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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

#321

Post by Ekaros »

Jtarii wrote: post #227
esjeon wrote: post #202

Earlier quoted context omitted.

Exactly. Much of the intellectual work is, in fact, intellectual labor . It’s mostly about combining various information in one place — the exact task that LLM far outperforms human. People traditionally misclassified this class of work as “creative”. It’s not really.

Having a new insight that leads to the combination of two distinct ideas is definitionally creative. You can say this problem needed a low amount of total creativity, but saying it's void of all creativity seems wrong.

Creative bit is figuring out two or more bits that might work together for something new. Labour part is combining that especially if it is actually laborious.

Which get to other possibility of having list of distinct things and then iterating over all pairs or combinations. Which I probably would not qualify as "creative" work.

Re: Amateur armed with ChatGPT solves an Erdős problem

#322

Post by notahacker »

imiric wrote: post #175
CSMastermind wrote: post #141

Earlier quoted context omitted.

Worth mentioning, though, that people have already tried running all of them through LLMs at this point. So this is proof of the models actually getting stronger (previous generations of LLMs were unable to solve this one).

> So this is proof of the models actually getting stronger (previous generations of LLMs were unable to solve this one). No, it's not. While I don't dispute that new models may perform better at certain tasks, the fact that someone was able to use them to solve a novel problem is not proof of this. LLM output is nondeterministic. Given the same prompt, the same LLM will generate different output, especially when it i…

As others have pointed out, a key part of the prompt used here may have been "don't search the internet" as it would most likely have defaulted to starting off with existing approaches to that problem...

Re: Amateur armed with ChatGPT solves an Erdős problem

#323

Post by lima »

etaKl wrote: post #316

1) How do you know the clanker respects the instruction not to search the internet? 2) Jared Lichtman is indeed a mathematician at Stanford University but involved in the AI startup math.inc, which seems more relevant here. Terence Tao is involved in a partership program with that startup. 3) Liam Price is a general AI booster on Twitter. A lot of AI boosting on Twitter is not organic and who knows what help he got.…

> How do you know the clanker respects the instruction not to search the internet?

You can't, but given that it's a previously unsolved problem, it doesn't seem relevant? (nor are the author's potential biases - the claims are easily verified independently)

Re: Amateur armed with ChatGPT solves an Erdős problem

#324

Post by adQ28 »

simianwords wrote: post #242
missingdays wrote: post #239

Earlier quoted context omitted.

> ChatGPT equalizes intelligence Citation needed

how can you ask this question with on a post titled "Amateur armed with ChatGPT solves an Erdős problem"???? are you looking for some randomised control trial? omg

We just look at comments from AI boosters and it is self-evident that no intelligence is being equalized.

Re: Amateur armed with ChatGPT solves an Erdős problem

#325

Post by Anon1096 »

gorgoiler wrote: post #216

I asked ChatGPT to draw the outline of an ellipse using Unicode braille. I asked for 30x8 and it absolutely nailed it. A beautiful piece of ascii (er, Unicode) art. But I wanted to mark the origin! So I asked for a 31x7 ellipse instead. It completely flubbed it, and for 31x9 too. When a model gives a really good answer, does that just mean it’s seen the problem before? When it gives a crappy answer, is that not simpl…

I wouldn't ask an LLM to output this directly. For an ellipse ascii I would guess that having it write a python program to generate it and then run it would work much better. Using claude sonnet 4.6 on a free account it seemed to work (sorry in advance if the hacker news formatting is horrendous)

⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀ ⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏ ⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀ ⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀

Re: Amateur armed with ChatGPT solves an Erdős problem

#326

Post by wonger_ »

esjeon wrote: post #202
shybear wrote: post #139

It seems like alot of scientific advancements occurred by someone applying technique X from one field to problem Y in another. I feel like LLMs are much better at making these types of connections than humans because they 1) know about many more theories/approaches than a single human can 2) don't need to worry about looking silly in front of their peers.

Exactly. Much of the intellectual work is, in fact, intellectual labor . It’s mostly about combining various information in one place — the exact task that LLM far outperforms human. People traditionally misclassified this class of work as “creative”. It’s not really.

Yeah, I've been grappling with the definition of creativity too. There's a gamedev talk [0] on creativity that gave me useful perspective. Here's what I wrote elsewhere:

---

i've been thinking about raph's definition of creativity [0]: permuting one set of ideas with another set of ideas

(or trying an idea in new contexts)

this is a systematic process, doable even by machine once enough pattern libraries have been catalogued.

on a small scale, there's sprint.cards [1] or oblique strats [2]. on a large scale, there's llms...

it's freeing to approach creativity as a deliberate practice rather than waiting on some fickle muse. yet it's a bit disappointing to see idea generation so mechanical and dehumanized.

i am comforted by the value of mushy human abilities surrounding the creative process:

mostly 1) taste, the ability to recognize pleasing output,

...

[0] https://www.youtube.com/watch?v=zyVTxGpEO30

[1] https://sprint.cards/

[2] https://stoney.sb.org/eno/oblique.html

Re: Amateur armed with ChatGPT solves an Erdős problem

#327

Post by fragmede »

nandomrumber wrote: post #190
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 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.

Re: Amateur armed with ChatGPT solves an Erdős problem

#328

Post by jdmichal »

notahacker wrote: post #318
urutom wrote: post #265

Earlier quoted context omitted.

What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling…

The actual iteration through various learned approaches to dealing with problems I'd probably find fascinating if I understood the maths! Especially if I knew it well enough to know which approaches were conventional and which weren't. I find the AI pronouncing things "interesting!" less interesting on the basis that even though in this case it crops up in the thinking rather than flattering the user in the chat, it'…

I always assumed the "interesting!" markers were actual markers. A kind of tag for the system to annotate its context.

Re: Amateur armed with ChatGPT solves an Erdős problem

#329

Post by petra »

adamgordonbell wrote: post #3

Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…

I don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???

Re: Amateur armed with ChatGPT solves an Erdős problem

#330

Post by baxtr »

petra wrote: post #329
adamgordonbell wrote: post #3

Here is the chat: don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem. {{problem}} REMEMBER - this unconditional argument may require non-trivial, creative and novel elements. Then "Thought for 80m 17s" https://chatgpt.com/share/69dd1c83-b164…

I don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???

Give it hard enough problems?
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