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Mathematicians issue warning as AI rapidly gains ground

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Re: Mathematicians issue warning as AI rapidly gains ground

#121

Post by math_dandy »

turzmo wrote: post #48

Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public. Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question. The annoying thing about recent AI advances is that they target questio…

To me, the most interesting feature of the OpenAI solution of the Unit Distance (Erdös) Problem is that the solution - using deep algebraic number theory as a source of extremal combinatorial/geometric constructions - is much more interesting than the problem’s elementary statement might lead one to expect.

Writing off Erdös’s problems as random, useless, or meaningless dismisses his mathematical intuition, second-to-none, and strikes me as somewhat uncharitable.

Finally, I agree that AI threatens mathematical training by rendering an entire class of acolyte-level research problems solvable by prompt. But the Unit Distance Problem is not of this class.

Re: Mathematicians issue warning as AI rapidly gains ground

#122

Post by bo1024 »

ck2 wrote: post #58

I still don't understand how "AI" is ready for serious use beyond entertainment purposes Every time I ask ChatGPT to make a table for a subject I know well, I will find an error in one of the results and it is very confident about it until I question it in detail Every time I ask ChatGPT for nutritional breakdown of some dense food source and give it a quantity like 8 ounces and ask for the weight of each ingredient,…

There are basically two kinds of applications. One is where you want to correctly solve the problem at least 99 out of 100 times. LLMs generally don't (and not everybody realizes that) so there are a lot of debates and research around how useful and reliable they are or how to make them so.

The other kind of application is where you can try 100 times and you only need to be right once. Solving a mathematical research problem is like that.

Re: Mathematicians issue warning as AI rapidly gains ground

#123

Post by ajs1998 »

silveraxe93 wrote: post #5

> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

Spoken like someone that has no idea why mathematicians are important.

Re: Mathematicians issue warning as AI rapidly gains ground

#124

Post by nphardon »

joelthelion wrote: post #117
modriano wrote: post #68

> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers. Math is a tool to solve problems. Some mathematicians might only love the process of using the tool,…

It's also a way to model the world and produce new useful abstractions. It's not just about solving problems.

Yea, math is a crazy thing. just "a tool to solve problems" is a wild take. On one extreme, there's an edgy but logical / plausible hypothesis that we live in a universe of mathematical objects, and at the other, math also discovers a lot of questions, the exact opposite of solving problems.

Re: Mathematicians issue warning as AI rapidly gains ground

#125

Post by bdamm »

brador wrote: post #70
BigGreenJorts wrote: post #60

Earlier quoted context omitted.

Sounds like yet another example of how AI is kneecapping industries from the bottom by "removing the barrier to entry" but really just removing the training path by doing the work itself with no guidance for juniors.

We are on tiny 1-5T parameter models with local power stations. We can reach Q models just by throwing resources at it. That’s a million times current B models.

Is this a known or quantifiable thing? I thought that the limit had already been determined i.e. the existing models top out and at some point it doesn't matter how much time or energy you let the model consume, it won't improve the result. And with regards to training parameters, I thought we were equally limited there, e.g. the existing models can't benefit from a larger parameter space.

I was under the impression that improvements are arriving via how the models are trained and how model prompting context is constructed, rather than just by how much data or how much energy is spent searching over the model space for a particular prompt.

Is there some evidence that we have not reached a pleateau with just resource consumption on existing models?

Re: Mathematicians issue warning as AI rapidly gains ground

#126

Post by bdamm »

zerobees wrote: post #115
silveraxe93 wrote: post #5

> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

Culturally, mathematics is a jobs program for nerds. The field very explicitly takes pride in working on problems that have no obvious applications, and most practitioners are funded publicly or supported by private endowments, with zero pressure to deliver specific results. Of course, this produces useful results every now and then, but it's not like we pursued ruthless efficiency / maximum rate of knowledge advance…

Except, it was true before and it is still true today that the best "artists" whether graphic or mathematic, are the ones that do somehow manage to cross the chasm of pure research and providing a tangible benefit to their benefactors. That aspect of understanding your customer is not changed by the presence of AI.

Re: Mathematicians issue warning as AI rapidly gains ground

#127

Post by orbital-decay »

zerobees wrote: post #115
silveraxe93 wrote: post #5

> However, the declaration argues math is more than a machine for producing correct answers. There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.

Culturally, mathematics is a jobs program for nerds. The field very explicitly takes pride in working on problems that have no obvious applications, and most practitioners are funded publicly or supported by private endowments, with zero pressure to deliver specific results. Of course, this produces useful results every now and then, but it's not like we pursued ruthless efficiency / maximum rate of knowledge advance…

Pure mathematics != applied mathematics

Re: Mathematicians issue warning as AI rapidly gains ground

#128

Post by max-amb »

n64controller wrote: post #75
knollimar wrote: post #66

Math for non mathematicians is a tool. Math for mathemeticians is an art in the same way an artisan takes pride in his work. That's why there's a disconnect when you go from math for engineers to the stuff above it. It feels less useful and very different

If spending millions of hours rote memorizing formulas and rules like a robot is "art" then sure

This seems like an intentionally reductive view on mathematics, however it is true it can be taught like so.

If you are interested, perhaps check out 3Blue1Brown on youtube, they manage to show some of the (very) real beauty in mathematics!

Edit: Also, theoretical computer science is a subset of mathematics, and considering where we are on the internet, I get the feeling you like computer science.

Re: Mathematicians issue warning as AI rapidly gains ground

#129

Post by Silamoth »

n64controller wrote: post #75
knollimar wrote: post #66

Math for non mathematicians is a tool. Math for mathemeticians is an art in the same way an artisan takes pride in his work. That's why there's a disconnect when you go from math for engineers to the stuff above it. It feels less useful and very different

If spending millions of hours rote memorizing formulas and rules like a robot is "art" then sure

It’s a sad state of affairs when so many think math is about “rote memorizing formulas and rules like a robot”. That’s how math is taught through freshman or sophomore material for a somewhat ‘general’ audience. But real math is nothing like that - it requires far more creativity. You need to discover formulas and rules. You invent new rules and see what the consequences are. This all requires a great deal of creativity. Nothing “rote” about it.

If you don’t believe me, crack open a text on something like graph theory (that’s pretty accessible, and if you’re a programmer, you’re familiar with graphs) and read through some proofs. Or better yet, try to prove some theorems yourself. No amount of rote memorization of formulas or rules will replace the creativity needed to write these proofs. Doubly so for discovering the facts in the first place.

Re: Mathematicians issue warning as AI rapidly gains ground

#130

Post by fragmede »

psychoslave wrote: post #67
fragmede wrote: post #18

Earlier quoted context omitted.

People need jobs. What's wrong with nerds having jobs via a program?

People need many things, there are all kind of theories ready to assess and assimilate if deemed worth it out there. A job is not part of any I’m aware of, though it can encompass some human needs in some cases, or go straight against them in some other case.

Every human needs a vocation, better if it's of their choosing.
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