Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

AI isn’t outthinking mathematicians, it’s out-remembering them

davidepiffer.com

Post reply on HN
Print view View original

151–160 of 545 posts

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#151

Post by a2ff6eeb0 »

chongli wrote: post #137
a2ff6eeb0 wrote: post #106

Earlier quoted context omitted.

You asked for examples, for a technology that we're still building. Maybe you can see the issue with that? Anyways, people benefitted greatly from Newton's laws of gravity, even though we still don't have a quantum-compatible set of laws for it. The laws of gravity are still incomprehensible for people, but the approximation that we've observed is still immensely valuable.

No, I gave you a lot more leeway than that. Take any utterly incomprehensible piece of writing from the entire history of civilization and demonstrate its value. You keep falling back on "incomprehensible for some people" but that wasn't the claim. It was about a text which is incomprehensible in principle ; that is, utterly impossible for any human to ever understand .

Can you give me an example single piece of writing that the author didn't claim they understood? I don't think that any utterly incomprehensible writing exists.

If you want examples where nobody but the author understands it, examples are a dime a dozen.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#153

Post by Eufrat »

solid_fuel wrote: post #136

Aka - it’s a stochastic parrot with a good memory, for anyone still struggling to understand this. It should be obvious, imo, but some people seem to have trouble with the concept.

I don’t understand why this is such big news. OpenAI has essentially made a bunch of marketing copy by gussying up an algorithm being given a near unlimited budget to stochastically permute through its lossy memory.

I think the real scandal is that we are almost 3-4 years into this (I think the release of GPT 3.5 is a good marker of when this public frenzy started) and all we’ve seen is OpenAI and the other major AI frontier companies constantly retracting their preposterous claims every time. We appear to have reach a local maxima in that it has some value in places that tend to be a little easier to scope and limit (computer programming, mathematical proofs). So, given the actual useful economic value this has provided, does this justify the investments? I think we are approaching 1 trillion in CapEx for AI [0]. For context, I believe the annual GDP of Norway is $600 billion.

[0] https://www.fool.com/research/ai-companies-spending-on-data-...

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#154

Post by cgearhart »

Animats wrote: post #33

Yes. That's how LLMs do programming, mostly. It's also why LLMs don't need abstractions or parsimony as much as humans. They can work on something complicated without simplifying it first. This has major implications that haven't been fully realized yet. On the math side, there are long machine generated proofs. On the code side, there are high volumes of code with similar code not being folded into functions.

This is the exact opposite of what I’ve been dealing with for awhile. LLMs absolute cannot work on something without an understanding unless they can outsource the understanding to a verifier. If you’ve got an easy to check function to measure progress then “keep going” is all the prompt you need. But if you need it to figure out “I pushed the up button and it moved up and left” then it’ll find the same bug five ways without realizing it’s just one bug in the underlying math.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#155

Post by pfdietz »

tossandthrow wrote: post #146
okamiueru wrote: post #139

Earlier quoted context omitted.

> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology. That sentiment makes me cringe. If you understand how LLMs work, you'd know it'll never be possible without a fundamental change in how these work. We're also supposed to be reaching that point, somehow, without the LLMs ever being intelligent (in the…

Maybe you can enlighten us. In what way aren't LLMs able to make new contributions. LLMs in agentic harnesses are Turing complete. To my best knowledge, we don't know of any greater computational model that the brain is a part of, that LLMs are not.

Obviously actual intelligence has an ineffable essential aspect, just like unicorn farts do.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#156

Post by okamiueru »

tossandthrow wrote: post #146
okamiueru wrote: post #139

Earlier quoted context omitted.

> The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology. That sentiment makes me cringe. If you understand how LLMs work, you'd know it'll never be possible without a fundamental change in how these work. We're also supposed to be reaching that point, somehow, without the LLMs ever being intelligent (in the…

Maybe you can enlighten us. In what way aren't LLMs able to make new contributions. LLMs in agentic harnesses are Turing complete. To my best knowledge, we don't know of any greater computational model that the brain is a part of, that LLMs are not.

First of all, the argument isn't that LLMs (with I assume some automation) cannot be used in searching a problem space. I'm assuming this is what you're referring to, in terms of contributions?

That's the part where LLMs are used as tools. Which there are plenty of places where they are useful.

Also, do you know what turning completeness is? Why are you bringing that up here?

The crowd that AI psychosis has brought to HN is interesting. But not in the "I'd love to learn more" kind

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#157

Post by Eufrat »

smokel wrote: post #46
orphereus wrote: post #16

C'mon AI companies, pivot to lawyers or doctors already. Trying to convince us that mathematics and software engineering are "solved" is getting very tiring. The pushback would probably be too much for the soon-to-be IPO-ed companies.

Mathematics is typically concerned with "proofs" [1], which similarly to code, often allow for strict validation. Thanks to reinforcement learning techniques, it is now possible to train LLMs to perform very well on code generation, and mathematical proof generation. Law and medicine are fundamentally harder fields to obtain decent training data for, and LLM results are therefore expected to be less powerful. Also, m…

> Law and medicine are fundamentally harder fields to obtain decent training data for

I think this bubble has given a lot of people software brain and are trying to apply it to fields it is wholly inappropriate for, though. Law is about argumentation and rhetoric. It is about providing a persuasive argument. This is how it is taught. The actual legal code is a way to formalize parts of it, but increasingly I see people angrily insisting that the only thing that matters is the text.

As you might imagine, I find textualism a load of applesauce, but I don’t think the vast majority of people making this argument even understand textualism as jurisprudence. It seems to stem from Crypto bros and the whole “code is law” argument which is just codswallop.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#158

Post by donbox »

atleastoptimal wrote: post #97
chongli wrote: post #26

Earlier quoted context omitted.

We don’t trillions of dollars in LLM investment to build things mathematicians don’t understand. We already have plenty of those, even from ancient times. As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they…

If humans have nothing to contribute then shared understanding is a pointless endeavor. It makes sense now in the "centaur" period where human + AI > AI alone, but when AI mathematicians are both more rigorous and more elegant, then taking the time dumbing down their proofs to a human level of understanding is like requiring that we ensure all our current proofs be understandable by a monkey.

But but but... Does not AI exists (or has to exist) to only serve us.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#159

Post by AndrewDucker »

AndrewDucker wrote: post #112
ryeights wrote: post #48

Earlier quoted context omitted.

Your brain is a stochastic generator. Have you read 4chan?

Your brain is not just a stochastic generator.

It also creates and updates models, uses those models to make predictions, guides the stochastic generation by comparing the output to those models and reworks them in real time.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#160

Post by devmor »

Arainach wrote: post #140
hilariously wrote: post #89

Earlier quoted context omitted.

Ok Sabina, everyone is string theory is all just a bunch of egotistical morons.

Spending your life's work on a theory that is widely agreed to be untestable is certainly a form of ego, or at least is more philosophy than science.

This is a pretty silly belief to hold about science. Plenty of strong, well held standards of the modern era were considered ridiculous fringe beliefs a century ago.
Post reply on HN