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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

#341

Post by minraws »

jongjong wrote: post #301
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…

>> 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.

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

#342

Post by xyzzyz »

umvi wrote: post #243
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

My example was contrived, I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax. At a certain point though, your layman has to know the "atomic" (as in, you can't break them down further) mathematical concepts like "functions" and "infinity": `sum function(x) from x=0 to x=infinity`

I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax.

And somehow, none of the thousands of very smart mathematicians have done that, or if they had, it has not seen wide adoption. I recommend contemplating on this: if math could be made easier by changing notation, why hasn't this already happened?

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

#343

Post by aleph_minus_one »

scubbo wrote: post #333
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…

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 has studied, say, mathematics, physics or computer science.

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

#344

Post by traes »

pfdietz wrote: post #331
traes wrote: post #229

Earlier quoted context omitted.

This is not true at all. The parameter space is absolutely MASSIVE. The counterexample is a degree 7 polynomial in 3 variables, which means 360 coefficients. There's no particular way to bound these coefficients or even the degree or number of variables apriori, but assume you somehow did. Also assume you were confident that it would work with integer coefficients bounded from -12 to 12. Now you have to iterate over…

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.

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

#347

Post by gameshot911 »

HNisCIS wrote: post #190
petesergeant wrote: post #136

Earlier quoted context omitted.

I think we have a couple of years of "being good at talking to the LLM about your field of expertise" being a useful human skill, until that too gets washed away

Maybe? At the end of the day, even if they are some insane oracle (pun intended), they're still bounded by training data and how it relates to the real world. Even if they're a near perfect tool, we are still the interface between them and our lived experience. If that stops being the case then why do we care about the output? This assumes it doesn't graduate to just killing all of us and doing it's own thing, but wi…

>Even if they're a near perfect tool, we are still the interface between them and our lived experience.

Until they are embedded into automatons that can interact with the world.

(To be clear, I'm both on board with this, and I think it's the natural progression. Currently they are bounded by their training set, but interaction with the world is the imperative for theory -> test -> analysis -> update that is essential for growth and creativity.)

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

#348

Post by monk_grilla »

epolanski wrote: post #252
ValentineC wrote: post #202

Earlier 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.

That's an interesting observation. I wonder if simply prompting for that in your personal system prompt might help?

"Be aware of 'xy problems': when the user asks x but really, they need the answer to y to further their understanding. ..."

The models are so capable now I think a lot of these real limitations can be solved by prompting, harnesses or fine-tuning.

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

#349

Post by buzzin_ »

jongjong wrote: post #301
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…

>> 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 ::)

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

#350

Post by uncivilized »

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...

What's worse is that HN doesn't even try to figure out how such a result could be obtained. They just take it at face value and go into dear diary mode.

Reddit has some good discussions on the topic.

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