[minimaxir]

> just repeatedly saying "keep going" to ChatGPT

For posterity, this indeed works for most problems where an agent might give up. LLMs don't inherently know something is impossible.

The phrase I tend to use in my harder prompts to automate this with a sane loop breaker:

> **REPEAT THIS PROCESS UNTIL CONVERGENCE AND YOU ARE OUT OF OPTIMIZATION IDEAS.** You have permission to keep iterating.

[Xcelerate]

I’m a bit surprised OpenAI isn’t finding these big results far faster than the product’s user base. With no limits on runtime, access to dev models, custom tuning, and top talent, you’d think there’d be a constantly running internal project with the goal of solving famous math problems. And who knows, perhaps there is, but it would be interesting to compare the rate of success per unit “effort” of the internal mathematics work with that of the user base.

[pdpi]

"OpenAI's internal team solves famous maths problem" is technically impressive but dispiriting. Non-experts solving a problem by just throwing resources at it is kind of the worst possible optics for knowledge workers. It's just disempowering.

"Famous mathematician uses ChatGPT to solve famous math problem" is equally technically impressive, but now you're telling those very same knowledge workers "that famous mathematician could've been you". It puts you in the driver's seat, and provides a clear path forward — subscribe, use our product, and reap the rewards.

[tyre]

I don't think they care if it's disempowering. They'd gain more in market share by indicating that this is God than missing out on a few subscriptions from math theory people.

My guess is they don't do this because they don't have time. They're all trying to build a company that makes them generationally wealthy before the music stops.

[qsera]

Why would they want to do it when the people paying them would do the same for them?

[rlt]

Then they should give grants of tokens to famous mathematicians.

EDIT: oh, they do offer grants of $1000 of API credits to researchers https://help.openai.com/en/articles/10139500-researcher-acce...

[eru]

> Then they should give grants of tokens to famous mathematicians.

Depends. The headline 'some rando solved a famous problem with a consumer grade subscription' might be a really good way to sell these subscriptions.

"Some already famous guy with special access solved a problem" might not be as inspiring.

[wrsh07]

Note, in posts like the following, the author indicates they are able to get free subscriptions from OpenAI

As an aside, there's this idea in math that when you create a new field you shouldn't solve all the easy problems - you need to entice other people to learn about the field!

I expect there's some element of that here. It's much better for OpenAI and Anthropic if their users are the ones discovering and writing up the results of the AI solving hard math. Look at the high school and college age students who have become ai power users and potentially learned how to use git to contribute ai generated solutions

(Related: I believe Terry has also gotten all of the subscriptions gifted to him)

https://xenaproject.wordpress.com/2026/07/20/human-mathemati...

[staticshock]

You're surprised they didn't eat the tokens to churn on lots of open problems instead of asking others to pay for those tokens? They're in the token business. If they're eating the tokens, it's in support of a marketing effort, not in support of innovation across the frontier of all the other academic disciplines. The collective frontier is way too big for them to just "solve it" without asking society to at least help them break even on such an enormous public good.

[wrsh07]

It's also much better to distribute the challenge of identifying problems amenable to which prompts

Could they do it? Sure, but to what end? It would make more people hate them and feel even more "take our interesting work." Pitching it as a useful tool just makes more sense on all levels

[ivewonyoung]

They do have some of those.

https://openai.com/index/model-disproves-discrete-geometry-c...

[gaigalas]

Confirmation bias. There's likely a wide portion of chats in which "keep going" derails to madness. We then stop saying "keep going" because we notice there is something wrong, and we start another chat. In the end, we largely remember much better the interactions in which "keep going" resulted in something good, and forget about our role in stopping the train when it derails, which is something much harder to do unattended by a human.

[lanstin]

Had you heard of these “famous unsolved problems” before now? If you aren’t a trained mathematician, you won’t know where to point the LLM towards achievable goals. Having it solve some Erdos problems is pretty different than a Millenium prize, and even some of those might be unknown to the general non-mathematical public. Finding counter examples, unattended, to various algebraic geometry conjectures is amazing but still a ways off from the a definitive disposition of the Riemann hypothesis, P vs NP, the Navier-Stokes problem (although I wouldn’t be shocked if Professor Tao put an LLM towards a counter example for that based on his technique of encoding machines into initial conditions of PDEs).

Although if I were a mathematical quantum physicist I might be trying to prompt one into a % mathematical field formalized quantum field theory. Weirdly this sort of obvious step has not been accomplished in the last 100 years.

[vatsachak]

How could they?

That's why the free market works, millions of agents in parallel beats any planned economy (by humans)

[eru]

The free market is mostly the glue that binds lots of tiny and not so tiny planned economies together. (I mean companies and even family budgets.)

[lanstin]

As long as that N is high enough for each market, it’s good enough. When you are down to 3 producers, well there are reports of tigers there.

[eru]

Yes.

As a small wrinkle: the actual observed number of producers can be small, but the market still be competitive. See https://en.wikipedia.org/wiki/Contestable_market for one case: when potential suppliers are waiting on the sidelines.

[vatsachak]

But each company itself is composed of multiple agents. It's just that companies are a scale of consolidation.

The exact same thing happens in the cortex, 10s of thousands of cortical columns coalesce into a single action.

[xyzsparetimexyz]

I have a pi extension that just runs the same prompt in a loop 25 times. I tried giving it a loop breaker but I found that it'd give up too readily. When the task is actually complete each iteration didn't do a lot of work so it was efficient enough. I suppose another way is to call out to a separate context to check if the task is complete?

[Normal_gaussian]

Commands like /goal and similar are the more complex version of this; you write a prompt like it was a singular iteration, it runs one iteration, then runs an "evaluator" to determine if the goal has been reached, then runs the prompt again with a little extra to make it go again - and so on. The evaluator is just an LLM with most of the result or context looking at the original goal and the state and answering the question "has the goal been met".

The interesting part of this: while some leading implementations use the same LLM and context for the evaluator, some call out to a different context, some to a tuned LLM and different context; so which is better? many blog-scale benchmarks are calling it a toss-up that is highly dependent on the primary model.

[eru]

For mathematical research, you can just run until you have a computer checkable Lean proof.

[gf000]

Given that it was formalized correctly, which is far from trivial in many cases

(Of course LLMs can help there, get it right etc, just a caveat that people have to keep in mind)

[eru]

Agreed. But also formalising the statement of a theorem, or rather understanding the formalisation that the LLM suggested to you, is often a lot easier than understand the whole proof, especially if it's a formal proof.

[xyzsparetimexyz]

Sounds overengineered to me

[Normal_gaussian]

I was surprised at how little improvement they could eek out of tuning it; but it is a non-trivial improvement which is much less likely to wastefully spin if your validation is more expensive than you realise.

Makes sense that its in the major harnesses and not the self-built ones.

[markfsharp]

What I am thinking is the way you make it 'keep going' and when you have people of the calibre of Tao doing it I kept thinking how many breakthroughs is he going to cause the LLM to find with his targetted questions :D Amazing that we have the privilege of witnessing a true expert in such a way question the LLM.

[appplication]

Do notice he is quite Socratic, the approach works well for LLMs they love to please so you have to be careful in how you lead them.

[lattalayta]

Maybe it's just me, but does anyone else feel goofy speaking to a computer this way?

[zx8080]

Just relax and welcome the nondeterministic world as a non-programmer. Also, forget what you were taught in Theory of Computation, no one needs it anymore. AI will do everything for you. /s

Marketing for huge bucks sounds like this.

You will own nothing and will be happy (that you are still alive). Probably.

[MikhailTal]

this is /goal in claude code/codex. also basically a slightly improved ralph loop

[rubyn00bie]

I’ll have to try this exact phrasing. I had a lot of trouble with GPT 5.5 more or less completely ignoring similar prompts and instructions and entering a sort of “doom loop” or just consistently trying to prematurely end the chat.

I would love any tips for other folks who have successfully used similar approaches.

[floam]

You have this problem after paying for Pro?

[paxys]

Aka /goal