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Amateur armed with ChatGPT solves an Erdős problem

scientificamerican.com

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Re: Amateur armed with ChatGPT solves an Erdős problem

#121

Post by amazingman »

nopinsight wrote: post #80
userbinator wrote: post #13

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 th…

> "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,…

> 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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#122

Post by javawizard »

SR2Z wrote: post #72
y0eswddl wrote: post #48

Earlier quoted context omitted.

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#123

Post by cuttothechase »

tptacek wrote: post #37
userbinator wrote: post #13

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 th…

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?

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#125

Post by komali2 »

tomlockwood wrote: post #42
gdhkgdhkvff wrote: post #9

Earlier quoted context omitted.

Why do you care about either of those questions?

Because it could be a massive waste of time and money.

Capitalism already is a poor allocator of human effort, resources, and energy, why lock in on this specifically? There's entire professions that are essentially worthless to society that exist only to perpetuate the inherent contradictions of this system, why not focus more on all that wasted human effort? Or the fact that everyone has to do some arbitrary sellable labor in order to justify their existence, rather than something they might truly enjoy or might make the world better?

Re: Amateur armed with ChatGPT solves an Erdős problem

#127

Post by tptacek »

cuttothechase wrote: post #123
tptacek wrote: post #37

Earlier quoted context omitted.

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?

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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#128

Post by chrishare »

resident423 wrote: post #8

I wonder if the rationalizations people come up with for why this isn't real intelligence will be as creative as ChatGPTs solution.

LLMs are definitely intelligent - just not general like humans, and very very jagged (succeedingand failing in head-scratching ways).

Re: Amateur armed with ChatGPT solves an Erdős problem

#129

Post by emp17344 »

tptacek wrote: post #117
0xBA5ED wrote: post #55

Earlier quoted context omitted.

And how about the creative rationalizations about how statistical text generation is actual intelligence? As if there is any intent or motive behind the words that are generated or the ability to learn literally any new thing after it has been trained on human output?

2022 called, wants this argument back. When you're "statistically generating text" to find zero-day vulnerabilities in hard targets, building Linux kernel modules, assembly-optimizing elliptic curve signature algorithms, and solving arbitrary undergraduate math problems instantaneously --- not to mention apparently solving Erdos problems --- the "statistical text" stuff has stopped being a useful description of what'…

But the systems that do that impressive work are no longer just LLMs. Look at the Claude Code leak - it’s a sprawling, redundant maze relying on tools and tests to approximate useful output. The actual LLM is a small portion of the total system. It’s a useful tool, but it’s obviously not truly intelligent - it was hacked together using the near-trillions of dollars AI labs have received for this explicit purpose.

Re: Amateur armed with ChatGPT solves an Erdős problem

#130

Post by ButlerianJihad »

tptacek wrote: post #37
userbinator wrote: post #13

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 th…

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?

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

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