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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#761

Post by GPerson »

david-gpu wrote: post #596
shimman wrote: post #544

Earlier quoted context omitted.

Of course there's a meaningful analogy. The poster wants to make Tao sound unreasonable and against "progress" while ignoring the very real concerns Tao has. It's what fanatics do when they want to enforce their view on the world, they have to attack anyone with a reasonable viewpoint because they can't imagine a world where someone tells them they don't like what they're doing.

I do not want to make him sound unreasonable. He is a brilliant man. But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development, so I wanted to highlight some historical similarities, imperfect as they can only be. As for the rest of your comment, I hope you have a great day.

He’s not shell-shocked. He’s had an extremely consistent narrative for years now. You are experiencing a bias where you project your own views onto others, probably because you are not very informed on this.

Re: A misalignment of AI in mathematics

#762

Post by SpicyLemonZest »

glitchc wrote: post #698
SpicyLemonZest wrote: post #387

Earlier quoted context omitted.

He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things. He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's und…

> He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Co…

The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead.

Re: A misalignment of AI in mathematics

#763

Post by pseudotensor »

Tao et al. are effectively calling for diseases like childhood cancer to remain persistent for longer.

Physics and Biology will see major breakthroughs that WILL fundamentally alter our world. That is one key thing missing from alot of discussion here is the narrow focus on math (or parallels with software engineering). Doing well in math is key to doing well in physics and other sciences.

Re: A misalignment of AI in mathematics

#764

Post by qlte »

ndriscoll wrote: post #721
SpicyLemonZest wrote: post #686

Earlier quoted context omitted.

It's valuable for you , the person who's going to spend a bunch of deep design effort, to make POCs. Is it valuable for someone else to drive by, dump some POCs on your lap, and then leave you to do the deep design effort while they run away to study AI? If that person then runs around telling people that they're the real author of your project, because they generated the original POC, would you consider that an accu…

Your analogy is far enough away from the way that the real world works that I'm not sure that I can really even strain my experiences to fit within it. Sure, I guess that would be annoying? But mathematicians define their field. They're smart people. They're capable of recognizing when someone just did a vibecoded throwaway PoC and when someone has a well structured proof. Actually even before LLMs they'd publish new…

Yes, mathematicians will clearly need to rewrite the qualifying criteria for prizes to better align with the actual goals and value they were hoping to get from a solved problem. The field as a whole assumed good faith actors and collaboration, not expecting a few trillion dollar companies to walk in and start turning in piles of Lean no human understands to be able to claim "first".

This letter includes someone like Terrance Tao who publicly expressed a lot of optimism about AI for solving novel math like with the Erdos problems. It's not sour grapes but the first steps to define those new expectations for the future to reduce the perverse incentives.

And yet, predictably, people are accusing him of "gatekeeping" and ignoring the arguments he has made here and elsewhere about the benefits vs. harm in different ways of using AI.

Re: A misalignment of AI in mathematics

#765

Post by gammarator »

ardme wrote: post #414
causalmodels wrote: post #365

Earlier quoted context omitted.

The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private. They're valid.

It's really tough to come to terms with it but making academic contributions in general from the outside (with or without AI tbh) is not often welcome and the whole process feels very gate-kept.

(academic.) Unfortunately the overwhelming majority of outsiders are missing core knowledge (or are cranks), so the optimal prior from a time management perspective is to ignore them. AI just makes engaging more costly because there’s more volume and it’s harder to get signal on whether they know what they are talking about.

Re: A misalignment of AI in mathematics

#766

Post by dmoniz »

The rise of AI is going to lead to a lot of similar issues in many fields as it grows and develops further. This can be seen form 2 perspectives. The death of intelligence as we no longer need to think for ourselves or understand anything since AI can do it.

Alternatively, and this is what I choose to believe, it will lead to further intellectual enlightenment and advancement for use as a species as we start to discover new problems and areas of research that we had never conceived of before.

If we let AI take over all of our thinking then we are heading in the wrong direction. If we continue to ise it as the tool it is it will help us grow and advance as a species.

Re: A misalignment of AI in mathematics

#767

Post by GPerson »

tmhn2 wrote: post #200

As 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 some of the current problems are.

Re: A misalignment of AI in mathematics

#768

Post by gammarator »

pickleRick243 wrote: post #662
paulhebert wrote: post #623

Earlier quoted context omitted.

Do you really think people dedicate their life to mathematics for clout? If clout was the goal I don’t think becoming a lifelong mathematics academic would be the first step

for many fairly strong mathematicians, the career calculus is fame and status (mild though it may be) through mathematics or anonymity but financial reward in tech or finance. Yes, clout by becoming a lifelong academic is in fact rational for some and part of their motivation. Of course they really like what they do as well, but earning the respect of the peers they know are also respected by a large swathe of societ…

I think you’re right that some of the angst here is due to a fairly insular community having its culture disturbed by commercial forces.

Re: A misalignment of AI in mathematics

#769

Post by nullbio »

Sounds like the field needs to adapt. The world is different now, better get used to it. Trying to artificially hold back progress just so people can continue to flex on their peers is cowardice. Every single industry throughout history has had moments like this, and looking back, we'd have changed none of it.

Re: A misalignment of AI in mathematics

#770

Post by qlte »

mosura wrote: post #489
magicalist wrote: post #326

Earlier quoted context omitted.

> The fact is these fields are supported by society because of the benefits to everyone else. Once the same results can be achieved in a cheaper and faster way that is what will be done. Maybe it's worth double checking that you know how these fields benefit everyone else? Proving the blowup of the Navier Stokes equations in 3D isn't going to make your gas cheaper or make harvesting food easier or make drones easier…

Math people absolutely are important to things like the SpaceX landing control systems, hypersonic gliders, 5G networks and so on. If you can make breakthroughs on such areas as fluid dynamics, control theory or information theory with AI then that absolutely is a big deal with real technological implications.

A long complex proof to something we have been able to simulate in fidelity forever doesn't do any of that though.
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