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Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

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Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#371

Post by p1necone »

napoleoncomplex wrote: post #21

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.

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.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#372

Post by dullcrisp »

metanonsense wrote: post #315
ecshafer wrote: post #31

Terrance Tao's chatgpt conversation is really interesting for a variety of reasons: 1. The counter example wasn't just a brute force selection, the polynomial is structured in a very specific way that ends up getting the result. 2. Terry Tao's questions are very specific and prompts the AI in a useful way, that without high math training you are not going to get the same information out of it. Terry seems to see some…

It feels very humbling that here is one of the smartest humans on the planet asking questions, and the LLM keeps answering in this "Yes, it's really simple if you think about it" way, like a professor talking to a talented student.

I hate it when it picks that register. I think it stops if you contradict it more, which he’s not doing.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#373

Post by esikich »

gcgbarbosa wrote: post #62

I find it amazing how people can use AI to do things that seem hard but yesterday I could not figure out how to install a package on my system. It kept suggesting dependencies that don't exist, and telling me to use functions that are not in the system. The math does not math...

How were you expecting it to know what your system setup was? Did you ask it for some bash commands to get it the info it would need to get unstuck? Or were you just expecting magic?

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#374

Post by pdpi »

Xcelerate wrote: post #340
minimaxir wrote: post #106

Earlier quoted context omitted.

> 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.

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 mathem…

"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.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#375

Post by ivewonyoung »

Xcelerate wrote: post #340
minimaxir wrote: post #106

Earlier quoted context omitted.

> 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.

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 mathem…

They do have some of those.

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

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#376

Post by pfdietz »

traes wrote: post #344
pfdietz wrote: post #331

Earlier quoted context omitted.

Here the search wouldn't have been chosing the coefficients independently. Note that one intermediate variable is a polynomial in the input variables, and it is used in other polynomials. A search over expressions like the ones in the counterexample would have a much smaller search space.

1) How do you know this structure is the correct one a priori 2) You are starting at 10^500 possibilities. "Much" smaller is not enough, the order of magnitude of the order of magnitude needs to be changed. 3) You still need all of the other assumptions, which were completely unfounded Impossible.

If I pull out the two terms 1+xy and 3 + 4xy as new variables, then make three polynomials that are The coefficients are mostly 1, so biasing toward that would make it much faster.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#377

Post by gjm11 »

buzzin_ wrote: post #349
jongjong wrote: post #301

Earlier quoted context omitted.

>> Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, deadlock, stack, queue, race, atomic, event loop, coroutine, async, database, transaction, index, replication, sharding, consistency, serialization, DNS, load balancer, container, namespace, and so on. ... communication protocol, method signatures, web components, ssh, CSS media queries, HTTP headers, WebSockets, timeouts,…

Nice list. I like it how you also included some made up terms. For completeness, those are not real: ETag, SAML, CSP, BGP, haproxy, helm file, k8s, SOCKS5, Lamport OTS, Winternitz OTS, SPHINCS, lattice-based, pg-vector, sameSite, httpOnly. (Or, at least, i have no idea what those are ::)

Apologies if I am simply missing a joke (which I think is true with p~=0.3), but:

At least some of these are definitely real things. For instance: "BGP" is the Boundary Gateway Protocol. "Lamport OTS" is a one-time digital signature scheme due to Leslie Lamport. k8s is an abbreviation for a piece of software called Kubernetes.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#379

Post by rubyn00bie »

minimaxir wrote: post #106
napoleoncomplex wrote: post #21

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.

> 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.

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.

Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample

#380

Post by agrounds »

aleph_minus_one wrote: post #336
ChrisClark wrote: post #303

Earlier quoted context omitted.

But... what is a ring? What is a formal variable? What is a vector space? What does "algebra over the ring" mean? His point is the terms are dense too

> But... what is a ring? What is a formal variable? What is a vector space? What does "algebra over the ring" mean? All these terms were taught to computer science (and of course math, physics, ...) students as part of getting their degree in computer science, because these concepts are important for many algorithms.

I studied a lot of abstract algebra in college and grad school and I’m surprised that rings and algebras would come up in a CS degree. What algorithms topics used those concepts? Something about polynomials?
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