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

davidepiffer.com

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

#431

Post by lelanthran »

groundzeros2015 wrote: post #399
breezybottom wrote: post #398

Earlier quoted context omitted.

I don't know where you're getting that from. The sorting of students into "gifted" and "non-gifted" categories is very common. You don't need to look further than your local school district for proof.

> don't need to look further than your local school district for proof. Yeah mine didn't have it. And the teachers fought every attempt to do so because it hurt their metrics (who gets stuck with the lower class average). Are you by chance part of the PMC and your local school district is of similar demographics?

What's PMC?

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

#433

Post by fhe »

hibikir wrote: post #198

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…

extreme cases aside, memory and intelligence have always been found to have very strong correlation. so much that you might even just call them the same thing.

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

#434

Post by zelphirkalt »

philipfweiss wrote: post #102

One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible. But AI agents have no such limitations and can publish and re-use negative traces easily. There have been some recent projects ( https://www.theoremdb.org ) aimed at…

A great scientist once said, that the scientific method also includes stating, why what one "found out" could be wrong, and that one might need to retry experiments, whose results one relies upon. I think it was in "Cargo Cult Science" by Feynman.

In a way what they are doing, only publishing positive results is no longer good science.

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

#435

Post by elbear »

margorczynski wrote: post #289
re-framer wrote: post #252

I can't help but think of Michael Nielsen's essay "Augmenting Long-Term Memory" [1]. > Many people's model of accomplished mathematicians is that they are astoundingly bright, with very high IQs, and the ability to deal with very complex ideas in their mind. A common perception is that their smartness gives them the ability to deal with very complex ideas. Basically, they have a higher horsepower engine. > It's true…

> many top mathematicians have, through hard work, internalized many more complex mathematical chunks than ordinary humans Do you really think an average person can internalize complex math? Them compressing it effectively and then remembering it is a sign of (very) high intelligence.

If explained in a specific way and order, yes, it's likely.

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

#436

Post by badgersnake »

This is not surprising. I find LLMs in general have pretty limited utility, but there a niches where they are good and one of those niches is finding little snippets of information in a way that you used to have to sift through pages and pages of google results to find.

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

#437

Post by traes »

awesome_dude wrote: post #342
scarmig wrote: post #147

Earlier quoted context omitted.

Take something like (1+x*y)^3*z+y^2*(1+x*y)*(4+3*x*y);y+3*x*(1+x*y)^2*z+3*x*y^2*(4+3*x*y);2*x-3*x^2*y-x^3*z|0,0,-1/4|1,-3/2,13/2 If a thousand monkeys typed at a character per second, on a keyboard with the 23 relevant characters, it would take roughly 10^136 years for them to come up with this counterexample. Though, to be fair to monkey scenario, there's a large family of them known now, so it's not quite this bad:…

Just FTR - 1 character per second is glacially slow - it's 12 wpm - fine for (slow) transcription, but the monkey typing exercise doesn't require them to know what they are typing out

How fast do your monkeys type?

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

#438

Post by rowanG077 »

techpression wrote: post #304
rowanG077 wrote: post #233

Earlier quoted context omitted.

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.

Humans are really bad at everything we do compared to the specialized creatures in nature, it’s just that we can do many things that sets us apart. A humanoid robot is incredibly dumb for that reason. At least add a set of arms and legs and 360 vision. And obviously dislocated joints than can move freely and hands should have two thumbs and more fingers. It’s not hard to come up with a bunch of improvements for human…

Adding arms and 360 vision is not free. Look at octopi with their insane nervous system required to support their tentacle. The one who wins is not the one that makes the best robot ever. The one who wins is the one who builds a robot that can do the most, while being the cheapest.

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

#439

Post by pm215 »

andai wrote: post #429
gcanyon wrote: post #366

Earlier quoted context omitted.

I find my memory is very selective. I wanted to get in touch with a coworker from five years ago: I had to look up his name on linkedin. My wife texted me "Hotlips died" and with no effort I texted back, "Oh no, Loretta Swit or Sally Kellerman?" Mind you, I haven't watched MASH the TV show in forever, and I haven't seen MASH the movie since my parents took me when it first came out. I have zero reason to remember Lor…

Yeah this matches my experience too. I noticed this in Anki. Some cards are effortless, some take a bit of practice, and some I fail over and over again no matter how many times I practice them. Anki kept flagging my relatives birthdays as "leeches!" I found it kind of hilarious and infuriating that the software I used to remember things tells me "this thing is hard for you to remember so you should just give up."

Well, it was originally created for language learning. With vocabulary there really is so much of it that you're better off learning the stuff that sticks and moving on from the handful of items that just don't. In some other fields you really do need to memorise the whole set of items, but that's just never going to happen for second language vocab.

The other thing about leeches is that they're a sign that you probably want to try to change something about the way you're trying to learn them, because what you're doing now is obviously not working for those things.

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

#440

Post by traes »

soupspaces wrote: post #363
fooker wrote: post #173

This misses a very important point. It’s not just about out remembering, it’s about breadth. Mathematicians are all about depth. It’s pretty much impossible to become an expert in more than one narrow field of mathematics. AI is happily applying techniques and abstractions across these silos.

Euler would like a word. Maybe it's our institutions.

There was no depth to mathematics in Euler's time, he made the depth. He arguably didn't understand analysis on a technical level as well as a modern undergraduate; as I recall, he was confident that all smooth functions are analytic. He had incredible intuition and was able to make great progress by trusting it, but playing around with tools you don't understand stops being effective once a field is past its infancy.
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