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Can AI do maths yet? Thoughts from a mathematician

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Re: Can AI do maths yet? Thoughts from a mathematician

#151

Post by zmgsabst »

vouaobrasil wrote: post #146
busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

I was just thinking about this. I already posted a comment here, but I will say that as a mathematician (PhD in number theory), that for me, AI signficantly takes away the beauty of doing mathematics within a realm in which AI is used. The best part of math (again, just for me) is that it was a journey that was done by hand with only the human intellect that computers didn't understand. The beauty of the subject was…

Presumably people who get into math going forward will feel differently.

For myself, chasing lemmas was always boring — and there’s little interest in doing the busywork of fleshing out a theory. For me, LLMs are a great way to do the fun parts (conceptual architecture) without the boring parts.

And I expect we’ll such much the same change as with physics: computers increase the complexity of the objects we study, which tend to be rather simple when done by hand — eg, people don’t investigate patterns in the diagrams of group(oids) because drawing million element diagrams isn’t tractable by hand. And you only notice the patterns in them when you see examples of the diagrams at scale.

Re: Can AI do maths yet? Thoughts from a mathematician

#152

Post by xienze »

thomashop wrote: post #110
lordnacho wrote: post #93

Earlier quoted context omitted.

The only thing I've consistently had issues with while using AI is graphs. If I ask it to put some simple function, it produces a really weird image that has nothing to do with the graph I want. It will be a weird swirl of lines and words, and it never corrects itself no matter what I say to it. Has anyone had any luck with this? It seems like the only thing that it just can't do.

Ask it to plot the graph with python plotting utilities. Not using its image generator. I think you need a ChatGPT subscription though for it to be able to run python code.

Shouldn’t ChatGPT be smart enough to know to do this automatically, based on context?

Re: Can AI do maths yet? Thoughts from a mathematician

#153

Post by nyrikki »

busyant wrote: post #138

As someone who has a 18 yo son who wants to study math, this has me (and him) ... worried ... about becoming obsolete? But I'm wondering what other people think of this analogy. I used to be a bench scientist (molecular genetics). There were world class researchers who were more creative than I was. I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". Nevertheless, I…

What LLMs can do is limited, they are superior to wet-wear in some tasks like finding and matching patterns in higher dimensional space, they are still fundamentally limited to a tiny class of problems outside of that pattern finding and matching.

LLMs will be tools for some math needs and even if we ever get quantum computers will be limited in what they can do.

LLMs, without pattern matching, can only do up to about integer division, and while they can calculate parity, they can't use it in their calculations.

There are several groups sitting on what are known limitations of LLMs, waiting to take advantage of those who don't understand the fundamental limitations, simplicity bias etc...

The hype will meet reality soon and we will figure out where they work and where they are problematic over the next few years.

But even the most celebrated achievements like proof finding with Lean, heavily depends on smart people producing hints that machines can use.

Basically lots of the fundamental hints of the limits of computation still hold.

Model logic may be an accessable way to approach the limits of statistical inference if you want to know one path yourself.

A lot of what is in this article relates to some the known fundamental limitations.

Remember that for all the amazing progress, one of the core founders of the perceptron, Pitts drank him self to death in the 50s because it was shown that they were insufficient to accurately model biological neurons.

Optimism is high, but reality will hit soon.

So think of it as new tools that will be available to your child, not a replacement.

Re: Can AI do maths yet? Thoughts from a mathematician

#154

Post by red75prime »

lupire wrote: post #131
red75prime wrote: post #85

Earlier quoted context omitted.

> there is no reason to believe a connection between the mechanical model and what happens in organisms has been established The universal approximation theorem. And that's basically it. The rest is empirical. No matter which physical processes happen inside the human brain, a sufficiently large neural network can approximate them. Barring unknowns like super-Turing computational processes in the brain.

That's not useful by itself, because "anything cam model anything else" doesn't put any upper bound on emulation cost, which for one small task could be larger than the total energy available in the entire Universem

Either the brain violates the physical Church-Turing thesis or it's not.

If it does, well, it will take more time to incorporate those physical mechanisms into computers to get them on par with the brain.

I leave the possibility that it's "magic"[1] aside. It's just impossible to predict, because it will violate everything we know about our physical world.

[1] One example of "magic": we live in a simulation and the brain is not fully simulated by the physics engine, but creators of the simulation for some reason gave it access to computational resources that are impossible to harness using the standard physics of the simulated world. Another example: interactionistic soul.

Re: Can AI do maths yet? Thoughts from a mathematician

#156

Post by bongodongobob »

Radim wrote: post #150
deepsun wrote: post #142

Earlier quoted context omitted.

By the way, don't trust Nobel laureates or even winners. E.g. Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel.

> don't trust Nobel laureates or even winners Nobel laureate and winner are the same thing. > Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel. Can you be more specific, what garbage? And which Nobel prize do you mean – Pauling got two, one for chemistry and one for peace.

Eugenics and vitamin C as a cure all.

Re: Can AI do maths yet? Thoughts from a mathematician

#157

Post by 0points »

> How much longer this will go on for nobody knows, but there are lots of people pouring lots of money into this game so it would be a fool who bets on progress slowing down any time soon.

Money cannot solve the issues faced by the industry which mainly revolves around lack of training data.

They already used the entirety of the internet, all available video, audio and books and they are now dealing with the fact that most content online is now generated by these models, thus making it useless as training data.

Re: Can AI do maths yet? Thoughts from a mathematician

#158

Post by bongodongobob »

GuB-42 wrote: post #136
glimshe wrote: post #27

Earlier quoted context omitted.

Isn't Wolfram Alpha a better "ChatGPT of Math"?

Wolfram Alpha can solve equations well, but it is terrible at understanding natural language. For example I asked Wolfram Alpha "How heavy a rocket has to be to launch 5 tons to LEO with a specific impulse of 400s", which is a straightforward application of the Tsiolkovsky rocket equation. Wolfram Alpha gave me some nonsense about particle physics (result: 95 MeV/c^2), GPT-4o did it right (result: 53.45 tons). Wolfra…

You're using it wrong, you can use natural language in your equation, but afaik it's not supposed to be able to do what you're asking of it.

Re: Can AI do maths yet? Thoughts from a mathematician

#159

Post by deepsun »

Radim wrote: post #150
deepsun wrote: post #142

Earlier quoted context omitted.

By the way, don't trust Nobel laureates or even winners. E.g. Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel.

> don't trust Nobel laureates or even winners Nobel laureate and winner are the same thing. > Linus Pauling was talking absolute garbage, harmful and evil, after winning the Nobel. Can you be more specific, what garbage? And which Nobel prize do you mean – Pauling got two, one for chemistry and one for peace.

Thank you, my bad.

I was referring to Linus's harmful and evil promotion of Vitamin C as the cure for everything and cancer. I don't think Linus was attaching that garbage to any particular Nobel prize. But people did say to their doctors: "Are you a Nobel winner, doctor?". Don't think they cared about particular prize either.

Re: Can AI do maths yet? Thoughts from a mathematician

#160

Post by cruffle_duffle »

alphan0n wrote: post #64

As far as ChatGPT goes, you may as well be asking: Can AI use a calculator? The answer is yes, it can utilize a stateful python environment and solve complex mathematical equations with ease.

It still has to know what to code in that environment. And based on my years of math as a wee little undergrad, the actual arithmetic was the least interesting part. LLM’s are horrible at basic arithmetic, but they can use python for the calculator. But python wont help them write the correct equations or even solve for the right thing (wolfram alpha can do a bit of that though)
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