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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#112

"how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place." That sounds like an "us problem", not an AI or OpenAI/Anthropic problem.

That's how I read it too, Terry Tao, who has been a "pro-AI math guy" is going through the same emotions and confusion that us SWE folks are going through, "oh, wait... this might mean I'm not going to be special anymore!?" I don't mean to be a dick, but I've talked about it previously. These folks are grieving. I get it, I've lived through this sort of life changing thing before, it sucks... but yeah.

Yeah given he had been very pro-AI for years, I expected he made peace with the issue many many years ago (like I did back in 2018), and when this time would come he would explain to other mathematicians how to live with it.

I am a bit disappointed by him.

Re: A misalignment of AI in mathematics

#113
post #65

Everyones outraged all the time. It doesn't mean anything anymore. It's that meme from years ago about the red ants and the black ants living in a box peacefully until someone shakes the box and they start trying to kill each other. They go after each other and not the one shaking the box. OpenAI/Anthropic are shaking the box.

I don't understand how that metaphor applies here, you seem to contradict yourself. The mathematicians are mad at openai. If the mathematicians are the black ants and OpenAI is shaking the box, who are the red ants?

Everyone that will now pick sides. Just wait, I’m already seeing it on Reddit.

Re: A misalignment of AI in mathematics

#114
In the Economist article Tao links, Hugo Duminil-Copin, draws a comparison: airdropping someone on the summit of Mount Everest is very different from climbing it.

The fundamental issue with AI solving any perceived difficult problem is that we have lost the journey. The sight atop Mount Everest looks much different when you have climbed compared to being dropped from above.

Re: A misalignment of AI in mathematics

#116
post #90

Earlier quoted context omitted.

The same incentive there always was: Because you wanna know. What incentive were you thinking of?

The usual incentives in academia: publishing papers. Consider the difference between publishing a paper that introduces a novel method to do X, versus publishing a paper that merely interprets Claude’s method to do X. The latter might not even be publishable.

That means that academia is outdated not that LLM math is bad

Re: A misalignment of AI in mathematics

#117
post #89

If you internalise that AI might actually reach super intelligence then logically the question becomes "so what exactly are humans for if literally everything can be done better by machines?". Then mathematics and all intellectual work, as argued for here, becomes quite clearly a recreational pursuit.

Humans are the one single intelligence that we know which has not been created by another one.

Re: A misalignment of AI in mathematics

#118
post #37

The concerns seem valid. I'm unclear what the ask is, though. What, even in theory, is a practical and realistic fix?

When writing math papers, many (but unfortunately not all) mathematicians go through a post-processing step, where they take their ideas and proofs, and try to reduce them to simple and reusable core ideas that can be understood by the reader. Good writers will often also provide some representative examples that guided the proofs, explaining why various intermediate results can't be strengthened and why the proof can't be made much shorter without inventing new techniques. If AI-generated proofs were required to go through such a post-processing step before being published, that would go a long way towards improving the situation.

Re: A misalignment of AI in mathematics

#119
post #65

Everyones outraged all the time. It doesn't mean anything anymore. It's that meme from years ago about the red ants and the black ants living in a box peacefully until someone shakes the box and they start trying to kill each other. They go after each other and not the one shaking the box. OpenAI/Anthropic are shaking the box.

You're looking too closely. Whether or not mathematicians are actually outraged makes little difference to how this article plays. Hell, lying would likely INCREASE revenue.

Re: A misalignment of AI in mathematics

#120
post #6

> solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. This is the effect of AI on most intellectual disciplines, and it’s a real worry.

Yeah. My other favorite example are books. Why do nonfiction books exist? There are some pathologies and corner cases, but fundamentally: to develop and share new ideas. Downstream from that, if it reads well and if you're lucky, you make some money.

But now, LLMs can generate hundreds of books per hour. They make up 80-90% of new arrivals in many nonfiction categories on Amazon. They short-circuit the system, allowing their "authors" to extract money from the system with zero effort by crowding out human work. And it's not even the question of whether these books are good or bad (although overwhelmingly, they're terrible). It's whether it's actually accomplishing anything worthwhile, or just destroying incentives for humans to write or go into any other sort of intellectual work.

In fact, I see many professions push back. Artists, writers, now mathematicians. And I'm amazed that our profession doesn't and that we have so many people who are hooked on vibecoding. I'm still waiting for that 10x payoff. All this velocity and somehow, the landscape of the software I want to use still looks the same as it did in 2021.

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