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

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

#351

Post by archonis »

a2ff6eeb0 wrote: post #56
archonis wrote: post #53

Earlier quoted context omitted.

A good mother doesn't raise children to be dependent upon her for all their needs. For this to actually work in a way that benefits our species, humans will need to become something else/next through their interaction with the technology.

It's inevitable -- we won't have the machinery to compete, so we either have an aligned AI taking care of us, or we end up with a big problem. Anyways, sipping wine on the beach and doing puzzles when I feel like sounds nice.

Permanant vacation is great for an individual. I'd love one.

However, for our species, extinction follows domestication.

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

#352

Post by importantbrian »

fma wrote: post #322
grahamburger wrote: post #210

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!

I remember for math tests in high school/college it was easier for me to derive formulas than to remember it.

I used to think I wasn’t very good at math, because I struggled to route memorize formulas and the like. Then I had a calculus professor in class that took a bunch of time explaining how to derive the formulas we were using and it unlocked everything for me. I’m much better at deriving from core principles than trying to remember a bunch of formulas and algorithms for solving problems.

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

#353

Post by chongli »

atleastoptimal wrote: post #307
chongli wrote: post #199

Earlier quoted context omitted.

Where is the value in an unintelligible gibberish proof? We already have countless examples of such filling up the arXiv, written by hacks long before LLMs started writing proofs. No one cares about them. You might as well build a box blasting radio static into the void. You could save a lot of electricity that way.

An unintelligible but correct proof is better than no proof. These first AI proofs may be overly complex and un-elegant, but they are the worst that frontier math proofs will ever be. AI math in 2030 will be leaps and bounds ahead of humans both in rigor and elegance.

Those are some strong claims. I’m deeply skeptical of all of them.

I believe Terry Tao when he says the bottleneck will no longer be the writing of proofs, it’ll be everything else: reading them, reviewing, publishing, and teaching from them. A bunch of proofs that nobody reads are of no use to anyone.

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

#354

Post by yieldcrv »

alterom wrote: post #195
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…

The bandwidth is absolutely there ("we tried this and it didn't work" is totally the stuff of conference discussions). The incentives are not. The incentives are skewed towards "a magician never reveals her secrets". The results are presented as if a rabbit got pulled out of a hat, with a maximum ta-da! effect, and little backstory of how the hell did we get there . Don't get me wrong, these things are discussed , of…

I think its a total travesty of our society that people are desired to identify both the problem and the solution

people without solutions are told not to point out the problem

and people with the skillset to bring solutions dont have the skillset to search for problems or apply their seemingly unrelated disciplines to it

so you get a lot of capital and energy thrown at people who purport to be both

If AI can address this too, that would be profoundly impactful. The cross disciplinary work that a single college course is supposed to reveal, finally realized

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

#355

Post by fragmede »

the__alchemist wrote: post #134
aurareturn wrote: post #100

Earlier quoted context omitted.

When people make these comments about string theory, are they at the forefront of quantum physics theory and have spent years on modern string theory? Or did they just watch a YouTube video and then keep parroting this?

You could reductio ad-absurdum this logic quite broadly. We all form beliefs about the world and its aspects, and almost always through fallible sources. Should one be confident about ones of questionable provenance? I say no. But forming beliefs from the information we have is a useful skill.

In the age of infinite bullshit generators, the even more useful skill is being able to say "I don't know." Or "I'm not qualified to have a useful opinion on this so I'm just not going to say anything." I could write a bunch of stuff about my personal opinions on string theory and waste everyone's time, or I could just shut up and not be a human stoichastic parrot.

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

#356

Post by fragmede »

nobodyandproud wrote: post #194
devmor wrote: post #160

Earlier quoted context omitted.

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.

They were testable, no?

Well, we can test it, but you'll need to give me a ton of money in order for me to test it.

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

#357

Post by basch »

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…

There is also an element of how you process information. Some people jump to instantly refute an idea with a counter example. Some people jump to statistical likelihood. There’s elements of trust vs trust but verify.

Some people, through practice and experience are better than others at breaking down foreign information and making sense of it, or jumping to an assumption.

I also think there’s an element of just remembering what my final conclusion was on an opinion, vs all my old opinions and all the work to get there. It’s easier to just store current belief and re-work-it out how I got there later.

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

#358

Post by fragmede »

whythismatters wrote: post #283
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.

My octopus will outperform your humanoid by doing the dishes, fixing the plumbing, and preparing a Caesar salad, all at the same time!

Yeah. Can't wait to see three or four armed robots. Or five or six!

How do you train a robot to use three hands effectively when we only have two? Then again, why is the robot limited to being one robot? If two humanoid robots are in the same area, they don't have to be distinctly controlled. If they're both controlled by the same AI, a third arm on one body is the same as that arm being attached to another body.

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

#359

Post by chongli »

a2ff6eeb0 wrote: post #348
chongli wrote: post #341

Earlier quoted context omitted.

That’s still comprehensible. Incomprehensible chemistry instructions simply could not be followed by any human. They would be of no use to anyone.

You're using a very bad definition of incomprehensible. We don't understand the chemistry behind how these things work, it's that simple. If you're going to argue it's comprehensible, you'd better show how it works and go collect your Nobel prize. All we know is that if we melt the right rocks together, we get a superconductor that works in some mysterious way that we can't explain. We know it's not Cooper pairs.

No, I’m using the right one [1]. You are the one using a bizarre definition for your own purposes.

I can see there is no further productive discussion to be had with you at all. I bid you good day.

[1] https://www.merriam-webster.com/dictionary/incomprehensible

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

#360

Post by a2ff6eeb0 »

chongli wrote: post #359
a2ff6eeb0 wrote: post #348

Earlier quoted context omitted.

You're using a very bad definition of incomprehensible. We don't understand the chemistry behind how these things work, it's that simple. If you're going to argue it's comprehensible, you'd better show how it works and go collect your Nobel prize. All we know is that if we melt the right rocks together, we get a superconductor that works in some mysterious way that we can't explain. We know it's not Cooper pairs.

No, I’m using the right one [1]. You are the one using a bizarre definition for your own purposes. I can see there is no further productive discussion to be had with you at all. I bid you good day. [1] https://www.merriam-webster.com/dictionary/incomprehensible

Since it's comprehensible, please point me to someone that can comprehend high temperature superconductivity and how it works, and then explain why they didn't explain it.

With the definition you seem to want to use, it's impossible for anything to be incomprehensible, and therefore it's tautological that there's no incomprehensible LLM output: nothing at all is incomprehensible.

Do you have an example of anything incomprehensible? Anything at all? Even the things that Gödel would say are inaccessible could, in theory, become accessible: we just don't know with absolute certainly that the mathematics it was based on got all the axioms right, though we see no errors now.

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