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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

#201

Post by hn3er1q »

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…

There are many similarities in your comment to how grandmasters discuss engines. I have a hunch the arc of AI in math will be very similar to the arc of engines in chess.

https://www.wired.com/story/defeated-chess-champ-garry-kaspa...

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

#202

Post by vouaobrasil »

zmgsabst wrote: post #151
vouaobrasil wrote: post #146

Earlier quoted context omitted.

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, wh…

Just a counterpoint, but I wonder how much you'll really understand if you can't even prove the whole thing yourself. Personally, I learn by proving but I guess everyone is different.

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

#203

Post by vouaobrasil »

hn3er1q wrote: post #201
vouaobrasil wrote: post #146

Earlier quoted context omitted.

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…

There are many similarities in your comment to how grandmasters discuss engines. I have a hunch the arc of AI in math will be very similar to the arc of engines in chess. https://www.wired.com/story/defeated-chess-champ-garry-kaspa...

I agree with that, in the sense that math will become more about who can use AI the fastest to generate the most theories, which sort of side-steps the whole point of math.

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

#204

Post by peterbonney »

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…

If you looked at how the average accountant spent their time before the arrival of the digital spreadsheet, you might have predicted that automated calculation would make the profession obsolete. But it didn't.

This time could be different, of course. But I'll need a lot more evidence before I start telling people to base their major life decisions on projected technological change.

That's before we even consider that only a very slim minority of the people who study math (or physics or statistics or biology or literature or...) go on to work in the field of math (or physics or statistics or biology or literature or...). AI could completely take over math research and still have next to impact on the value of the skills one acquires from studying math.

Or if you want to be more fatalistic about it: if AI is going to put everyone out of work then it doesn't really matter what you do now to prepare for it. Might as well follow your interests in the meantime.

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

#205

Post by hn3er1q »

vouaobrasil wrote: post #203
hn3er1q wrote: post #201

Earlier quoted context omitted.

There are many similarities in your comment to how grandmasters discuss engines. I have a hunch the arc of AI in math will be very similar to the arc of engines in chess. https://www.wired.com/story/defeated-chess-champ-garry-kaspa...

I agree with that, in the sense that math will become more about who can use AI the fastest to generate the most theories, which sort of side-steps the whole point of math.

As a chess aficionado and a former tournament player, who didn’t get very far, I can see pros & cons. They helped me train and get significantly better than I would’ve gotten without them. On the other hand, so did the competition. :) The average level of the game is so much higher than when I was a kid (30+ years ago) and new ways of playing that were unthinkable before are possible now. On the other hand cheating (online anyway) is rampant and all the memorization required to begin to be competitive can be daunting, and that sucks.

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

#206

Post by bongodongobob »

CamperBob2 wrote: post #184
bongodongobob wrote: post #158

Earlier quoted context omitted.

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.

You know, "You're using it wrong" is usually meant to carry an ironic or sarcastic tone, right? It dates back to Steve Jobs blaming an iPhone 4 user for "holding it wrong" rather than acknowledging a flawed antenna design that was causing dropped calls. The closest Apple ever came to admitting that it was their problem was when they subsequently ran an employment ad to hire a new antenna engineering lead. Maybe it's…

It's not an LLM. You're simply asking too much of it. It doesn't work the way you want it to, sorry.

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

#207

Post by watt »

asddubs wrote: post #14
aithrowawaycomm wrote: post #9

I am fairly optimistic about LLMs as a human math -> theorem-prover translator, and as a fan of Idris I am glad that the AI community is investing in Lean. As the author shows, the answer to "Can AI be useful for automated mathematical work?" is clearly "yes." But I am confident the answer to the question in the headline is "no, not for several decades." It's not just the underwhelming benchmark results discussed in…

it can take my math and point out a step I missed and then show me the correct procedure but still get the wrong result because it can't reliably multiply 2-digit numbers

it's a "language" model (LLM), not a "math" model. when it is generating your answer, predicting and outputing a word after word it is _not_ multiplying your numbers internally.

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

#208

Post by blagie »

peterbonney wrote: post #204
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…

If you looked at how the average accountant spent their time before the arrival of the digital spreadsheet, you might have predicted that automated calculation would make the profession obsolete. But it didn't. This time could be different, of course. But I'll need a lot more evidence before I start telling people to base their major life decisions on projected technological change. That's before we even consider tha…

It's important to base life decisions on very real technological change. We don't know what the change will be, but it's coming. At the very least, that suggests more diverse skills.

We're all usually (but not always) better off, with more productivity, eventually, but in the meantime, jobs do disappear. Robotics did not fully displace machinists and factory workers, but single-skilled people in Detroit did not do well. The loom, the steam engine... all of them displaced often highly-trained often low-skilled artisans.

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

#209

Post by vouaobrasil »

hn3er1q wrote: post #205
vouaobrasil wrote: post #203

Earlier quoted context omitted.

I agree with that, in the sense that math will become more about who can use AI the fastest to generate the most theories, which sort of side-steps the whole point of math.

As a chess aficionado and a former tournament player, who didn’t get very far, I can see pros & cons. They helped me train and get significantly better than I would’ve gotten without them. On the other hand, so did the competition. :) The average level of the game is so much higher than when I was a kid (30+ years ago) and new ways of playing that were unthinkable before are possible now. On the other hand cheating (…

Hey I play chess too. Not a very good player though. But to be honest, I enjoy playing with people who are not serious because I do think an overabundance of knowledge makes the game too mechanical. Just my personal experience, but I think the risk of cheaters who use programs and the overmechanization of chess is not worth becoming a better player. (And in fact, I think MOST people can gain satisfaction by improving just by studying books and playing. But I do think that a few who don't have access to opponents benefit from a chess-playing computer).

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

#210

Post by int_19h »

Someone wrote: post #187
beng-nl wrote: post #99

Earlier quoted context omitted.

It’s that a bit of an unfair sabotage? Naturally, humans couldn’t do it, even though they could edit the input to remove the X’s, but shouldn’t we evaluate the ability (even intelligent ability) of LLM’s on what they can generally do rather than amplify their weakness?

Why is that unfair in reply to the claim “At this stage I assume everything having a sequencial pattern can and will be automated by LLM AIs.” ? I am not claiming LLMs aren’t or cannot be intelligent, not even that they cannot do magical things; I just rebuked a statement about the lack of limits of LLMs. > Naturally, humans couldn’t do it, even though they could edit the input to remove the X’s So, what are you clai…

If you have a million Xs on the end of each line, when a human is looking at that file, he's not looking at the entirety of it, but only at the part that is actually visible on-screen, so the equivalent task for an LLM would be to feed it the same subset as input. In which case they can all answer this question just fine.
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