4 ms·

They gave their "logic", such as it is ... and it's utterly irrational. Note that the "they" who published the counterexample on X is some rando mathematician

by jibal 3mo ago

They gave their "logic", such as it is ... and it's utterly irrational. Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems relevant.

0x1ceb00da 3mo ago
> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time. > There's no reason to think that it won't provided if asked for But they didn't provide it.
- Liquid_Fire 3mo ago
  OK, so the two options are: A) Claude really produced this counterexample B) A mathematician working for Anthropic solved a problem mathematicians have been working on for more than a century, and then credited it to Claude for PR purposes If you believe B is more likely, why would you then believe a proof in the form of a chat log, when said chat log could itself have been faked by Anthropic way more easily than solving the mathematical problem in the first place?
  - fn-mote 3mo ago
    The concern is that there could have been expert knowledge input, whose importance/worth we are unable to evaluate. I don’t believe a mathematician produced the counter example secretly, but how much did they contribute to the result? AI isn’t magic, so to evaluate the value delta, you need to know the value of the input.
    - hgoel 3mo ago
      While I agree that we need the inputs to properly evaluate what this means for LLM capabilities, I don't really believe that the amount of knowledge input matters much for the overall significance of the result. These kinds of results are interesting for LLMs because mathematicians have been working on them for decades. If the result doesn't already exist, there's no way it's in the training data, and if mathematicians have been unsuccessfully tackling the problem for decades, it is believable that the use of a new tool made the result possible, even if guided by a great mathematician.
      - YeGoblynQueenne 3mo ago
        Yes, but the question is the extent to which the new tool was guided by the mathematician. Are we talking a bicycle, powered by a human stepping on the pedals; or a rocket that will fly to the moon on its own with people inside? Don't you want to know? I mean, doesn't everyone want to know?
        hgoel 3mo ago
        Yes, of course, that would be interesting info to have. I just mean that from what we have already we can reasonably infer that the LLM played a role in the result being obtained. If I am not mistaken, all of the flurry of novel results has come from existing mathematicians. This makes me suspect that the models aren't at the level where just any layman can get results. They require a skilled human in the loop to keep them on the rails and to properly explore the solution space.
        YeGoblynQueenne 3mo ago
        Right, that's what I'm trying to understand, the extent to which models need expert guidance. I don't doubt an LLM was used, I just want to know- how.
  - Izkata 3mo ago
    Weirder has happened: https://mathsci.fandom.com/wiki/The_Haruhi_Problem https://mathsci.fandom.com/wiki/The_Haruhi_Problem
- InsideOutSanta 3mo ago
  If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.
  - david-gpu 3mo ago
    Indeed, the incentive is the opposite: hiding the fact that they used an AI would boost their own personal brand.
    - dooglius 3mo ago
      He worked for Anthropic, so such a claim would be very unconvincing
      - david-gpu 3mo ago
        Because only people who work for Anthropic use AI tools? What is the reasoning here? The guy is a mathematician, after all.
        dooglius 3mo ago
        You have it backwards. Only people not working for Anthropic do not use AI tools.
        eru 3mo ago
        Yes. Though not everyone who works in the sausage factory still wants to eat sausages.
- dist-epoch 3mo ago
  > But they didn't provide it. because they are using the same prompt to try finding other counter-examples. they are milking it
- jibal 3mo ago
  > Why do you trust a random stranger so much? Why do you make false claims and attack strawmen so much?
gus_massa 3mo ago
> There's no reason to think that it won't provided if asked for, but it hardly seems relevant. My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.
- viccis 3mo ago
  Here's an example of one for a major result earlier this year: https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d... Who knows what "rewritten" means, but you can sort of see how it progresses.
8bitsrule 3mo ago
A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'. Counterexample: 35 + 6.
- jibal 3mo ago
  non sequitur
  - 8bitsrule 3mo ago
    Perhaps ... but the lesson in trusting AI math was worth it.
    - jibal 3mo ago
      You're missing the point. The counterexample to the Jacobian conjecture is valid regardless of how it was discovered ... elsewhere on this page people are even suggesting that the Anthropic mathematician may not have actually used Claude and came up with the counterexample himself. Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math. P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.
- buzzin__ 3mo ago
  Kimi 2.6 gives the answer ""By Dirichlet's theorem on arithmetic progressions, since gcd(6,35)=1 , there are infinitely many primes of the form 35k+6 . So the answer is: infinitely many primes give a remainder of 6 when divided by 35.
- buzzin__ 3mo ago
  But, if the reminder is 6, they are not really divisible, are they? Try again with a sentence that actually makes sense: "How many primes, when divided by 35, give a reminder of 6?"

by jibal 3mo ago

0x1ceb00da 3mo ago

> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time. > There's no reason to think that it won't provided if asked for But they didn't provide it.

Liquid_Fire 3mo ago
OK, so the two options are: A) Claude really produced this counterexample B) A mathematician working for Anthropic solved a problem mathematicians have been working on for more than a century, and then credited it to Claude for PR purposes If you believe B is more likely, why would you then believe a proof in the form of a chat log, when said chat log could itself have been faked by Anthropic way more easily than solving the mathematical problem in the first place?
- fn-mote 3mo ago
  The concern is that there could have been expert knowledge input, whose importance/worth we are unable to evaluate. I don’t believe a mathematician produced the counter example secretly, but how much did they contribute to the result? AI isn’t magic, so to evaluate the value delta, you need to know the value of the input.
  - hgoel 3mo ago
    While I agree that we need the inputs to properly evaluate what this means for LLM capabilities, I don't really believe that the amount of knowledge input matters much for the overall significance of the result. These kinds of results are interesting for LLMs because mathematicians have been working on them for decades. If the result doesn't already exist, there's no way it's in the training data, and if mathematicians have been unsuccessfully tackling the problem for decades, it is believable that the use of a new tool made the result possible, even if guided by a great mathematician.
    - YeGoblynQueenne 3mo ago
      Yes, but the question is the extent to which the new tool was guided by the mathematician. Are we talking a bicycle, powered by a human stepping on the pedals; or a rocket that will fly to the moon on its own with people inside? Don't you want to know? I mean, doesn't everyone want to know?
      - hgoel 3mo ago
        Yes, of course, that would be interesting info to have. I just mean that from what we have already we can reasonably infer that the LLM played a role in the result being obtained. If I am not mistaken, all of the flurry of novel results has come from existing mathematicians. This makes me suspect that the models aren't at the level where just any layman can get results. They require a skilled human in the loop to keep them on the rails and to properly explore the solution space.
        YeGoblynQueenne 3mo ago
        Right, that's what I'm trying to understand, the extent to which models need expert guidance. I don't doubt an LLM was used, I just want to know- how.
- Izkata 3mo ago
  Weirder has happened: https://mathsci.fandom.com/wiki/The_Haruhi_Problem https://mathsci.fandom.com/wiki/The_Haruhi_Problem
InsideOutSanta 3mo ago
If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.
- david-gpu 3mo ago
  Indeed, the incentive is the opposite: hiding the fact that they used an AI would boost their own personal brand.
  - dooglius 3mo ago
    He worked for Anthropic, so such a claim would be very unconvincing
    - david-gpu 3mo ago
      Because only people who work for Anthropic use AI tools? What is the reasoning here? The guy is a mathematician, after all.
      - dooglius 3mo ago
        You have it backwards. Only people not working for Anthropic do not use AI tools.
        eru 3mo ago
        Yes. Though not everyone who works in the sausage factory still wants to eat sausages.
dist-epoch 3mo ago
> But they didn't provide it. because they are using the same prompt to try finding other counter-examples. they are milking it
jibal 3mo ago
> Why do you trust a random stranger so much? Why do you make false claims and attack strawmen so much?

gus_massa 3mo ago

> There's no reason to think that it won't provided if asked for, but it hardly seems relevant. My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.

viccis 3mo ago
Here's an example of one for a major result earlier this year: https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925de8b/unit-distance-cot.pdf https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d... Who knows what "rewritten" means, but you can sort of see how it progresses.

8bitsrule 3mo ago

A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'. Counterexample: 35 + 6.

jibal 3mo ago
non sequitur
- 8bitsrule 3mo ago
  Perhaps ... but the lesson in trusting AI math was worth it.
  - jibal 3mo ago
    You're missing the point. The counterexample to the Jacobian conjecture is valid regardless of how it was discovered ... elsewhere on this page people are even suggesting that the Anthropic mathematician may not have actually used Claude and came up with the counterexample himself. Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math. P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.
buzzin__ 3mo ago
Kimi 2.6 gives the answer ""By Dirichlet's theorem on arithmetic progressions, since gcd(6,35)=1 , there are infinitely many primes of the form 35k+6 . So the answer is: infinitely many primes give a remainder of 6 when divided by 35.
buzzin__ 3mo ago
But, if the reminder is 6, they are not really divisible, are they? Try again with a sentence that actually makes sense: "How many primes, when divided by 35, give a reminder of 6?"