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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

#521

Post by dash2 »

WarmWash wrote: post #224
minraws wrote: post #151

Earlier quoted context omitted.

This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…

> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…

Yeah, as a scientist I can read most Science or Nature articles in most fields, and get a rough idea. Not every piece of jargon, but I can understand roughly what they did, read the graphs and figure out the result. A friend sent me his maths PhD and I did not understand a single sentence.

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

#522

Post by jongjong »

reverius42 wrote: post #476
buzzin_ wrote: post #349

Earlier quoted context omitted.

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 ::)

"helm file" is, of course, supposed to be "helm chart".

You're right, I was typing each term as it came to my mind. Helm chart is the correct term but DevOps people would know what I meant.

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

#523

Post by jstummbillig »

michaelchisari wrote: post #12
lukebuehler wrote: post #8

It’s endlessly fascinating to read the AI transcript of an expert who _really_ knows how to cut to the chase. It just shows how much you can potentially squeeze out of these models. I’m also surprised to see that even Terrence Tao seems to use it in a way that resembles, in progression, how I use llms in my area of expertise (emphasis on progression and usage patterns, not absolute skill, obv I don’t match that): sho…

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

That is probably not going to be the important difference.

You can't use it for theoretical physics because you have no meaningful question and there is no result that you can do anything with.

In contrast you don't need to be a coder to understand if your to-do list for cats works: You have an idea of what you want. You know the rough shape of what an app is and what it can do. You can put it in front of your can and look at it go. Or not.

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

#524

Post by [deleted] »

WarmWash wrote: post #224
minraws wrote: post #151

Earlier quoted context omitted.

This is also true for almost every other field, even within computer science. The only difference is that a lot of people operate at a very surface level without realizing just how much background knowledge they have accumulated. Think about the number of keywords your average SWE is expected to know. It is rather insane. Cache, stack, heap, process, thread, socket, file, tcp, http, tls, websocks, socks, soc2???, dea…

> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…

[deleted]

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

#525

Post by jongjong »

minraws wrote: post #341
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,…

Coinbase not a startup built by recent graduates... You overestimate Coinbase's engineering rigor. But yes security in modern software systems is a joke. I don't even get paid to fix security bugs everytime I raise them the answer is to slap a sandbox and proxy and call it done.

Yep, about 10 years ago, the security of most major systems was relatively robust; I could not have hacked them. The people who worked there knew much more than I did and they didn't leave many gaps.

Now I could hack essentially any system I want. At least DoS or crash them for sure, with minimal computing on my end. They're much more complex than they used to be. Security-through-obscurity used to be a no-no and sometime in the last 10 years it became the main security paradigm.

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

#526

Post by mkagenius »

baq wrote: post #500
mkagenius wrote: post #491

Earlier quoted context omitted.

They are solving jacobian conjectures, I don't think they will hallucinate till masters level of any subject. Edit: do give counter examples if you have any in maths, physics, chemistry, biology etc

Both fable and sol are confidently wrong all the time in their most cherished domain - software engineering - I can’t quote anything because they’re working on my employer’s code bases. They’re much less wrong than their predecessors and they’re also quite good at point out their mistakes, but they’re still wrong a lot.

they are wrong on the specific nuance of my codebase too, i am talking about learning something - i can still learn everything about software engineering talking to a bot.

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

#527

Post by BoxOfRain »

mkagenius wrote: post #491
case wrote: post #486

Earlier quoted context omitted.

I think the issue is that LLMs can be so confidently and convincingly wrong about anything. And if we (LLM tool operators) don’t know the subject matter in question, we can’t easily distinguish what they are right or wrong about.

They are solving jacobian conjectures, I don't think they will hallucinate till masters level of any subject. Edit: do give counter examples if you have any in maths, physics, chemistry, biology etc

One area that LLMs tend to do badly in still is sailing. I sail casually and I have friends who are instructors, basically all the LLMs we tried gave really unsafe advice for a particular manoeuvre. Claude was the notable exception getting it mostly right, but even so I wouldn't rely on it there.

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

#528

Post by victorbjorklund »

jstummbillig wrote: post #523
michaelchisari wrote: post #12

Earlier quoted context omitted.

It reinforces how to "learn AI" is to first master the problem domain. I can use AI for coding after decades of coding. I can't use it for theoretical physics because I can't evaluate the responses.

That is probably not going to be the important difference. You can't use it for theoretical physics because you have no meaningful question and there is no result that you can do anything with. In contrast you don't need to be a coder to understand if your to-do list for cats works: You have an idea of what you want. You know the rough shape of what an app is and what it can do. You can put it in front of your can an…

Depends on what you are building. Yes, a todo app is easy. What would the physics version be? Probably ask ”what are the acceleration of a failing object?”

But if you are building some complex data science statistical model and you don’t have any domain knowledge you won’t even know what to ask for.

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

#529

Post by jongjong »

WarmWash wrote: post #270
mrpf1ster wrote: post #236

Earlier quoted context omitted.

Your translation only makes intuitive sense to you because you are well versed in programming. I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them

The thing is that you basically cannot explain the math like you can the programming. Tables, algos, and variables are all things people can generally quickly grasp. The construction is abstract but the function is tangible. The math is working entirely on abstract objects, using abstract tools, governed by abstract rules. It's just all so desperately far away from anything even technical people have contact with.

This is true. Math is more abstract. Some aspects are more tangible; this is what they teach at school and undergrad university... But once you get to master level and PhD, it tends to become increasingly abstract... The utility is only visible to PhD engineers in very specific areas and in those cases, even the mathematicians themselves can't fully grasp the utility of their work and they probably don't really need to.

They don't seem to have any desire to reconcile their 'craft' with real world applications and this is probably why they're particularly good at it.

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

#530

Post by melagonster »

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…

I’m curious whether we could get the same results by gathering a large number of PhD students and having Terence Tao treat them as an AI.
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