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

davidepiffer.com

291–300 of 545 posts

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

#291
post #166

Earlier quoted context omitted.

> The entirety of human civilization is human shaped. That's the marketing pitch. A plumbing robot doesn't need to be humanoid, an octopus shape may well be better for all the awkward corners. A robot police officer could be the municipality itself for sensory nodes (essentially the sales pitch of Flock etc.), plus some drones or robot dogs to perform arrests*. The robot vacuum cleaners and lawnmowers we already have…

You are not understanding what humanoid robots are about. Those are specialist robots you are describing. The promise is of course one robot that can do the plumbing, clean your house, do the dishes, build a house, and basically every physical job a human can do. It's extreme lly likely that at least a somewhat humanoid shape is required for that.

Things you need to take into account that you've almost certainly glossed over:

Safety. Human-robot interactions are generally dangerous and avoided, unless the robot is specifically designed to interact with people. In those cases you often sacrifice speed, strength, and flexibility for safety and softness. Having someone come in with a specialized plumbing robot makes sense, you owning one probably doesn't, and you owning a generalize android capable of plumbing makes less sense still.

Cost. The more compact, complex, and interactive your robot is the more it costs. Make a strong, compact, complex robot safe for interactions with people in the wild is non-trivial and adds costs. The software required to do all of this is hypothetical, but obviously also costly.

Need. I understand the dream of a robot to do whatever you want is very much part of our culture, but when you consider the downsides do you really need it? I don't need a plumber living in my house any more than I need a carpenter or a landscaper to live on premises. At most these are services I would need occasionally or on a schedule. I also doubt my need for them will overlap much, unless we're talking about building a new dwelling.

So why do I need a generalist in my life that's going to cost more than you can imagine, when the means to hire existing human generalists is cheap, quick, and frankly less likely to accidentally punch a hole in you.

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

#292

Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. 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.

It's going to produce proofs far more intricate than humans can understand

The thing is, some number of advanced proofs start out "too intricate for most mathematicians to understand" but many of these get rephrase and reframed until they're accessible to undergraduates. Hopefully, AI math can be guided to do that sort of reframing to increase the level of accessible math as well as extend the border of math.

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

#294

Earlier quoted context omitted.

That's because his examples are obvious and not at all interesting, since we've already seen them. His original claim amounts to creating an AI that takes its place above humans as some kind of electronic God, delivering edicts to humanity that we cannot comprehend, but which somehow have value to us. It's unskeptical, pseudo-religious nonsense.

I don't see that at all. Nowhere did this person evoke placing AI above people or even remotely evoke religious imagery. You imagined that yourself, and that creeps me out.

It’s right here:

The age of humans comprehending things is coming to an end [1]

[1] https://news.ycombinator.com/item?id=49312914

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

#295

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or se…

Could just be that you aren’t an ideas guy/a lateral thinker

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

#296

Earlier quoted context omitted.

People have told me I was smart since I was a kid, but I can't remember for shit. I had a thought when I was fairly young that the only reason I was (maybe, sometimes) outperforming others intellectually is that I was habitually compensating for my poor memory by working things out on the fly, while others could rely more on rote memorization. Anyway, takes all kinds I guess!

Same. I have bad "factual" memory, but very good "conceptual" memory. I might not remember exactly what someone told me, but I probably gathered a keyword, and a feeling and idea of what they told me. Almost like it takes what they said then compresses it into my mind in a nice little multi-key lookup table.

Yes. "Weak detail recall but strong fluid reasoning, conceptual/gist memory, and adaptive problem-solving" is how GPT sums up what I feel. And "high fluid intelligence" is a label it gave that I won't be using anytime soon... But I like the sound of it.

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

#297

Earlier quoted context omitted.

Thanks, I feel seen.

In my, admittedly extremely small sample set, concept-focused memory is common for people with any degree or kind of dyslexia. I used to struggle with understanding how people couldn't understand things, now that I'm more mature it makes sense how people struggled with me not being able to spell things :).

I do not have dyslexia. I’ve been reading since I was a little kid. I don’t easily recall words or things that I’ve heard. But I’ve got a very good visual memory, especially remembering patterns. And I can easily visualize things too, even the somewhat abstract concepts.

So if I put a visual bend on something I can quickly understand it and remember it, but that bend has to be mind (even when helped by an image on a book). If it’s someone else’s, I’ll be very hard pressed to remember it (but I can easily remember where it was).

So at school, when I had to cram, I fill my head with images and things like that. And with the help of the exams (written) and memory of the classes, I worked out the answers.

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

#298
Seeing what AI has been doing to maths conjectures recently, I decided to give theoretical physics a go.

I threw some random "crank" ideas into GPT 5.6 Ultra and let it consume most of my weekly Pro subscription quota.

I'm actually pretty impressed with what can be achieved! If your simply ask it to use adversarial agents and include honest self-ratings, it can produce output competitive with a smart but not exceptional PhD. Not imaginative, but the effort that it sinks into even the smallest matters is just amazing to watch.

Did I get anywhere by applying AI to my toy models? Probably not! I ran out of quota before I could tackle anything really interesting.

But... GPT did seem to discover something genuinely new by essentially brute-force effort of combing through hundreds of papers on ArXiV: a new "constant" extracted from a formula over quark masses that seems to evaluate to exactly 3/4 at the one-loop level and then with various corrections at two-loop and higher. Link: https://chatgpt.com/s/t_6a80f2c794388191971350733a6f4378

This is "novel" in the sense that it found a vaguely similar formula in a paper where the authors simply missed the opportunity to extract a simple ratio from quark masses, combined with updated constants the AI found in in later papers that allowed it to guess that this might be exactly 3/4.

This is the super-power of mechanised attention!

We've produced a truly ludicrous amount of scientific and mathematical output, far past the ability of any single human mind to be even vaguely aware of all of it.

Now we can scrape together all of the jigsaw pieces we have made and see what fits together.

I wouldn't be surprised if someone, perhaps even a hobbyist comes up with a viable theory-of-everything in the next year or two simply by feeding in some clever starting point and then turning the handle on the machine until a complete and consistent theory pops out the other side.

Exciting times!

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

#300

It's also "out-brute forcing them." It just never gets tired. If a mathematician picks a research direction and spends a whole week on it and it doesn't pan out, they will likely be annoyed, need a break for a while, etc. This thing just does not ever get tired or discouraged or care; it's just onto the next thing until something ends up working.

Counterpoint: something has happened in frontier models, and yes they now get discouraged and will sometimes prefer to not continue working on a problem unless you tell them to anyway. I don't know how or why this would be trained on behavior, but no, it isn't true anymore that models don't say things like, "Ugh," or "this is going to take hours and maybe we should stop here."

I think it's to combat runaway token usage.
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