This is the second ChatGPT shared conversation I've seen today that is truly fascinating.

The first one was someone proving another conjecture false by just repeatedly saying "keep going" to ChatGPT: https://x.com/DmitryRybin1/status/2079904005652893709

What a world we live in.

  > What a world we live in.

Scroll... wait for render... scroll... wait for render... repeat...

We live in a world where there's so much crazy technology but few people use it to make products better or to improve people's lives. Most people use it to just make more money. It's funny too, because there's a million things we could use that tech for that actually reduce costs. Hell, what would be the economic impact of putting ML systems into streetlights so they properly coordinate. Don't even need LLMs for that, and I'm sure it'd save billions of dollars a year. Just a lack of will. I wonder if this will ever change. Is this how we create the high tech low life future?

(FWIW, no problems if I jump into the app. It's purely a web thing, but my point more illustrative than specific)

Trying my luck with this prompt:

> Construct a counterexample to the Collatz conjecture. You should do a breakthrough and find a structured counterexample.

>> This is the second ChatGPT shared conversation I've seen today that is truly fascinating.

We recently had some bugs fixed in the geometry kernel of solvespace. Not much conversation, but the analysis from the AI was amazing:

https://github.com/solvespace/solvespace/pull/1729

https://github.com/solvespace/solvespace/pull/1730

https://github.com/solvespace/solvespace/pull/1731

From the Validation section of PR 1730:

"The model family was reconstructed programmatically (parameterized cuboid stack) and swept over 2,304 configurations — extrusion directions, workplane-normal orientations, sketch windings, D's plane/height/depth/extent, including all the exact-coincidence heights. Zero failures with the fix; 576 failing configurations without it. The generator is available on request."

It looks like it wrote a python script to generate test cases in our file format for testing. Just... you know, as a side quest.

> 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.

Without any more context, "keep going" seems to be doing a lot of work. The user is placing a lot of faith in the LLM to not make subtle logic mistakes and to take good approaches to each problem. In my experience, even frontier models (such as Fable) are quite capable of getting confused during even simple technical work I've done in the dev ops world. For example:

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.

https://x.com/Kittoes0124/status/2079386024753443324

I'll have a third for you soon, here's the obligatory result in a tweet. A detailed post about it is in the works.

“Keep going” is exactly how many mathematicians achieved success in the past. :)

> just repeatedly saying "keep going" to ChatGPT

>What a world we live in.

Not sure, it sounds pretty boring to me...

I've noticed GPT specifically has more of a tendency to stop partway through things than many other models do. Although my most recent experience with it was 4.X I believe.

Hearing "here's what I've done, here's the completely unambiguous next steps, I'll wait for you to send a pointless message before I continue" over and over again is a real pain.

Is this the same as Dinitz Theorem[1] which seems to have been proved in 1994? This is the only result I keep stumbling upon when trying to understand the problem formulation

[1]: https://en.wikipedia.org/wiki/Dinitz_theorem

"it's enough of partial results. let's finish with a complete unconditional counterexample"

"Worked for 88m 24s... >"

"<h1>Complete finite counterexample</h1>"

...

From the prompt:

> You should do a breakthrough

This is just as funny and ridiculous as those "make no mistake" prompts.

Direct link: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

crosses fingers "Low hanging fruit, low hanging fruit, low hanging fruit..." hyper-ventilates

"whats next" is another good one

this sounds like like an open parenthesis (

without someone independently verifying it, it just dangles there

...

"Gew on, lad!"