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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

#321

Post by rednerrus »

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

It's pretty easy to test when it makes coding mistakes as well. It's also really good at "Hey that didn't work, here's my error message."

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

#322

Post by advisedwang »

4ad wrote: post #57

> FrontierMath is a secret dataset of “hundreds” of hard maths questions, curated by Epoch AI, and announced last month. The database stopped being secret when it was fed to proprietary LLMs running in the cloud. If anyone is not thinking that OpenAI has trained and tuned O3 on the "secret" problems people fed to GPT-4o, I have a bridge to sell you.

It's perfectly possible for OpenAI to run the model (or prove others the means to run it) without storing queries/outputs for future. I expect Epoch AI would insist on this. Perhaps OpenAI would lie about it, but that's opening up serious charges.

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

#323

Post by cheald »

jampekka wrote: post #19

I just spent a few days trying to figure out some linear algebra with the help of ChatGPT. It's very useful for finding conceptual information from literature (which for a not-professional-mathematician at least can be really hard to find and decipher). But in the actual math it constantly makes very silly errors. E.g. indexing a vector beyond its dimension, trying to do matrix decomposition for scalars and insisting…

LLMs have been very useful for me in explorations of linear algebra, because I can have an idea and say "what's this operation called?" or "how do I go from this thing to that thing?", and it'll give me the mechanism and an explanation, and then I can go read actual human-written literature or documentation on the subject.

It often gets the actual math wrong, but it is good enough at connecting the dots between my layman's intuition and the "right answer" that I can get myself over humps that I'd previously have been hopelessly stuck on.

It does make those mistakes you're talking about very frequently, but once I'm told that the thing I'm trying to do is achievable with the Gram-Schmidt process, I can go self-educate on that further.

The big thing I've had to watch out for is that it'll usually agree that my approach is a good or valid one, even when it turns out not to be. I've learned to ask my questions in the shape of "how do I", rather than "what if I..." or "is it a good idea to...", because most of the time it'll twist itself into shapes to affirm the direction I'm taking rather than challenging and refining it.

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

#324

Post by cheald »

threeseed wrote: post #240
dns_snek wrote: post #137

Earlier quoted context omitted.

What evidence do we need that AI companies are exploiting every bit of information they can use to get ahead in the benchmarks to generate more hype? Ignoring terms/agreements, violating copyright, and otherwise exploiting information for personal gain is the foundation of that entire industry for crying out loud.

Some people are also forgetting who is the CEO of OpenAI. Sam Altman has long talked about believing in the "move fast and break things" way of doing business. Which is just a nicer way of saying do whatever dodgy things you can get away with.

OpenAI's also in the position of having to compete against other LLM trainers - including the open-weights Llama models and their community derivatives, which have been able to do extremely well with a tiny fraction of OpenAI's resources - and to justify their astronomical valuation. The economic incentive to cheat is extreme; I think that cheating has to be the default presumption.

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

#325

Post by whimsicalism »

FiberBundle wrote: post #308
whimsicalism wrote: post #305

Earlier quoted context omitted.

Ingredients to a top HN comment on AI include some nominal expert explaining why actually labor won’t be replaced and it will be a collaborative process so you don’t need to worry sprinkled with a little bit of ‘the status quo will stay still even though this tech only appeared in the last 2 years’

It didn't appear in the last two years. We have had deep learning based autoregressive language models (like Word2Vec) for at least 10 years.

totally, and i’ve been working with attention since at least 2017. but i’m colloquially referring to the real breakout and substantial scale up in resources being thrown at it

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

#326

Post by qnleigh »

hyhconito wrote: post #186
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…

Let's put it this way, from another mathematician, and I'm sure I'll probably be shot for this one. Every LLM release moves half of the remaining way to the minimum viable goal of replacing a third class undergrad. If your business or research initiative is fine with that level of competence then you will find utility. The problem is that I don't know anyone who would find that useful. Nor does it fit within any exis…

I think there's a pretty good case to be made that LLMs paired with automated theorem provers will become a useful tool to working mathematicians in the next few years. Another thread here links to a lecture from a professor of mathematics who makes this point about halfway in, based solely on Alpha Proofs current abilities (https://www.youtube.com/watch?v=vYCT7cw0ycw [54min]). Terence Tao, well-known mathematician at UCLA has been saying similar things for years. He's blogged about LLMs helping to learn new tools (like Lean) and occasionally helping with brainstorming.

At this stage, the point they're making isn't 'OMG AGI!!!' but rather something like 'having an enthusiastic, often wrong undergrad assistant who's available 24/7 can be useful, if you use it carefully.'

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

#327

Post by qnleigh »

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…

Highly recommend this lecture by a working mathematician shared above (https://www.youtube.com/watch?v=vYCT7cw0ycw [54min]). It's very much grounded in history and experience, much more so than in speculation. I wrote a brief summary of some main points in that thread.

But specifically to your worry about humans just dotting i's and crossing t's, he predicts that exactly the opposite will happen. At the end he emphasizes that the ultimate goal of mathematics is more about human understanding than proving theorems.

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

#328

Post by rfurmani »

Syzygies wrote: post #247

"Can AI do math for us" is the canonical wrong question. People want self-driving cars so they can drink and watch TV. We should crave tools that enhance our abilities, as tools have done since prehistoric times. I'm a research mathematician. In the 1980's I'd ask everyone I knew a question, and flip through the hard bound library volumes of Mathematical Reviews, hoping to recognize something. If I was lucky, I'd get…

Absolutely agree. There's some interesting articles in a recent [AMS Bulletin](https://www.ams.org/journals/bull/2024-61-02/home.html?activ...) giving perspectives on this question: what does it do to math if there's a strong theorem prover out there, in what ways can AI help mathematicians, what is math exactly?

I find that a lot of AI+Math work is focused on the end game where you have a clear problem to solve, rather than the early exploratory work where most of the time is spent. The challenge is in making the right connections and analogies, discovering hidden useful results, asking the right questions, translating between fields.

I'm getting ready to launch [Sugaku](https://sugaku.net), where I'm trying to build tools for the above, based on processing the published math literature and training models on it. The kind of search of MR that you mentioned doing is exactly what a computer should do instead. I can create an account for you and would love some feedback.

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

#329

Post by mdp2021 »

casenmgreen wrote: post #80
mdp2021 wrote: post #54

Earlier quoted context omitted.

> AI is basically Very many things conventionally labelled in the 50's. You are speaking of LLMs.

Yes - I mean only to say "AI" as the term is commonly used today.

> as the term is commonly used today

Which is, wrongly: so, don't spread the bad notion and habit.

Bad notion and habit which has a counter-helpful impact on debate.

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

#330

Post by busyant »

qnleigh wrote: post #327
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…

Highly recommend this lecture by a working mathematician shared above ( https://www.youtube.com/watch?v=vYCT7cw0ycw [54min]). It's very much grounded in history and experience, much more so than in speculation. I wrote a brief summary of some main points in that thread. But specifically to your worry about humans just dotting i's and crossing t's, he predicts that exactly the opposite will happen. At the end he empha…

Thank you.
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