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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#581

Post by SpicyLemonZest »

bluecheese452 wrote: post #535
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…

Isn’t it more like it merges the code without a dev reviewing or understanding it?

No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything.

Re: A misalignment of AI in mathematics

#582

Post by vvilliamperez »

echoangle wrote: post #546
david-gpu wrote: post #141

Tao'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…

Wasn’t the criticism of photography kind of correct though? I don’t think people think of photography as an art as much as painting is an art. There aren’t a lot of photographs that a layman couldn’t in principle also take, but only a few people could replicate a good painting.

It's not exactly correct. Photography is just as much an art, but it's a very different medium and pieces are judged differently.

Realism isn't difficult, so critique shifts towards composition, narrative, context, process, and emotional impact.

Taking a clear photograph is easy with modern equipment, which means the bar for what's considered "good" is high.

Re: A misalignment of AI in mathematics

#583

Post by ralph84 »

paulhebert wrote: post #561
ralph84 wrote: post #523

Earlier quoted context omitted.

> primarily as a marketing exercise Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine.

These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers. OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems. Don’t you see how that’s different?

I see how it can be devastating to their ego, but no, I don't see a particular difference in a company spending money for clout vs. a person spending time for clout. The underlying motivation is the same.

Re: A misalignment of AI in mathematics

#584

Post by david-gpu »

robotpepi wrote: post #513
david-gpu wrote: post #455

Earlier quoted context omitted.

I am very specifically addressing what I have read Terrence Tao say on AI and mathematics, as that is the subject of this submission. Are we on the same page?

I don't see any meaningful analogy with your cites of Baudelaire. First of all, Baudelaire discusses art, which is very different to science. Several new forms of art have emerged, and then slowly integrated, despite the strong opinions of some. Here, Tao's letter discusses mainly practical aspect of scientific research. It is not about what a "failed mathematician" would do, or if "LLM can only record what already e…

> It is not about what a "failed mathematician" would do, or if "LLM can only record what already existed"

This is what I was alluding to:

I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce [0]

[0] https://mathstodon.xyz/@tao/117237320796901560

Re: A misalignment of AI in mathematics

#585

Post by lbrito »

dhbradshaw wrote: post #493
lll-o-lll wrote: post #486

> We are witnessing a general threat to intellectual work This is the crux of it and goes far beyond Mathematics or Computer Science. To get a bunch of humans to do anything, you have to motivate them. Kleos and Timē; renown and stuff. These AI companies threaten to rip this away from everyone but themselves, and this recent millennium prize is the perfect example. Solving this problem as a human would have led to tr…

These are both big motivations but not the only ones. But there's still play. There's still curiosity. And there's still the drive to understand something for yourself.

Play and curiosity usually make poor breadwinners.

Re: A misalignment of AI in mathematics

#586

Post by atomicthumbs »

echoangle wrote: post #546
david-gpu wrote: post #141

Tao'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…

Wasn’t the criticism of photography kind of correct though? I don’t think people think of photography as an art as much as painting is an art. There aren’t a lot of photographs that a layman couldn’t in principle also take, but only a few people could replicate a good painting.

i think that's just you

Re: A misalignment of AI in mathematics

#587

Post by dbmikus »

bluecheese452 wrote: post #535
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…

Isn’t it more like it merges the code without a dev reviewing or understanding it?

Pretty close, but IMO not quite. A math proof in and of itself is useless unless either:

   (A) it furthers human knowledge
   (B) it gets used in applied sciences, engineering, etc.
If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :)

Re: A misalignment of AI in mathematics

#588

Post by fdupress »

vatsachak wrote: post #151
kccqzy wrote: post #134

Earlier quoted context omitted.

Okay so you are saying the old incentive structure is outdated. What is the new incentive structure in the LLM era? What exactly makes people want to understand LLM-produced math?

I actually read through a bunch of LLM slop on the weekends trying to catch white whales I couldn't during my math PhD. The incentive is solving the problem and understanding the solution.

And that homes, feeds and waters you how?

Re: A misalignment of AI in mathematics

#589

Post by nadermx »

jaccola wrote: post #461
nadermx wrote: post #196

Back in the day you could think of a cool idea. I don't know maybe a plane that could fly without drag. To even see if this was feasable you had to understand physics, engineering, and then from there you had to have a math person see if it was actually possible. Now, I can ask ChatGPT about this and get back a proof that shows "a passive airframe cannot sustain zero-drag motion through still, viscous air" So, I thin…

This is a pretty moronic take. You only have to understand the first thing about physics (e.g., a 14-year-old's understanding) to know that a dragless airplane is impossible. If you are suggesting there is some new model of physics or groundbreaking technology that would allow such a dragless plane, then don’t let me discourage you! But AI won’t help at all, since it will only regurgitate conventional wisdom…

Well, there is physics for an alcubierre drive, so these moronic takes have answers too, I guess I must of understood the second thing of physics, not the first.

Re: A misalignment of AI in mathematics

#590

Post by kzz102 »

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…

The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem.
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