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A misalignment of AI in mathematics
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Re: A misalignment of AI in mathematics
#972cc my comment from reddit : This is true of almost any field - if we have black-box technology that only the AI can understand / fix / augment / extend, then we will lose the ability for humans to learn and understand that tech. Its similar to outsourcing manufacturing, you lose the ability to manufacture. If you don't exercise a muscle, it atrophies. If some people dont learn to write code [ or do math or write musi…
I don't think this is a perfect analogy, but i think it's closest to the original articles declaration.
I wish they had stayed this as the very first paragraph.
Maybe I'm too stupid to grok the original declaration. Does anyone have a better summation?
Re: A misalignment of AI in mathematics
#973Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…
Both of Baudelaire’s criticisms were reasonable, and the same thing happened again when AI image generation showed up. You think the opponents look ridiculous because you’re viewing the history from the winner’s side. As for “the public,” people had a real demand for photography as a way to record things, which is also why it won. There is no comparable public demand for proving Fermat’s Last Theorem.
> There is no comparable public demand for proving Fermat’s Last Theorem.
It's a capability demo, not the main point. There is plenty of demand for intelligence on tap. These flashy results are necessary though, otherwise people keep claiming AI is just hype, it can't do anything etc. So they need something to point at. And it seems to be working because the anti-AI narrative has changed from the previous stance that it's just the new NFT that will simply go away to how it will replace human intellectual work and will be bad for artists and desk workers.
Re: A misalignment of AI in mathematics
#974Earlier quoted context omitted.
Tao doesn't go as far as Baudelaire, but there are some similarities. In particular, Tao has criticized that AI is not being used to create new interesting conjectures, and that the rush to prove old conjectures is not giving human mathematicians enough time to carefully analyze and understand the proofs and the methods used in those proofs. My answer to both is the same: nothing stops mathematicians from doing both…
There are no similarities whatsoever, other than them having opinions on a new tech that affects their field. > nothing stops mathematicians from doing both of those things Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful th…
> get funding
It all comes down to this. Yes, they will need to give a good and convincing argument to the taxpayer. And at the end of the day, if the circumstances change, and you're unsuccessful in making your case in your plead, the taxpayer and their representatives may not want to keep the same level of funding and instead put that money to use elsewhere. So make a good argument why your job is still worth that cash under the new circumstances. The argument can appeal to aesthetics and art and philosophy and a kind of feeling of religious elegance and so on, it's fine. I can't say how well that will work, but it's worth a try. Taxes also fund theology and other pursuits with no tie to cold hard engineering etc. But that level of funding is not the same as for math currently. That gap may shrink.
Re: A misalignment of AI in mathematics
#975To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…
> To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding.
I think you're missing key details in the statement. You can hate problems and sprinting towards solutions, and still have a deep impact in mathematics – Grothendieck once famously said you can often "soak the walnut" to crack open an issue. Rather, it's how frontier labs are inherently commercial incentivized to act like this, because it is in their best fiduciary interest. That is the misalignment.
Re: A misalignment of AI in mathematics
#976Earlier quoted context omitted.
"Lean-verified" is not some magical incantation that makes a supposed proof irrefutable. Even disregarding potential bugs in the kernel as others have said. Say that AI gives you a Lean proof and says it proves Theorem X . It could just as easily give you the same proof but claim that it proves (not X ). How would you know the difference? Nothing can really be considered proven unless a human expert can read the Lean…
I'm not totally sure what you mean. You can validate the proof using lean, which is what it's for--the whole magic of it is you don't have to just trust what AI says. That said, to your larger point, there are loopholes, and we'd certainly better be able to read the statement in lean, etc.
What I’m saying is that you can’t just trust what the AI says because it produces a Lean artifact.
The statement of the theorem has to be correctly translated from English into Lean code.
It’s like translating user requirements into code. The code could run without bugs but not do what the users want.
The only way to know the AI did it correctly is to check. You can’t just take it at face value.
Re: A misalignment of AI in mathematics
#977Earlier quoted context omitted.
It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…
I don’t see why the two are mutually exclusive to be honest. I’m not a mathematician, but I’m a software engineer and whether I like it or not, AI has changed my field dramatically forever. I understand the distaste for the way AI might be affecting the field of mathematics, but the genie is out of the bottle, and it will never be the same. It just took a little longer for it to hit the math community. Software engin…
The difference is that most software engineers don't care about bringing up a new generation to keep their field alive when they retire. Software engineers usually don't give a flying fuck for other software engineers, young or old, nor for software engineering itself. Mathematicians apparently care deeply for their subject, their field, and its future.
Re: A misalignment of AI in mathematics
#978As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…
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Re: A misalignment of AI in mathematics
#979Earlier quoted context omitted.
Soon AI mathematics will be 10x or 100x or 1000x more productive than humans in the proofing theorems business. Mathematics of old style is dead, they should develop ideas how to deal with that as a math community.
If a human doesn't understand the proof, it might be useful for certain kinds of engineering, but not really that useful for mathematics except as an existence test.
I don't known, can't we just also indirectly observe the wide platonic landscape of mathematics through observing AI results which humanity could not produce in a 1,000,000 years.
Re: A misalignment of AI in mathematics
#980As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”. I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader. What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these aut…
One key idea to understand about human behavior is that people are focused on their status among their peers and their next level superiors with power to lift their status. You are not among either, so you don't matter to them. This is nothing special about mathematicians, though, people work the same way everywhere, in every field, community etc.