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A misalignment of AI in mathematics

mathandai.org

321–330 of 641 posts

Re: A misalignment of AI in mathematics

#321

Earlier quoted context omitted.

Now you piqued my interest. Any good AI-written books out there? I thought it's all slop.

Given the witch hunts around AI creative output, nobody who has put in work to avoid the stigma is going to out themselves.

Why would they have had to put work in?

Re: A misalignment of AI in mathematics

#322

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…

Wonder what would've Baudelaire said about generative art as in diffusion-based imagery.

Re: A misalignment of AI in mathematics

#323

This reads like people lamenting a bygone era and making a desperate attempt to bring it back. I'm sorry. Outside of the good ol' boys club, no one cares about some process they've romanticized simply because "that's how its always been done". Absolute nonsense. We are moving forward and if that means no human wins a fields medal because they didnt spend three decades working on a problem that could be solved in thre…

And who is "we" in your story?

[deleted]

Re: A misalignment of AI in mathematics

#324
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.

It's also known as "commodification of labour", and AI is just the latest and greatest tool to do it.

Luddites complained that the trajectory of technology was to allow less skilled workers to mass produce goods via machines owned by factory owners, as opposed to helping skilled workers build up and use their skills while passing them on.

Now we have a lot of money and time focused on LLMs owned by a few companies, making it easier for them to monetize low skill labour(prompting versus art/research/artisanry)

Re: A misalignment of AI in mathematics

#325
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, rea…

It’s not going to be ubiquitous? There hasn’t been a single frontier model where generation n costs less than generation n-1 to run. So the reasonable thing is to assume that GPT-7 will cost even more than GPT-6, and more and more of the frontier of knowledge will be locked behind a giant paywall. Participating in any field will mean ponying up to the oligarchs that own the infrastructure that runs the model.

Re: A misalignment of AI in mathematics

#326
post #290

Earlier quoted context omitted.

It's not a simple matter of "becoming good at", and yes, I could very well have similar concerns, depending on how it impacts the field. The statement itself mentions that such concerns exist in many other fields. I doubt OpenAI will take such a combative stance and accuse these mathematicians of "demanding" things, as you do. As I said, the purpose of this is marketing and the statement simultaneously undermines the…

So let’s say OpenAI cure cancer and put every cancer researcher out of work depriving them of intellectual satisfaction, this would also be a problem? It would certainly impact the field. 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. We should mourn this in the same way we do bugg…

> 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 to protect against. Maybe consider the deeper effects at work?

Re: A misalignment of AI in mathematics

#327

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 o…

What defines important and why must it be solved in haste? Many issues and other problems arise during the journey in solving all problems; those that are needed and those that are pursuits for their own sake.

If AI gave us the plane to reach Everest without us having gone through the journey of aviation and flight, what would we have lost without that process?

But the most important problems to be solved are not technological challenges but social ones, involving humans and our relationship to one another. An area AI will forever ill-suited to handle.

Re: A misalignment of AI in mathematics

#328
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, rea…

There ought to be more to life than sitting in a pod receiving sufficient nutrients from a tube, even if there was no doubt that humanity would in this way survive until the sun expands and makes the earth uninhabitable.

Re: A misalignment of AI in mathematics

#329
post #160
post #148

Earlier quoted context omitted.

At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.

I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.

Scale the problem down to an email. You're saying AI won't disrupt writing an email, when the text is vetted and authored by a person. True!

But now let chatGPT write lengthy emails unrestricted and now no one wants to read your slop anymore. That's what is being advocated against.

Re: A misalignment of AI in mathematics

#330
post #198
post #122

And I am outraged by their dinosaur mindset and the gatekeeping mentality that force every student to follow their same archaic system that no longer makes sense 20 years ago, let alone now.

What do you suggest? Giving money to the aspiring intelligence gatekeepers and IP thieves with trillion dollar valuations?

Reform the way math is taught and researched. Right now, the aspiring mathematicians have to follow a ritual and system for 15+ years: undergrad -> PhD -> postdoc -> faculty, specializing on very narrow fields and god forbid if they have even a slight interest in quantitative finance. You could go through 4 years of undergrad classroom and had no idea what research math is (even at top schools like MIT, Harvard or Stanford), how it's done, etc. and the people who do it are typically the one "already in the system" (e.g. parents are professors, or in academia, or have connections to do research).

In the age of AI, there's no reason one has to follow the kind of classes like Algebra, Topology or PDE. Teach just enough so that good students can understand the basic, and go straight into seminar and research math. I don't think a top student in sophomore year cannot understand or work on some combinatorics research problem and get some results, with proper mentoring and guidance.

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