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AI isn’t outthinking mathematicians, it’s out-remembering them
251–260 of 545 posts
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#252I 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 that top mathematicians are usually very bright. But here's a different explanation of what's going on. It's that, per Simon, many top mathematicians have, through hard work, internalized many more complex mathematical chunks than ordinary humans. And what this means is that mathematical situations which seem very complex to the rest of us seem very simple to them. So it's not that they have a higher horsepower mind, in the sense of being able to deal with more complexity. Rather, their prior learning has given them better chunking abilities, and so situations most people would see as complex they see as simple, and they find it much easier to reason about.
I once tried out his Anki approach during a math lecture. Whenever I reiterated a card, say about some lemma, I noticed something interesting about it. This was delightful and many lemmas became much more streamlined over time. It's not a "solution" to mathematics, but I found it delightful while it lasted (before akrasia or lack of time kicked in and I stopped doing it).
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#253I 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…
Since it is so much easier to test for memory than understanding society grew to confuse the two. Only now faced with these other entities are people beginning to question it.
I know people that got to post grad math without understanding a thing but they could remember a lot easily, while many of those that understood but had a harder time remembering every last variation of everything got penalized.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#254C'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.
Look up OpenEvidence
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#255I 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…
> I don't think I've had a truly original idea in my life.
There’s no such thing as a truly original idea. It is all just combining A+B!
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#256Earlier 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 can relate to this, but always explained it away in the opposite direction: I never trained my memory very much because I was able to work things out on the fly. Who knows, maybe there isn't much of a link between the two at all.
> I never trained my memory very much because I was able to work things out on the fly
I actually always thought it was the opposite for me – I had to figure out how to work things out from scratch because I could never remember anything.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#257It'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.
We're just going to slowly deconstruct every element that could be a factor of intelligence. It's not out-thinking, it's just out-remembering It's not out-thinking, it's just out-working It's not out-thinking, it's just able to consider more things simultaneously It's not creative, it's just randomly generating things and then selecting viable ones
That's insightful. AI is teaching us things about our own intelligence by simply evolving under our eyes.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#258Earlier 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…
The idea about the goal of mathematics being shared understanding seems to come at a convenient time. Mathematicians have never been known to communicate their ideas very clearly. Regardless, even that target llms will likely win - an llm will likely be more efficient at teaching me string theory than a professor in a room with 463 other students. The llm is the shared understanding.
I don't think "shared knowledge" means "shared knowledge between mathematicians and lay persons" (there is no much point in that, the same way a smartphone technician knows how a smartphone works deep down to the details but there is no big interest for society to have every lay persons being informed about it). I think it means "shared knowledge between mathematicians".
And at this level, while there are anecdotical exceptions, mathematicians have always been pretty decent (with their conferences, workshops, paper publications, international collaborations, ...).
So, it does not mean "teaching the subject", it means "creating a human network of people that share the understanding". LLM can be useful at telling a human, but you still need a human. The point of Tao is not that LLM is not good at providing explanations, it is that "providing explanations" is not the contribution to science, "the human network" is. It's like saying "LLM are great cook, they generate tons of food in space", but the point of having cooks is so that people can eat food and not die. Having LLM generating mathematical proofs is as useless as having LLM generating food that no one can access: the point was never to "generate proofs" or "generate food", the point was "creating a shared human understanding" or "eating the food so human can survive".
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#259I 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…
I suspect any new thing created/discovered/etc is just combining knowledge from existing things with memories being an example. Outremembering while certainly not the only method helps massively with combining knowledge from existing things. I don't see new knowledge coming out of nothing.
Re: AI isn’t outthinking mathematicians, it’s out-remembering them
#260I 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…
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.