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

davidepiffer.com

111–120 of 545 posts

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

#111
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.

For greenfield projects LLMs don't need abstractions, but as the project gets more complex, the right abstractions save a pot on input tokens (less code to read) and reasoning tokens (less work to do to figure out the code), so they free the context window for higher purposes

Also I suspect that, apart from that, the results on smaller, cleaner codebases are better. LLMs degrade when following more than N instructions (where N depends on the model) even if the context window is not full yet; I suspect they also degrade when code has too many unnecessary concepts and details

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

#112
post #38

Earlier quoted context omitted.

You’re prescribing elegance to a stochastic generator trained on the wealth of humanity, including 4chan. Let’s set our expectations a bit.

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

Your brain is not just a stochastic generator.

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

#113
post #24

Earlier quoted context omitted.

It's not only going to be "connection maker". If and when robotics advance to a point where the LLMs are embodied, they can run experiments in the physical world and find new knowledge.

Being embodied is not the important barrier to running experiments. It's having access to a body of resources (i.e. funding and infrastructure).

yeah but LLMs might be even cheaper than grad students

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

#114

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.

Also out-speeding them, and that was before high speed inference.

Out-ralphing them, you might say!

https://ghuntley.com/ralph/

AGI ≈ artificial stupidity × infinite persistence

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

#115

Earlier quoted context omitted.

> 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. Your timelines are a bit unambitious. There's nobody expecting to make significant progress with a week of work.

> There's nobody expecting to make significant progress with a week of work. You underestimate my ADHD. Source: I am mathematician.

Hell, I underestimate my own ADHD.

Source: the post-it notes, ALL OF THEM.

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

#116
post #95
post #57

Earlier quoted context omitted.

AI has sitzfleisch https://en.wikipedia.org/wiki/J._Robert_Oppenheimer#:~:text=...

This is fantastic. Now I have a sophisticated-sounding german word for my attention deficit.

There's also a less flattering reading of the word, where Sitzfleisch means having a "flat ass" (from sitting too much, e. g. Sitzfleischparade describing a group of flat-arsed people, or something like Sitzfleischmaxxer, and so on).

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

#117
post #59

Earlier quoted context omitted.

Robots in labs already exist, but mercifully they're not hooked up to anything as unpredictable as an LLM. Robots tend to work best as specialists doing high-throughput, extremely repetitive tasks which nonetheless require a degree of precision. Giving a robot a "human" body makes very little sense if we're talking about the needs and productivity of a non-human; humanoid robots are marketing for humans.

Humanoid robots are obviously more than marketing. The entirety of human civilization is human shaped. Making robots that are human shaped is easier and more efficient than redesigning and rebuilding everything that exists.

Counterpoint: cars. It takes sustained effort to prevent civilization from being modified to accommodate new technology, e.g. Stop Kindermoord.

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

#118
post #24

Earlier quoted context omitted.

It's not only going to be "connection maker". If and when robotics advance to a point where the LLMs are embodied, they can run experiments in the physical world and find new knowledge.

Being embodied is not the important barrier to running experiments. It's having access to a body of resources (i.e. funding and infrastructure).

For some research funding is mostly the salaries of the people doing the research.

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

#119
post #101

Earlier quoted context omitted.

I've been working on generating a large code base for the last couple of weeks. Finally got around to generating a sort of code-duplication report and have spent the last week just having it de-duplicating logic that had been strewn all over the place (eg 11 different functions all doing date math to add x days to a date). dozens of items that had each been similar functions duplicated numerous times. crazy. (opus-5-…

Can LLMs not do this for you? Or would they go too far?

They add and add new code to the point when adding more is going to become very messy and then spagetti

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

#120
While TFA itself makes sense I disagree with the title and the conclusion. I would not consider referencing working memory during thinking as “remembering” but as a part of thinking itself. Working memory is the RAM to the much larger but higher latency indexed database that is our long-term memory. As such I would say AI is out-thinking us, even if in a brute force sort of way.

I think where you could say it is out-remembering us is when it can contemplate the vast universe of patterns, gleaned from essentially all human disciplines, encoded in its weights, that may let it draw connections that a human could not, unless they just happen to be familiar with multiple disciplines.

Which is why I think the analogy with Von Neumann / Einstein is also a bit off. From TFA it seems Von Neumann was more akin to what AI does, than Einstein. I don’t get the impression that it was Einstein’s memory but his ability to look at things from a radically different perspective. So far I don’t know that we can categorically say that LLMs can or cannot do that.

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