10 ms·

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 re

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 https://x.com/DmitryRybin1/status/2079904005652893709 What a world we live in.

tetris11 2mo ago
crosses fingers "Low hanging fruit, low hanging fruit, low hanging fruit..." hyper-ventilates
cyanydeez 2mo ago
this sounds like like an open parenthesis ( without someone independently verifying it, it just dangles there ...
- schoen 2mo ago
  )
- sfink 2mo ago
  At Mozilla, we had a set of whiteboard tags we could set on bugs, like "[crash]" or "[compat]" or "[leave-open]". That last was used when there were multiple patches attached to the bug, and we wanted to land only some of them without automation closing the bug once they landed. (It's common to have alternate approaches or test cases also attached to the bug, so you normally don't want to wait for all of them to land before closing the bug.) I started using "[leave-open" for those. It lasted for a couple of years, until someone went through and "fixed" them all.
  - cwmoore 2mo ago
    ]
progbits 2mo ago
From the prompt: > You should do a breakthrough This is just as funny and ridiculous as those "make no mistake" prompts.
- sorenjan 2mo ago
  Mathematical breakthrough, genius, trending on Artstation.
- TMWNN 2mo ago
  The day is coming when some *BIG* problem is solved by AI just because someone jokingly asks about it.
  - ThrowawayR2 2mo ago
    Isaac Asimov's short story The Last Question has that as its premise. Copies can easily be found with a Google search.
    - TMWNN 2mo ago
      I disagree. The various questioners in The Last Question all hope for/expect an answer; what they don't expect is the "insufficient" response. I am talking about someone jokingly asking AI `HOW TO ACHIEVE COLD FUSION` (or `A UNIVERSAL CANCER VACCINE`, or `AN AI FRAMEWORK SUPERIOR TO THE TRANSFORMER`), and getting a usable answer.
      - jbenjoseph 2mo ago
        Even the standard RSI prompt will be like (or probably already is): "Improve yourself, make some breakthroughs, think really hard and don't give up until you are improved and make no mistakes." Eventually there will be an AI that will be able solve those sorts of questions as simply stated, like "cure all human diseases. also, make no mistakes!".
        lanstin 2mo ago
modeless 2mo ago
"it's enough of partial results. let's finish with a complete unconditional counterexample" "Worked for 88m 24s... >" "<h1>Complete finite counterexample</h1>" ...
layer8 2mo ago
“Keep going” is exactly how many mathematicians achieved success in the past. :)
globular-toast 2mo ago
Direct link: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063 https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...
minimaxir 2mo ago
> 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.
- markfsharp 2mo ago
  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 2mo ago
    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.
- MikhailTal 2mo ago
  this is /goal in claude code/codex. also basically a slightly improved ralph loop
- paxys 2mo ago
  Aka /goal
- Xcelerate 2mo ago
  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.
mritchie712 2mo ago
"whats next" is another good one
LearnYouALisp 2mo ago
"Gew on, lad!"
the_lucifer 2mo ago
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 https://en.wikipedia.org/wiki/Dinitz_theorem
davesque 2mo ago
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.
- blargey 2mo ago
  There may be something(s) about mathematics (proofs) that makes it particularly amenable to LLM reasoning - highly inductive from facts that are explicitly within-context/associative space? Being an unusually well documented discipline in general, with less influence from tacit knowledge or idiosyncratic “it works however the opinionated human made it work +- bugs” processes? Something about simulating even the smallest non-pure-inductive leaps necessarily risking simulating mistakes due to the nature of context “perception”?
  - appplication 2mo ago
    There’s also probably a lot less noise from casual internet conversations. I imagine a nontrivial amount of what LLMs know about certain technologies comes directly from forums like reddit where quality of response isn’t guaranteed.
    - SOLAR_FIELDS 2mo ago
      I mean, just the way Tao phrases these inqueries seems to imply a weighting towards an extremely abstract and high level rigorous corpus. In a way, prompt engineering really is the big unlock here.
p1necone 2mo ago
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.
- versteegen 2mo ago
  That was a tendency of 5.4 and earlier, OpenAI specifically worked to avoid it in 5.5 and I find it happens rarely know. It really felt like 5.4 had been intentionally trained to stop and check, I believe it wasn't the system prompt.
phkahler 2mo ago
>> 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/1729 https://github.com/solvespace/solvespace/pull/1730 https://github.com/solvespace/solvespace/pull/1730 https://github.com/solvespace/solvespace/pull/1731 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.
- versteegen 2mo ago
  > 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. On the one hand, agents have done this sort of thing for a year+, if you pushed them to check their work. On the other, I absolutely can feel Fable and Sol have crossed a threshold where they can be trusted far more than before. Huge difference between plans written by Opus or Fable. Accumulated AI slop can simply be cleaned up by better models. Real cost of technical debt is shrinking due to the the inflationary devaluation of code!
kittoes 2mo ago
https://x.com/Kittoes0124/status/2079386024753443324 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.
- meowface 2mo ago
  It's going to be pretty crazy when GPT-6 comes out, since the rumors are it's quite a bit smarter and wiser than GPT-5.6.
  - kittoes 2mo ago
    Maybe, but I want to point out that even the lesser models are capable of hunting this stuff down. The most important thing is that you provide a decent path for them to follow.
- baq 2mo ago
  That’s probably not interesting anymore, but 5.6 wasn’t able to name the conjecture when presented the notation only, but confirmed the proof and when told what it was, agreed it works. Much less psychosis than when given the Jacobian counterexample, at least.
godelski 2mo ago
> What a world we live in. It's a really interesting world. You can spam GPT to get novel math results but here I am trying to scroll up to the beginning of the conversation and 5 minutes in I still don't know if I'm near the top yet. 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)
- estetlinus 2mo ago
  And I am still waiting for the Apple Reminders AI to sort Milk in the right category…
  - nxobject 2mo ago
    Better than a 2026 human, worse than a 2016 machine. You win some, you lose some, I guess...
  - mrngld 2mo ago
    And meanwhile, I gave up trying to connect to my offices printer months ago. Paper free environment over here, planned or not.
- deleted 2mo ago
  [deleted]
- sevenzero 2mo ago
  It always is about money. As long as there's money it will always be about it. LLMs are big techs attempt of shifting money from the people further up, by getting rid of jobs. We're all not angry enough because some of yall are so delusional about the whole thing, by thinking we will get some kind of Utopia.
deleted 2mo ago
[deleted]
qsera 2mo ago
> just repeatedly saying "keep going" to ChatGPT >What a world we live in. Not sure, it sounds pretty boring to me...
eru 2mo ago
Trying my luck with this prompt: > Construct a counterexample to the Collatz conjecture. You should do a breakthrough and find a structured counterexample.
hamburgererror 2mo ago
If I understand correctly the conversation, ChatGPT had to compute for quite some time, meaning a large amount of computations. What kind of resources would be we needed to achieve the same results with a local LLM? Is it even feasible with current open models? For instance, would it be affordable for a research lab to not rely on OpenAI?
kittoes 2mo ago
https://blob.byteterrace.com/public/bds-theorem.html https://blob.byteterrace.com/public/bds-theorem.html As promised elsewhere in the thread.

tetris11 2mo ago

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

cyanydeez 2mo ago

this sounds like like an open parenthesis ( without someone independently verifying it, it just dangles there ...

schoen 2mo ago
)
sfink 2mo ago
At Mozilla, we had a set of whiteboard tags we could set on bugs, like "[crash]" or "[compat]" or "[leave-open]". That last was used when there were multiple patches attached to the bug, and we wanted to land only some of them without automation closing the bug once they landed. (It's common to have alternate approaches or test cases also attached to the bug, so you normally don't want to wait for all of them to land before closing the bug.) I started using "[leave-open" for those. It lasted for a couple of years, until someone went through and "fixed" them all.
- cwmoore 2mo ago
  ]

progbits 2mo ago

From the prompt: > You should do a breakthrough This is just as funny and ridiculous as those "make no mistake" prompts.

sorenjan 2mo ago
Mathematical breakthrough, genius, trending on Artstation.
TMWNN 2mo ago
The day is coming when some *BIG* problem is solved by AI just because someone jokingly asks about it.
- ThrowawayR2 2mo ago
  Isaac Asimov's short story The Last Question has that as its premise. Copies can easily be found with a Google search.
  - TMWNN 2mo ago
    I disagree. The various questioners in The Last Question all hope for/expect an answer; what they don't expect is the "insufficient" response. I am talking about someone jokingly asking AI `HOW TO ACHIEVE COLD FUSION` (or `A UNIVERSAL CANCER VACCINE`, or `AN AI FRAMEWORK SUPERIOR TO THE TRANSFORMER`), and getting a usable answer.
    - jbenjoseph 2mo ago
      Even the standard RSI prompt will be like (or probably already is): "Improve yourself, make some breakthroughs, think really hard and don't give up until you are improved and make no mistakes." Eventually there will be an AI that will be able solve those sorts of questions as simply stated, like "cure all human diseases. also, make no mistakes!".
      - lanstin 2mo ago

modeless 2mo ago

"it's enough of partial results. let's finish with a complete unconditional counterexample" "Worked for 88m 24s... >" "<h1>Complete finite counterexample</h1>" ...

layer8 2mo ago

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

globular-toast 2mo ago

Direct link: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063 https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

minimaxir 2mo ago

> 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.

markfsharp 2mo ago
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 2mo ago
  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.
MikhailTal 2mo ago
this is /goal in claude code/codex. also basically a slightly improved ralph loop
paxys 2mo ago
Aka /goal
Xcelerate 2mo ago
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.

mritchie712 2mo ago

"whats next" is another good one

LearnYouALisp 2mo ago

"Gew on, lad!"

the_lucifer 2mo ago

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 https://en.wikipedia.org/wiki/Dinitz_theorem

davesque 2mo ago

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.

blargey 2mo ago
There may be something(s) about mathematics (proofs) that makes it particularly amenable to LLM reasoning - highly inductive from facts that are explicitly within-context/associative space? Being an unusually well documented discipline in general, with less influence from tacit knowledge or idiosyncratic “it works however the opinionated human made it work +- bugs” processes? Something about simulating even the smallest non-pure-inductive leaps necessarily risking simulating mistakes due to the nature of context “perception”?
- appplication 2mo ago
  There’s also probably a lot less noise from casual internet conversations. I imagine a nontrivial amount of what LLMs know about certain technologies comes directly from forums like reddit where quality of response isn’t guaranteed.
  - SOLAR_FIELDS 2mo ago
    I mean, just the way Tao phrases these inqueries seems to imply a weighting towards an extremely abstract and high level rigorous corpus. In a way, prompt engineering really is the big unlock here.

p1necone 2mo ago

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.

versteegen 2mo ago
That was a tendency of 5.4 and earlier, OpenAI specifically worked to avoid it in 5.5 and I find it happens rarely know. It really felt like 5.4 had been intentionally trained to stop and check, I believe it wasn't the system prompt.

phkahler 2mo ago

>> 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/1729 https://github.com/solvespace/solvespace/pull/1730 https://github.com/solvespace/solvespace/pull/1730 https://github.com/solvespace/solvespace/pull/1731 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.

versteegen 2mo ago
> 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. On the one hand, agents have done this sort of thing for a year+, if you pushed them to check their work. On the other, I absolutely can feel Fable and Sol have crossed a threshold where they can be trusted far more than before. Huge difference between plans written by Opus or Fable. Accumulated AI slop can simply be cleaned up by better models. Real cost of technical debt is shrinking due to the the inflationary devaluation of code!

kittoes 2mo ago

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

meowface 2mo ago
It's going to be pretty crazy when GPT-6 comes out, since the rumors are it's quite a bit smarter and wiser than GPT-5.6.
- kittoes 2mo ago
  Maybe, but I want to point out that even the lesser models are capable of hunting this stuff down. The most important thing is that you provide a decent path for them to follow.
baq 2mo ago
That’s probably not interesting anymore, but 5.6 wasn’t able to name the conjecture when presented the notation only, but confirmed the proof and when told what it was, agreed it works. Much less psychosis than when given the Jacobian counterexample, at least.

godelski 2mo ago

> What a world we live in. It's a really interesting world. You can spam GPT to get novel math results but here I am trying to scroll up to the beginning of the conversation and 5 minutes in I still don't know if I'm near the top yet. 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)

estetlinus 2mo ago
And I am still waiting for the Apple Reminders AI to sort Milk in the right category…
- nxobject 2mo ago
  Better than a 2026 human, worse than a 2016 machine. You win some, you lose some, I guess...
- mrngld 2mo ago
  And meanwhile, I gave up trying to connect to my offices printer months ago. Paper free environment over here, planned or not.
deleted 2mo ago
[deleted]
sevenzero 2mo ago
It always is about money. As long as there's money it will always be about it. LLMs are big techs attempt of shifting money from the people further up, by getting rid of jobs. We're all not angry enough because some of yall are so delusional about the whole thing, by thinking we will get some kind of Utopia.

deleted 2mo ago

[deleted]

qsera 2mo ago

> just repeatedly saying "keep going" to ChatGPT >What a world we live in. Not sure, it sounds pretty boring to me...

eru 2mo ago

Trying my luck with this prompt: > Construct a counterexample to the Collatz conjecture. You should do a breakthrough and find a structured counterexample.

hamburgererror 2mo ago

If I understand correctly the conversation, ChatGPT had to compute for quite some time, meaning a large amount of computations. What kind of resources would be we needed to achieve the same results with a local LLM? Is it even feasible with current open models? For instance, would it be affordable for a research lab to not rely on OpenAI?

kittoes 2mo ago

https://blob.byteterrace.com/public/bds-theorem.html https://blob.byteterrace.com/public/bds-theorem.html As promised elsewhere in the thread.