Earlier quoted context omitted.
To further this assertion, there is almost no value to deeply esoteric math that is technically correct, but completely inapplicable to any scientific reality, and completely unintelligible to humans. Consider these findings deep, dark corners in the unfathomably large hyperspace of mathematics. My guess is AI will be incredibly adept at identifying these types of findings, and it will be exceedingly difficult for hu…
Works of Shinichi Mochizuki immediately come to mind. He is not AI but provides very good examples of math that is useless because it is incomprehensible by (other) humans.
Mathematicians issue warning as AI rapidly gains ground
81–90 of 366 posts
Re: Mathematicians issue warning as AI rapidly gains ground
#82Re: Mathematicians issue warning as AI rapidly gains ground
#83> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
We’re becoming increasingly embarrassing as a society.
Re: Mathematicians issue warning as AI rapidly gains ground
#84Earlier quoted context omitted.
Works of Shinichi Mochizuki immediately come to mind. He is not AI but provides very good examples of math that is useless because it is incomprehensible by (other) humans.
Do AIs produce answers whose work is incomprehensible to humans? It seems like you could just have the AI elaborate multiple times until you were satisfied with the explanation and documentation of what went into figuring out the answer. It’s not like the AI is one shotting the answer in a single opaque query anyways.
Consider the “Magnus Carlsen” of mathematics, who is more capable of understanding mathematics than any other human. But then also realize that that individual has probably devoted their entire career into a specific subdomain of mathematics. Within other deep recesses of mathematics, this Magnus equivalent will be less capable than their peers without years of rewiring their brain to understand the esoteric concepts and properties within that other subdomain.
LLMs will be able to dig deeper and broader than any human mathematician, and find results that are completely useless to humans because it would take more than an entire lifetime to “speak the language” of the concepts the LLMs have produced. The only way those results can become useful to humans is if then the LLM itself finds a way for it to be practical to humans once again.
So, no, I don’t think this represents the “democratization” of mathematics where mathematicians are no longer necessary because anyone can just prompt the LLM to explain it. The bar for entry level mathematics is lower, for sure, but research level mathematics will continue to be unapproachable for anyone who hasn’t devoted their career to it.
Re: Mathematicians issue warning as AI rapidly gains ground
#85> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
Probably one of the funniest things to read on a site like this, when you consider that eg. Boolean algebra was entirely abstract and had little practical purpose for almost 100 years until Shannon picked it up for use in circuits
By which I'm trying to make an abstract point about the inevitability of staying somewhat down to earth. I mean "pure" curiosity is great, except it isn't ever really pure, and abstract mathematics isn't ever totally abstract, it's just sort of meta in relation to practical things that humans care about.
Re: Mathematicians issue warning as AI rapidly gains ground
#86He states that he struggled to come up with problems which would be challenging for AI to solve (at the below site) and thus forced to accept that mathematicians have to rethink their profession.
FrontierMath: Benchmarking AI against advanced mathematical research by Epoch AI - https://epoch.ai/frontiermath
As a follow up to the above, see "First Proof: Mathematicians Putting AI to the Test" featuring eminent mathematicians - https://www.youtube.com/watch?v=AaICCTpkI7Q
Re: Mathematicians issue warning as AI rapidly gains ground
#87Earlier quoted context omitted.
Once you now something is correct, with a proof. It is MUCH easier to understand why it is correct. Than to start from a slate that you don't even know whether something is correct or not. In that sense AI that can just solve high level math problems is immensely useful. It allows a mathematician to explore ideas at a much more rapid pace.
Consider that since an LLM is really just an large encoding of data, the "proof" is in there already. All further work on it is effectively only rearranging words. Then all math an LLM is capable of is "done" and we have the "proof" in the LLM which by your definition is now "MUCH easier to understand" and this work is somehow sufficient. Do you see the problem with your reasoning?
A proof being latent in an LLM is no more significant than a proof being latent in a book, a theorem prover, or the axioms themselves. Einstein's papers were latent in the genetic code of his parents and the environment of his time. That doesn't mean general relativity was "already done" before Einstein was born.
By your logic, no computation has ever accomplished anything because the output was always implicit in the inputs.
The entire purpose of computation is extracting information from representations where it's difficult to see into representations where it's easy to see.
So no, this isn't a problem with the original reasoning. It's a problem with yours.
Re: Mathematicians issue warning as AI rapidly gains ground
#88Earlier quoted context omitted.
The most important part of math is advancing human understanding. A correct answer by itself is not as important as understanding why it is correct.
"What is the answer to the Ultimate Question of Life, the Universe, and Everything" 42
Re: Mathematicians issue warning as AI rapidly gains ground
#89>and the pursuit of knowledge for its own sake Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc? "Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?
Human mathematicians are being exposed the same way the "artists" are. It was always about the money and to look clever, superior to other humans. Whether its robotically spending millions of hours drawing until they can put something together at the level of a chatgpt 3 or the rote memorization of formulas and rules. They like people to think it all came naturally and that its genetic and that they are special snowf…
Both mathematics and art are comprised of two phases, the first, technical one, where the novice grinds the skill and the second, the creative one which can only be achieved if you have the means (skill) to express yourself. What you described is the technical phase, not the creative one. There is intrinsic value to it that has nothing to do with money or cleverness, something that if you ever experienced it yourself even once, wouldn't need to be explained to you. Only people who never reach phase two have your stance. Artists and mathematicians who pick academia didn't exactly have great commercial prospects before AI was a thing, yet they still chose those paths because that's what having a real passion looks like.
>They like people to think it all came naturally and that its genetic and that they are special snowflakes.
No, they don't. Most of them are the humble people that know the value of cultivating a skill and when they do pride themselves it's precisely because they know the staggering amount of hard work and commitment they invested. Most of them are worried for unemployment and don't want all their work to be reduced to training data and on top of that not be given well-deserved credit for it.
The only thing being exposed here, is how much AI in its current form was being underestimated and constantly labeled as "not real/good enough intelligence". This was and still is a shared sentiment even among tech people. Can't really blame them for going through a bargaining or acceptance stage.
And since you also sound like the kind of person who thinks prompting can replace the "robotically spending millions of hours" of practice, I've got news for you: it cannot. You are about to learn the hard way the value of skill and human understanding because as much as capitalism rewards "impact" and "results", the market never values easy things.
Re: Mathematicians issue warning as AI rapidly gains ground
#90Another mathematician already predicted this, but you didn't listen. His name was Theodore Kaczynski. It's time to reap what you've sown.
But what was his plan and how would you have proposed implementing it?