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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#161

Post by gritzko »

jimkleiber wrote: post #150
tmhn2 wrote: post #130

Earlier quoted context omitted.

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system…

I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more. That it makes life more ends and less means.

Let's take your argument one step further.

Suppose that tomorrow we learn that AI just exploited a bug in Lean and the proof is, in fact, bullshit. Or suppose it is the case, but we never learn that.

Where are "ends" and where are "means" here?

Re: A misalignment of AI in mathematics

#162

Post by sdeframond »

imdsm wrote: post #81
oytis wrote: post #59

Looks like mathematicians (like people in many other professions) have to redefine what their work means and how to define success. Hard to agree that a tool that can find a proof is detrimental by itself, rather it voids some assumptions people relied on previously

I am on this track too. If AI leads to advancements, objectively that's a positive (depending on the advancement I guess) but it's only when mathematicians realise they'll get beaten to every thing now that they're outraged.

Say AI becomes the best at everything. Best at chess/go, best at maths, philosophy, economics, romantic advices ... and so on. Then what's the point of thinking by oneself? Of talking to one another?

What's the point of being human if we dont do human things but entirely rely on AI?

I believe this is more or less these mathematicians' argument.

Re: A misalignment of AI in mathematics

#164

Post by sim04ful »

"We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose"

Suppose we eventually have GPT-7-class models running practically on $100 devices, with their activity transparent, inspectable, and reproducible. At that point, what exactly is left for us to fear from this threat?

Re: A misalignment of AI in mathematics

#165

Post by famouswaffles »

TSiege wrote: post #70
kenjackson wrote: post #36

"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.

Are you implying that OpenAI using someones unpublished research without their permission to solve an career defining math problem with their latest model in order to publish first is a problem with the mathematicians? My read on this document is that people's work isn't being fairly cited more than what does it mean to be a mathematician in this age.

>Are you implying that OpenAI using someones unpublished research without their permission to solve an career defining math problem

Good thing they never did that then

Re: A misalignment of AI in mathematics

#166

Post by pred_ »

kenjackson wrote: post #152
TSiege wrote: post #70

Earlier quoted context omitted.

Are you implying that OpenAI using someones unpublished research without their permission to solve an career defining math problem with their latest model in order to publish first is a problem with the mathematicians? My read on this document is that people's work isn't being fairly cited more than what does it mean to be a mathematician in this age.

I didn't know this article was about that issue at all. Yeah, if the issue is properly citing work then yes, OpenAI needs to do that. But the article read like it was tackling a completely different issue.

That's one of several issues, obviously a big one, and they do touch on it:

> Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions.

Re: A misalignment of AI in mathematics

#167

Post by road61 »

It's a turning point for science and beyond. AI has shown itself to be transformative. Even today, it is already changing the how research in math (and other sciences) is conducted. In the near future, whether it is LLMs or some other superior method, its capabilities are only expected to grow. The time to ask the question is now: Will AI be arguably the best tool at scientist's disposal, or will it instead be paraded around as a super brain collective that no human or group of humans can compete with, discouraging entire new generations of future scientists from ever entering the field? The jury is out on this one.

Re: A misalignment of AI in mathematics

#168

Post by prometheus1992 »

npinsker wrote: post #61
dwa3592 wrote: post #42

While I agree with this and appreciate Tao and other mathematicians to take the time to do this. There are similar concerns for many many other fields aka there is a general misalignment of technology. Take Software engineering for example, I can't believe there is a class of software engineers who wake up everyday and tell themselves, "today is the day I am going to automate the rest of my job". Lets forget the hype…

The point of transportation is to get from point A to point B, so almost nobody will care whether that's done via automation. The point of e.g. art isn't just to produce a finished piece, so people may care about more than the end result, making AI replacement of human artists more contentious. Tao is arguing that the point of math is also not just to produce solutions to problems.

>The point of transportation is to get from point A to point B so almost nobody will care whether that's done via automation.

Would you say the job of a musician is to just produce sound? and the job of a surgeon just to cut and suture??? Well then the job of a mathematician is also just to provide proofs. You completely misunderstood the above comment and Tao's argument.

Re: A misalignment of AI in mathematics

#169

Post by Art9681 »

boron1006 wrote: post #41

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.

Re: A misalignment of AI in mathematics

#170

Post by levocardia »

metanoia_ wrote: post #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.

But we don't pour billions of dollars of research funding into mountain climbing because we think it's going to lead to wider breakthroughs in science and technology. And when we need to get people on top of a mountain for an important purpose -- like a military or search and rescue operation, for example -- we absolutely do airdrop them right on the top.

So that raises the question: is mathematics simply a pursuit of passion? Are problems solved "because they're there"? If so, then mathematics can join the ranks of things like mountain climbing, cycling, and weight lifting. But if we are trying to accomplish something important (design better airplanes, find theoretical guarantees about cryptography, factor matrices faster), mathematics needs to become more like a military or search and rescue operation, using the best technology available to secure the outcome we need. Given that the NSF pours billions into scientific research every year, it sure seems like mathematicians want to think of themselves as being in the latter category.

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