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A misalignment of AI in mathematics

mathandai.org

211–220 of 633 posts

Re: A misalignment of AI in mathematics

#211

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…

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Re: A misalignment of AI in mathematics

#212

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…

Baader–Meinhof phenomenon:

Baudelaire popped up in this article two days ago.

https://www.noemamag.com/a-new-kind-of-creative-poverty/

Re: A misalignment of AI in mathematics

#213

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 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…

Is it not an option to make academia more like a normal job, where people focus on collectively achieved outcomes rather than credit, priority etc.?

Re: A misalignment of AI in mathematics

#214
post #31

Seems more like a misalignment b/w the people practicing mathematics and the people ultimately footing the bill for their work. Governments are invested in solving mathematical problems for practical purposes. Up to now, achieving these practical purposes relied on mathematicians doing their mathematician thing, which is better defined as a social activity than the achievement of a practical result. Now, governments…

>Governments are invested in solving mathematical problems for practical purposes. Very ignorant view of mathematics that also begs the question with an unspoken assumption of what a government is and wants while also ignoring the contingent nature of those things throughout history.

I'm genuinely surprised by this comment. I'm not talking about why a mathematician pursues math - I'm talking about where the stipend comes from.

Higher math is exceptionally useful for cryptography, defense, econometrics etc. I have a hard time thinking of other motivations that would hold a candle against such things.

Is the idea that government (for my purposes : folks w/ a monopoly on violence) is sincerely interested in promoting human flourishing, and is invested in mathematics insofar as it is a pure expression of human curiosity? I can also maybe see the glorification through monument building angle. If we're talking about math literacy in the population - that's distinct in my mind from higher mathematics.

It's dangerously naive to believe that science and math are pursued for majority benign purposes. No one here knows about Grothendieck?

Re: A misalignment of AI in mathematics

#216

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 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…

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

yeah beacuse no one trust any of their benchmark results now they are scrambling to find a signal thats undeniable

Re: A misalignment of AI in mathematics

#217

To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116 It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding. It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling sales…

Nothing is stopping these folks from continuing to study the problems and arriving at their own solutions so they can continue having whatever insights along the way. Well, one thing is stopping them. There will be no more adoration for their genius. If you truly do it for understanding and not the attention, carry on. AI should change nothing about your motivations.

> Nothing is stopping these folks from continuing to study the problems

My understanding is they are? And literally everything in this world is based around incentives. If you say “well you can continue to work on understanding, but your kids are going to starve” that’s not nothing.

Re: A misalignment of AI in mathematics

#219
post #5

Earlier quoted context omitted.

> Puts the onus on the AI companies to provide a specific replacement mechanism, no? Why? If someone makes an innovation that undercuts the underpinnings of some existing institution, why are they are responsible for cleaning up its failure?

Yes it seems odd. Out sourcing construction jobs was great for the economy while leaving entire cities in rubbles. But as soon as it hits the privileged class there is a call to "provide a specific replacement mechanism".

Math researchers are privileged class? I can guarantee - construction workers are extremely rich compared with math phds and most of postdocs. Talking about privileged class is absolutely laughable here.

Re: A misalignment of AI in mathematics

#220
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.

Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ?

Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ?

Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests.

What say the 1% ?

Just a thought.

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