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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

#511

Post by tty456 »

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.

But someone who is not well versed in coding can evaluate the output simply by running the built app and testing it, which is an oversimplification and omits the tech debt and eventual issues that an experienced developer would catch or restrict the output.

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

#512

Post by baq »

kittoes wrote: post #410
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.

https://x.com/Kittoes0124/status/2079386024753443324 I'll have a third for you soon, here's the obligatory result in a tweet. A detailed post about it is in the works.

That’s probably not interesting anymore, but 5.6 wasn’t able to name the conjecture when presented the notation only, but confirmed the proof and when told what it was, agreed it works. Much less psychosis than when given the Jacobian counterexample, at least.

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

#513

Post by traes »

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.

I would guess almost none, less than single digit percent. Only a small fraction of undergraduate math majors who happen to be interested in algebraic geometry would be able to understand this. The average HN user knows far less math than an average undergraduate math major. Of course there are also math PhDs and the like on here, but vanishingly few compared to the bulk of the site.

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

#514

Post by inigyou »

looofooo0 wrote: post #502
godelski wrote: post #427

Earlier quoted context omitted.

> 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?!

No, money and value have been decorrelated for a long time. At least 5 years and arguably since Reagan.

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

#515

Post by ooloncoloophid »

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…

Is there a site with other good AI conversations like this?

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

#516

Post by jongjong »

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 ::)

ETag is the HTTP response header which provides the shasum (hash) of a resource in order to allow the client to check if the resource has changed without having to load the resource. It's for client side (browser) caching.

SAML is Security Assertion Markup Language; an XML based SSO (Single Sign On mechanism).

CSP (Content Security Policy) which allows the application to specify additional security constraints for the browser to enforce.

BGP; border gateway protocol.

Haproxy is a load balancer.

Helm file; another word for helm chart.

SOCKS5 is a tunnelling protocol which allows you to tunnel through a machine over SSH; you can use it to browse the net or access remote services via another machine (hiding your IP)... It's a bit like a basic VPN. Very easy to setup, you can configure your browser (e.g. Firefox) to access the net via a SOCKS5 proxy so if the remote instance is in a different country, websites will treat you as though you are in that country... Just like a VPN except you have to control the remote machine yourself and log into it via SSH with the -D flag.

Lamport OTS is Lamport One Time Signature algorithm.

Winternitz serves a similar purpose but different tradeoffs and smaller signature size.

SPHINCS is a stateless hash-based signature scheme which works by building a tree of OTS keys (Lamport, Winternitz or other) which can be generated deterministically, on-demand.

Lattice-based cryptography is real.

pg-vector is a plugin for Postgres for vector embeddings and it provides some operators for finding records based on the nearest vector.

sameSite and httpOnly are cookie security settings.

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

#518

Post by kypro »

wiether wrote: post #211
xyzsparetimexyz wrote: post #104

Earlier quoted context omitted.

Time to get a VPN bucko

I'm in France using a French VPN and I'm being blocked by imgur (been going on for a few years now)

Yes, same here in the UK. I think imgur blocks VPN IPs so I suspect unless I register a private IP or something it's basically unusable.

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

#519

Post by dbdr »

looofooo0 wrote: post #502
godelski wrote: post #427

Earlier quoted context omitted.

> 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?!

In an ideal world, that would be true, but the actual world is very far from that. As an extreme example, AI is very useful to automate scamming people.
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