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.
LLM: This package hasn't made it to production.
ME: are you sure? i see it right here!
LLM: You're right to push back. I inferred that based on weak data. I see now that the package has been deployed!
If the above conversation is typical for me, how could one expect to achieve a sound result by repeatedly prompting an LLM to simply "keep going" in dense mathematical proofs? Perhaps the user in this case had actually checked the LLM's work before issuing the prompt, but I think you see my point anyway.
"Worked for 88m 24s... >"
"<h1>Complete finite counterexample</h1>"
...
> You should do a breakthrough
This is just as funny and ridiculous as those "make no mistake" prompts.
without someone independently verifying it, it just dangles there
...
I started using "[leave-open" for those.
It lasted for a couple of years, until someone went through and "fixed" them all.