Can AI do maths yet? Thoughts from a mathematician • Hacker News Board

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

#291

Post by vouaobrasil » Tue, Dec 24, 2024, 10:45 AM UTC

sourcepluck wrote: post #241

vouaobrasil wrote: post #130

My favourite moments of being a graduate student in math was showing my friends (and sometimes professors) proofs of propositions and theorems that we discussed together. To be the first to put together a coherent piece of reasoning that would convince them of the truth was immensely exciting. Those were great bonding moments amongst colleagues. The very fact that we needed each other to figure out the basics of the…

> Now, all of that will be done by AI. No "AI" of any description is doing novel proofs at the moment. Not o3, or anything else. LLMs are good for chatting about basic intuition with, up to and including complex subjects, if and only if there are publically available data on the topic which have been fed to the LLM during its training. They're good at doing summaries and overviews of specific things (if you push them…

I am talking about in 20-30 years.

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

#292

Post by reshlo » Tue, Dec 24, 2024, 11:12 AM UTC

sebzim4500 wrote: post #285

reshlo wrote: post #177

Earlier quoted context omitted.

Citation needed.

Which bit do you need a citation for? I can run the experiment in 10 mins.

> That's the equivalent to what we are asking the model to do.

Why?

What does it mean to give a model a calculator?

What do you mean “let it show its working”? If I ask an LLM to do a calculation, I never said it can’t express the answer to me in long-form text or with intermediate steps.

If I ask a human to do a calculation that they can’t reliably do in their head, they are intelligent enough to know that they should use a pen and paper without needing my preemptive permission.

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

#293

Post by Sparkyte » Tue, Dec 24, 2024, 11:52 AM UTC

After playing with and using AI for almost two years now it is not getting better from both a cost perspective and performance.

So the higher the cost the better the performance. While models and hardware can be improved the curve is still steep.

The big answer is what are people using it for? We'll they are using lightweight simplistic models to do targeted tasks. To do many smaller and easier to process tasks.

Most of the news on AI is just there to promote a product to earn more cash.

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

#294

Post by Sparkyte » Tue, Dec 24, 2024, 11:54 AM UTC

eleveriven wrote: post #276

amanda99 wrote: post #266

Earlier quoted context omitted.

> AI is often wrong, never knows when it's wrong, but people are like this too. When talking with various models of ChatGPT about research math, my biggest gripe is that it's either confidently right (10% of my work) or confidently wrong (90%). A human researcher would be right 15% of the time, unsure 50% of the time, and give helpful ideas that are right/helpful (25%) or wrong/a red herring (10%). And only 5% of the…

Do you think there’s potential for AI to develop a kind of probabilistic reasoning?

It think it is every sci-fiction dreamer to teach a robot to love.

I don't think AI will think conventionally. It isn't thinking to begin with. It is weighing options. Those options permutate and that is why every response is different.

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

#295

Post by [deleted] » Tue, Dec 24, 2024, 12:16 PM UTC

vlovich123 wrote: post #264

bufferoverflow wrote: post #259

Earlier quoted context omitted.

AI can already do a bunch of math. So "AI will not do math for us" is just factually wrong.

Can AI solve “toy” math problems that computers have not been able to do? Yes. Can AI produce novel math research? No, it hasn’t yet. So “AI will not do math for us” is only factually wrong if you take the weaker definition of “doing math for us”. The stronger definition is not factually wrong yet. More problematic with that statement is that a timeline isn’t specified. 1 year? Probably not. 10 years? Probably. 20 ye…

[deleted]

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

#296

Post by orbital-decay » Tue, Dec 24, 2024, 1:39 PM UTC

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…

This is only easy because the software does line wrapping for you, mechanistically transforming the hard pattern of millions of symbols into another that happens to be easy for your visual system to match. Do the same for any visually capable model and it will get that easily too. Conversely, make that a single line (like the one transformers sees) and you will struggle much more than the transformer because you'll have to scan millions of symbols sequentially looking for patterns.

Humans have weak attention compared to it, this is a poor example.

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

#297

Post by [deleted] » Tue, Dec 24, 2024, 1:43 PM UTC

portaouflop wrote: post #271

amanda99 wrote: post #266

Earlier quoted context omitted.

> AI is often wrong, never knows when it's wrong, but people are like this too. When talking with various models of ChatGPT about research math, my biggest gripe is that it's either confidently right (10% of my work) or confidently wrong (90%). A human researcher would be right 15% of the time, unsure 50% of the time, and give helpful ideas that are right/helpful (25%) or wrong/a red herring (10%). And only 5% of the…

A human researcher that is basically right 40%-95% of the time would probably an Einstein level genius. Just assume that the LLM is wrong and test their assumptions - math is one of the few disciplines where you can do that easily

[deleted]

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

#298

Post by aomix » Tue, Dec 24, 2024, 2:05 PM UTC

No comment on the article it's just always interesting to get hit with intense jargon from a field I know very little about.

I understood the statements of all five questions. I could do the third one relatively quickly (I had seen the trick before that the function mapping a natural n to alpha^n was p-adically continuous in n iff the p-adic valuation of alpha-1 was positive)

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

#299

Post by ccppurcell » Tue, Dec 24, 2024, 2:07 PM UTC

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…

The mathematicians of the future will still have to figure out the right questions, even if llms can give them the answers. And "prompt engineering" will require mathematical skills, at the very least.

Evaluating the output of llms will also require mathematical skills.

But I'd go further, if your son enjoys mathematics and has some ability in the area, it's wonderful for your inner life. Anyone who becomes sufficiently interested in anything will rediscover mathematics lurking at the bottom.

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

#300

Post by fire_lake » Tue, Dec 24, 2024, 2:17 PM UTC

exprofmaddy wrote: post #143

tananan wrote: post #89

Earlier quoted context omitted.

> Unless you believe in determinism and an overseeing god Or perhaps, determinism and mechanistic materialism - which in STEM-adjacent circles has a relatively prevalent adherence. Worldviews which strip a human being of agency in the sense you invoke crop up quite a lot today in such spaces. If you start of adopting a view like this, you have a deflationary sword which can cut down most any notion that's not mechani…

Agreed. If someone believes the world is purely mechanistic, then it follows that a sufficiently large computing machine can model the world---like Leibniz's Ratiocinator. The intoxication may stem from the potential for predictability and control. The irony is: why would someone want control if they don't have true choice? Unfortunately, such a question rarely pierces the intoxicated mind when this mind is preoccupi…

> Agreed. If someone believes the world is purely mechanistic, then it follows that a sufficiently large computing machine can model the world---like Leibniz's Ratiocinator.

I don’t think it does. Taking computers as an analogy… if you have a computer with 1GB memory, then you can’t simulate a computer with more than 1GB memory inside of it.