Comment by userbinator
11 hours ago
The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question.
Of course LLMs are still absolutely useless at actual maths computation, but I think this is one area where AI can excel --- the ability to combine many sources of knowledge and synthesise, may sometimes yield very useful results.
Also reminds me of the old saying, "a broken clock is right twice a day."
https://www.ams.org/notices/199701/comm-rota.pdf
I think when thinking about progress as a society, people need to internalize better that we all without exception are on this world for the first time.
We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death and you still only get to consume like 80*365=29200 books in the best case, from the millions upon millions of books that have been written.
So these "few tricks" are the accumulation of a lifetime of mathematical training, the culmination of the slice of knowledge that the respective mathematician immersed themselves into. To discover new math and become famous you need both the talent and skill to apply your knowledge in novel ways, but also be lucky that you picked a field of math that has novel things with interesting applications to discover plus you picked up the right tools and right mental model that allows you to discover these things.
This does not go for math only, but also for pretty much all other non-trivial fields. There is a reason why history repeats.
And it's actually a compelling argument why AI is still a big deal even though it's at its core a parrot. It's a parrot yes, but compared to a human, it actually was able to ingest the entirety of human knowledge.
> it actually was able to ingest the entirety of human knowledge
Even this, though, is not useful, to us.
It remains true that, a life without struggle, and acheivement, is not really worth living...
So, it is nice that there is something that could possibly ingest the whole of human knowledge, but that is still not useful, to us.
People are still making a hullabaloo about "using AI" in companies, and there was some nonsense about there will be only two types of companies, AI ones and defunct ones, but in truth, there will simply be no companies...
Anyways I'm sure I will get down voted by the sightless lemmings on here...
> "a broken clock is right twice a day."
The combinatorial nature of trying things randomly means that it would take millennia or longer for light-speed monkeys typing at a keyboard, or GPUs, to solve such a problem without direction.
By now, people should stop dismissing RL-trained reasoning LLMs as stupid, aimless text predictors or combiners. They wouldn’t say the same thing about high-achieving, but non-creative, college students who can only solve hard conventional problems.
Yes, current LLMs likely still lack some major aspects of intelligence. They probably wouldn’t be able to come up with general relativity on their own with only training data up to 1905.
Neither did the vast majority of physicists back then.
> Yes, current LLMs likely still lack some major aspects of intelligence.
Indeed, and so do current humans! And just like LLMs, humans are bad at keeping this fact in view.
On a more serious note, we're going to have a hard time until we can psychologically decouple the concepts of intelligence and consciousness. Like, an existentially hard time.
Yeah, they're great at interpolation - they'll just never be worth much at extrapolation.
Luckily for us, whole fortunes can be made by filling in the blanks between what we know and what we realize.
That deserves to be on a plaque somewhere.
I've been using LLMs for much the same purpose: solving problems within my field of expertise where the limiting factor is not intelligence per se, but the ability to connect the right dots from among a vast corpus of knowledge that I would never realistically be able to imbibe and remember over the course of a lifetime.
Once the dots are connected, I can verify the solutions and/or extend them in creative ways with comparatively little effort.
It really is incredible what otherwise intractable problems have become solvable as a result.
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And by having more of those blanks filled humans might be able to come up with much better extrapolations than what we have right now.
People keep saying this, but the only ways I know of for formalizing this statement, appear to be probably false?
I don’t know what this claim is supposed to mean.
If it isn’t supposed to have a precise technical meaning, why is it using the word “interpolate”?
> "a broken clock is right twice a day"
and homo sapiens, glancing at the clock when it happens to be right, may conjure an entire zodiac to explain it.
And homo sapiens, glancing at a system that gets better and better at solving problems, tries to deny it and comes up with the broken-clock analogy.
A stopped clock.
A broken clock can be broken in ways which result in it never being correct.
Those are just analog. If it's a broken digital clock, then all bets are off.
Wait, what do you mean "LLMs are still absolutely useless at actual maths computation"? I rely on them constantly for maths (linear algebra, multivariable calc, stat) --- literally thousands of problems run through GPT5 over the last 12 months, and to my recollection zero failures. But maybe you're thinking of something more specific?
They are bad at math. But they are good at writing code and as an optimization some providers have it secretly write code to answer the problem, run it and give you the answer without telling you what it did in the middle part.
Someone should tell the mathematicians if they use a calculator or a whiteboard or heavens forbid a computer they are "bad at math".
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What would I do to demonstrate that they are bad at math? If by "maths" we mean things like working out a double integral for a joint probability problem, or anything simpler than that, GPT5 has been flawless.
Are they bad at math? Or are they bad at arithmetic?
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What tier are you using? I have run lots of problems and am very impressed, but I find stupid errors a lot more frequently than that, e.g., arithmetic errors buried in a derivation or a bad definition, say 1/15 times. I would love to get zero failures out of thousands of (what sounds like college-level math) posed problems.
I have a standard OpenAI/ChatGPT Pro account; GPT5 is my daily driver for math, and Claude for code.
calc, stat etc from a text book is something they would naturally be good at but I don't think book based computations thats in the training set and its extrapolations is what is at question here.
They are not great at playing chess as well - computational as well as analytic.
I think this is wrong and a category error (none of the problems I've given it are in a textbook; they're virtually all randomized), but, try this: just give me a problem to hand off to GPT5, and we'll see how it does.
Further evidence for the faultiness of your claim, if you don't want to take me up on that: I had problems off to GPT5 to check my own answers. None of the dumb mistakes I make or missed opportunities for simplification are in the book, and, again: it's flawless at pointing out those problems, despite being primed with a prompt suggesting I'm pretty sure I have the right answers.
I only have rudimentary understanding of calculus, trigonometry, Google Sheets, and astronomy, but I was able to construct an accurate spreadsheet for astrometry calculations by using Grok and Gemini (both free, no subscription, just my personal account) to surface the formulas for measuring the distance between 2-3 points on the celestial sphere. The LLMs assisted me in also writing functions to convert DMS/HMS coordinates to decimal, and work in radians as well.
I found and fixed bugs I wrote into the formulas and spreadsheets, and the LLMs were not my sole reference, but once the LLM mentioned the names of concepts and functions, I used Wikipedia for the general gist of things, and I appreciated the LLMs' relevant explanations that connected these disciplines together.
I did this on March 14, 2026
>I rely on them constantly for maths (linear algebra, multivariable calc, stat)
That's one way to waste a ton of tuition money to just have a clanker do your learning for you.
Unless you're teaching it, in which case I hope your salary is cut by whatever percentage your clanker reduces your workload.
Perhaps learning how to get AI to solve your problems is the most important lesson to learn now? The rest seems like the current equivalent of learning cursive.
The ultimate generalist
Also just the sheer value of brute force.
80 hours! 80 hours of just trying shit!
It's 80 minutes, not 80 hours.
and you can be sure mathematicians spent way more than 80 hrs on it
80 minutes! 80 minutes of just trying shit!
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How long do you figure it’d take to solve the problem yourself?