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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

#651

Post by amelius »

mrguyorama wrote: post #629
amelius wrote: post #532

Earlier quoted context omitted.

But the AI can teach you to do theoretical physics, by guiding you through materials it selected for you, helping you with questions, etc.

Being good at "generating text" doesn't make you a good teacher. It was trained on internet users, not trained educators. Most people posting on the internet, especially people who know about more complex subjects, are terrible teachers. Teaching is it's own skill

AI certainly does not seem like "the average internet user" to me, which is what it would be if your comment was anywhere near a good explanation for how it works.

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

#652

Post by [deleted] »

danielezell wrote: post #649
smsm42 wrote: post #627

Earlier quoted context omitted.

> Everything you know about 6800 assembly will not make your note-taking app any better. It could. It could make a simple note-taking app not take gigabytes of memory and take visible delay on each click. Most people don't bother of course because simple note-taking app is not worth the effort. It's possible to do better, it's just often not practical.

Question from the peanut gallery here. Why not just train an LLM to write in Assembly? Or bare metal? Validate by compiling. Or binary, no compilation needed. Can't a frontier LLM find the bugs better than we? As long as the program is built from small, verifiable subunits, the pragmatic problem of creating an efficient program is in every careful planner's reach. Seems the friction is nearly gone. I have no skin in…

[deleted]

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

#653

Post by scubbo »

aleph_minus_one wrote: post #343
scubbo wrote: post #333

Earlier quoted context omitted.

I was amused and irritated in equal measure when a senior manager at $LAST_JOB demanded that documents include "no jargon", then went on to use many terms like those you've listed here with no indication of awareness of the contradiction. Just like the famous observation that "anyone driving slower than me is an idiot, and anyone driving faster than me is a maniac" - "jargon" is just any term-of-art that you're not c…

> I was amused and irritated in equal measure when a senior manager at $LAST_JOB demanded that documents include "no jargon", then went on to use many terms like those you've listed here with no indication of awareness of the contradiction. "No jargon" is alwys in reference to some assumed knowledge model. For example, when I claim that my own math texts include "no jargon", this assumes the knowledge of a person who…

Yep, exactly.

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

#654

Post by djmips »

LoganDark wrote: post #414
AgentME wrote: post #390

Earlier quoted context omitted.

Oh, GPT-3.5, recognizable in so many old screenshots by the green icon. If ever a popular model deserved the term "stochastic parrot", it was GPT-3.5. I wonder what percentage of people today still base their opinions of AI capabilities on their experiences with that model. That model was the only option for free ChatGPT users for the first year and a half of ChatGPT's existence, from November 2022 to May 2024.

GPT-3.5 was so nice because the safeguards were so easy to bypass and it wasn't lobotomized by RLHF. Newer models really don't hit the same spot and I'm not sure what I liked so much about that initial release. I look back at conversation logs I saved and I just can't replicate them nowadays.

have you experimente with https://huggingface.co/HauhauCS/Qwen3.5-9B-Uncensored-Hauhau... to test that conjecture? It's very easy to try.

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

#655

Post by djmips »

kypro wrote: post #66
personalityson wrote: post #60

This was my conversation with ChatGPT 4 years ago: https://i.imgur.com/WPaWgzZ.png Where will we be in another 4 years? What a time to be alive!

I'm from the UK. What's in the image?

firefox has a built in VPN now. I wonder if it would work for you.

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

#656

Post by elcritch »

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.

Terrance Tao is GOATed.

That’s what I got from reading about a third of that exchange.

I mean that’s clear from reading anything about the dude, but to _experience_ it so to speak is different.

A true mark of brilliance is someone who makes something difficult seem easy by framing it just right.

In this instance ChaGPT is just expanding upon his prompts. Not to diminish, it’s amazing what it’s capable of.

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

#657

Post by djmips »

atmosx wrote: post #501

This has received many upvotes and most focus on the interaction between human and machine, which is by all means interesting. I wonder how many ppl can actually follow what's happening, I mean the math.

That may be true of a lot of posts on programming and other topics, nevertheless they are still interesting.

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

#658

Post by RugnirViking »

gamerDude wrote: post #542
rkuodys wrote: post #531

Earlier quoted context omitted.

I am not sure if I'm ignorant or have too much self esteem, but in cases where domain is not my expertise I try to cross challenge using different models to get less-biased and hopefully more correct insights.

This is some work that I want to see in education. How do you validate if something is true or not. A lot of times that will take physical tests. Or in the case of math/logic, tests to validate each line or validated sources of previously proved theorems

You use the scientific method. Make a guess about how the system works, do experiments aimed to show that's not the case, adjust guess accordingly, and repeat

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

#659

Post by RugnirViking »

theplumber wrote: post #634
lanstin wrote: post #602

Earlier quoted context omitted.

That seems only partially true. I have no doubt it could crank out a UI like Facebook, but having it work for high volume is less well represented in the training data. Things that seems obvious to us, like sharding, using asynchronous messaging systems to provide more durability at the cost of instant consistency, traffic shedding, intelligent clients, conscious decisions on CAP properties in the light of user exper…

I call it BS. When you are hitting real scalability issues that the AI can no longer help you are already a successful business. The non technical founder will not know about async message passing but will ask the AI why the site is loading so slowly and sure enough the AI is able to implement caching and various mechanism to improve the performance and observability. You are hitting a wall when you do novel stuff (I…

Have you ever tried to get an LLM agent to improve performance in a complex system? It's not good at it at all, it doesn't have a very scientific mindset about it, loves to do premature optimisation and "fancy tricks" while ignoring/missing glaring issues/gains - I'm sure it could be taught to be more methodical (verify what is actually slow before attempting a fix) but it's anything but right now.

Even if you walk it through the process, it also has terrible intuition about what time certain things "should" take - dismissing the possibility of massive speedups because it thinks some number is normal etc

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

#660

Post by spopejoy »

dullcrisp wrote: post #372
metanonsense wrote: post #315

Earlier quoted context omitted.

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.

"Yes—and I actually think this is the right way to think about the construction."

Always the smarmy tone.

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