won't come up with new ideas > it's not because the model is figuring out something new > LLMs will NEVER be able to do that, because it doesn't exist It's not enough to say 'it will never be able t…

Do we know for a fact that LLMs aren't now configured to pass simple arithmetic like this in a simpler calculator, to add illusion of actual insight?

The major AIs have access to all sorts of tools, including a math library. I thought this was well-known. There's no "illusion of actual insight" - they're just "using a calculator" (in the sense that they call a math library when needed). AIs are not just LLMs.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#648

Post by int_19h » Wed, Mar 25, 2026, 3:01 AM UTC

razorbeamz wrote: post #301

gf000 wrote: post #247

Earlier quoted context omitted.

So you don't think 50T parameter neural networks can encode the logic for adding two n-bit integers for reasonably sized integers? That would be pretty sad.

They do not. The fundamental technology behind LLMs does not allow that to be the case. You are hoping that an LLM can do something that it cannot do.

You do realize that training a neural net to do addition is a beginner level exercise in ML?

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#649

Post by int_19h » Wed, Mar 25, 2026, 3:06 AM UTC

aurizon wrote: post #615

This is a lot like the 50 million monkeys on 50 million typewriters will eventually write shakespeare... We have all heard this, pity the poor proof readers who will proof them all in a search for the holy grail = zero errors. In a similar way, LLM's are permutational cross associating engines, matched with sieves to filter out the dross. Less filtering = more dross, AKA slop. It can certainly create enormous masses…

> This is a lot like the 50 million monkeys on 50 million typewriters will eventually write shakespeare...

"Eventually" here is something on the order of a few expected lifespans of the universe.

The fact that we're getting meaningful results out of LLMs on a human timescale means that they're doing something very different.

Re: Epoch confirms GPT5.4 Pro solved a frontier math open problem

#650

Post by scoofy » Wed, Mar 25, 2026, 3:10 AM UTC

hnfong wrote: post #631

scoofy wrote: post #600

Earlier quoted context omitted.

I studied philosophy focusing on the analytic school and proto-computer science. LLMs are going to force many people start getting a better understanding about what "Knowledge" and "Truth" are, especially the distinction between deductive and inductive knowledge. Math is a perfect field for machine learning to thrive because theoretically, all the information ever needed is tied up in the axioms. In the empirical wor…

> distinction between deductive and inductive knowledge There's also intuitive knowledge btw. Anyway, the recent developments of AI make a lot of very interesting things practically possible. For example, our society is going to want a way to reliably tell whether something is AI generated, and a failure to do so pretty much settles the empirical part of the Turing test issue. Or alternatively if we actually find som…

I don't want to do the thing where we fight on the internet. I don't know your background, but I'll push back here just because this type of comment that non-philosophers seem to present to me, which misses a lot of the points I'm trying to make.

(1) "intuitive knowledge" - whether or not you want to take "intuitive knowledge" as a type of knowledge (I don't think I would) is basically immaterial. The deductive-inductive framework dynamic is for reasoning frameworks, not knowledge. The reasoning frameworks are pointed in opposite directions. The deductive framework is inherited from rationalist tradition, it's premises are by definition arbitrary and cannot be justified, and information is perfect (excepting when you get rare truth values, like something being undecidable). Inductive/empirical framework is quite the opposite. Its premises are observations and absolutely not arbitrary, the information is wholly imperfect (by necessity, thanks Popper), and there is always a kind of adjustable resolution to any research conducted. Newton vs Einsteinian physics, for example, shows how zooming in on the resolution of experimentation shows how a perfectly workable model can fail when instruments get precise enough. I'll also note here that abduction is another niche reasoning framework, but is effectively immaterial to my point here.

(2) The Turing Test is not, and has never been, a philosophically rigorous test. It's effectively a pointless exercise. The literature about "philosophical zombies" has covered this, but the most important work here is Searle's "Chinese Room."

>The fact that AI seems to be able to (digitally) do anything we ask for is also very interesting.

I don't even know how to respond to this. It's trivially, demonstrably false. Beyond that, my entire point is that philosophy of language actually presents so hard problems with regards to what meaning actually is that might end up creating a kind of uncertainty principle to this line of thinking in the long run. Specifically Quine's indeterminacy of translation.