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.
Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
501–510 of 681 posts
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#502This 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.
> 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…
if people use it to make money, does this not mean that they providing some sort of service which is valued and hence it improves lifes?!
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#503Earlier 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.
Correctamundo. That's EXACTLY what I just wrote about. And how we'll create the next generation of people who know how to evaluate responses when we're creating a generation of people who are increasingly reliant on LLMs to do the work makes for a strange paradox. https://larsfaye.com/articles/ai-coding-will-prevent-experti...
The paradox is analogous to AI poisoning its own training data as more and more AI generated content is released on the Internet. Indeed, I see a hard terminus for both man and machine at some point.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#504Earlier quoted context omitted.
One thing I've repeatedly told people is that chatbots are often the most patient teachers we'll ever get (especially when explaining "stupid" questions) — compared to what we've encountered on StackOverflow or Reddit.
They lack the empathy to understand where and why you're struggling. I've given private math lessons and seen students struggle with ai, even though ai gave the right answers. My intuition is that humans spot xy problems easier when teaching (user ask x but really needs y), whereas llms will oblige writing about x.
Maybe that's a point in favor of LLMs? "XY problems" are my pet peevee, because nearly universally whenever I see one called out, it's actually the responder not being able to comprehend that the asker may actually just need X.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#505Earlier quoted context omitted.
I had a similar reaction with the language but also response times and language. It reminded me of a quote about Jon von Neumann from Edward Teller: "Von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."
Von Neumann is an interesting historical character that nobody has ever heard of , e.g: for such an accomplished inventor, that so few minutes of video footage exist of him. >I sometimes wondered if he used the same principle when he talked to the rest of us. I can come pretty close to a humbler example of this, as the more-extroverted "bad twin," of an identical set: my own genetic equal is bored to tears interactin…
What? Every CS grad learns of Von Neumman architecture and by extension of the man himself, at least I recall doing so, in much the same way as Turing and Church.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#506Earlier quoted context omitted.
Isaac Asimov's short story The Last Question has that as its premise. Copies can easily be found with a Google search.
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.
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!".
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#507Earlier 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 had a similar reaction with the language but also response times and language. It reminded me of a quote about Jon von Neumann from Edward Teller: "Von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."
I also think to do STEM well, one needs to find that inner child.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#508Earlier 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…
As mathematician, I actually agree. We could do a lot more to communicate ideas in a way non-experts can understand.
For instance, most people are familiar with polynomials. Take a polynomial in x (with integer coefficients) and substitute x for 5t everywhere. So for instance, 2x^3 - 8x + 3 becomes 250t^3 - 40t + 3.
The Rees algebra Z[5t] (here Z is the integers) is then just the set of all polynomials you can get this way.
If Wikipedia introduced it like this, I don't think most people would have a problem understanding.
The concept is not (at least not always) actually that complicated, like others are implying. It's our communication that is lacking.
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#509This 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.
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?
Re: Terence Tao's ChatGPT conversation about the Jacobian Conjecture counterexample
#510It’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.
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