Amateur armed with ChatGPT solves an Erdős problem

Post by Forgeties79 » Sun, Apr 26, 2026, 1:33 PM UTC

jackcarter wrote: post #346

bertil wrote: post #336

Earlier quoted context omitted.

> the AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…

It’s funny that this is probably due to bias in the training texts, right? Humans are way more likely to publish their “Eureka!” moments than their screwups… if they did, maybe models would’ve exhibit this behavior. Now that AI labs have all these “Nevermind” texts to train on, maybe it’s getting easier to correct? (Would require some postprocessing to classify the AI outputs as successful or not before training)

Post by epolanski » Sun, Apr 26, 2026, 1:38 PM UTC

bertil wrote: post #336

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 AI says things like “Interesting!” My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often…

Post by ndriscoll » Sun, Apr 26, 2026, 1:42 PM UTC

chvid wrote: post #273

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 am curious if there is a “harness” for maths out there (like the system prompt and tool collection in Claude code but for maths instead of coding)? Asking the llm to structure its response in plan and implementation, allowing it to call tools like python, sage, lean etc.

Post by _ccwi » Sun, Apr 26, 2026, 1:47 PM UTC

rjh29 wrote: post #331

rjh29 wrote: post #181

Earlier quoted context omitted.

You don't need to say "Minor aside" either. Thankfully language is a creative endeavour not a scientific one.

Context: parent originally said "you should not say 'worth mentioning', if it's worth mentioning you can just say it". That sentence has now been edited out so my comment looks weird.

Post by nextaccountic » Sun, Apr 26, 2026, 1:52 PM UTC

virgildotcodes wrote: post #250

nextaccountic wrote: post #194

Earlier quoted context omitted.

So this doesn't happen in the paid plans of ChatGPT? But why?

Paid plans give you access to much larger, more intelligent models which have thinking enabled (inference time compute). In the example here you can see GPT Pro taking 20-80 minutes to respond with the proof. All this is far more expensive to serve so it’s locked away behind paid plans.