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"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 ab

"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 a hit in three weeks. Internet search has shortened this turnaround. One instead needs to guess what someone else might call an idea. "Broken circuits?" Score! Still, time consuming. I went all in on ChatGPT after hearing that Terry Tao had learned the Lean 4 proof assistant in a matter of weeks, relying heavily on AI advice. It's clumsy, but a very fast way to get suggestions. Now, one can hold involved conversations with ChatGPT or Claude, exploring mathematical ideas. AI is often wrong, never knows when it's wrong, but people are like this too. Read how the insurance incidents for self-driving taxis are well below the human incident rates? Talking to fellow mathematicians can be frustrating, and so is talking with AI, but AI conversations go faster and can take place in the middle of the night. I don't want AI to prove theorems for me, those theorems will be as boring as most of the dreck published by humans. I want AI to inspire bursts of creativity in humans.

ninetyninenine 2y ago
Your optimism should be tempered with the downside of progress meaning that AI in the near future may not only inspire creativity in humans, but it can replace human creativity all together. Why do I need to hire an artist for my movie/video game/advertisement when AI can replicate all the creativity I need.
- wnc3141 2y ago
  There is research on AI limiting creative output in completive arenas. Essentially it breaks expectancy therefore deteriorates iteration. https://direct.mit.edu/rest/article-abstract/102/3/583/96779/Creativity-Under-Fire-The-Effects-of-Competition?redirectedFrom=fulltext https://direct.mit.edu/rest/article-abstract/102/3/583/96779...
- immibis 2y ago
  This was about mathematics.
  - ninetyninenine 2y ago
    Creativity isn’t limited to mathematics. My examples just didn’t use mathematicians.
- afroboy 2y ago
  Why do i need you as director if can ask AI to make movie for me?
  - ninetyninenine 2y ago
    you dont. that's my point. Probably don't even need the person who hires the director.
didibus 2y ago
I think I'm missing your point? You still want to enjoy doing math yourself? Is that what you are saying? So you equate "Can AI do math in my place?" with "Can AI drink and watch TV in my place?"
- bubble12345 2y ago
  AI will not do math for us, but maybe eventually it will lead to another mainstream tool for mathematicians. Along with R, Matlab, Sage, GAP, Magma, ... It would be interesting if in the future mathematicians are just as fluent in some (possibly AI-powered) proof verifying tool, as they are with LaTeX today.
  - bufferoverflow 2y ago
    AI can already do a bunch of math. So "AI will not do math for us" is just factually wrong.
    - fooker 2y ago
      Your idea of ‘do math’ is a bit different from this context. Here it means do math research or better, find new math.
    - vlovich123 2y ago
      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 years? Very likely. 100 years? None of us here will be alive to be proven wrong but I’ll venture that that’s a certainty.
      - khafra 2y ago
        This is a pretty strong position to take in the comments of a post where a mathematician declared the 5 problems he'd seen to be PhD level, and speculated that the real difficulty with switching from numerical answers to proofs will be finding humans qualified to judge the AI's answers. I will agree that it's likely none of us here will be alive to be proven wrong, but that's in the 1 to 10 year range.
amanda99 2y ago
> 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 time would a good researcher be confidently wrong in a way that ChatGPT is often. In other words, ChatGPT completely lacks the meta-layer of "having a feeling/knowing how confident it is", which is so useful in research.
- portaouflop 2y ago
  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 2y ago
    [deleted]
  - rednerrus 2y ago
    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."
  - amanda99 2y ago
    I think you are imagining a different class of "questions". To clarify, I was doing research on applied math. My field is not analysis, but I needed to prove some bounds on certain messed up expressions (involving special functions, etc), and analyze an ODE that's not analytically solvable. I used the COT model a fair bit. I would ask ChatGPT for hints/ideas/direction in proving various bounds, asking it for theorems or similar results in literature. This is exactly the kind of thing where a researcher would go "yeah this looks like X" or "I think I saw something like this in (book/article name)", or just know a method; or alternatively say they have no clue. ChatGPT most often will confidently give me a "solution", being right 10% of the time (when there's a pretty standard way to do it that I didn't see/know). On the whole it was quite useful.
heresie-dabord 2y ago
> Talking to fellow <humans> can be frustrating, and so is talking with AI, but AI conversations go faster and can take place in the middle of the night. I made a slight change to generalise your statement, I think you have summarised the actual marketing opportunity.
eleveriven 2y ago
The analogy with self-driving cars is spot on
deleted 2y ago
[deleted]
pontus 2y ago
I agree. I think it comes down to the motivation behind why one does mathematics (or any other field for that matter). If it's a means to an end, then sure have the AI do the work and get rid of the researchers. However, that's not why everyone does math. For many it's more akin to why an artist paints. People still paint today even though a camera can produce much more realistic images. It was probably the case (I'm guessing!) that there was a significant drop in jobs for artists-for-hire, for whom painting was just a means to an end (e.g. creating a portrait), but the artists who were doing it for the sake of art survived and were presumably made better by the ability to see photos of other places they want to paint or art from other artists due to the invention of the camera.
goalieca 2y ago
> 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. Improved tooling and techniques have given humans the free time and resources needed for arts, culture, philosophy, sports, and spending time to enjoy life! Fancy telecom technologies have allowed me to work from home and i love it :)
rfurmani 2y ago
Absolutely agree. There's some interesting articles in a recent [AMS Bulletin](https://www.ams.org/journals/bull/2024-61-02/home.html?active=allissues 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 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.

ninetyninenine 2y ago

Your optimism should be tempered with the downside of progress meaning that AI in the near future may not only inspire creativity in humans, but it can replace human creativity all together. Why do I need to hire an artist for my movie/video game/advertisement when AI can replicate all the creativity I need.

wnc3141 2y ago
There is research on AI limiting creative output in completive arenas. Essentially it breaks expectancy therefore deteriorates iteration. https://direct.mit.edu/rest/article-abstract/102/3/583/96779/Creativity-Under-Fire-The-Effects-of-Competition?redirectedFrom=fulltext https://direct.mit.edu/rest/article-abstract/102/3/583/96779...
immibis 2y ago
This was about mathematics.
- ninetyninenine 2y ago
  Creativity isn’t limited to mathematics. My examples just didn’t use mathematicians.
afroboy 2y ago
Why do i need you as director if can ask AI to make movie for me?
- ninetyninenine 2y ago
  you dont. that's my point. Probably don't even need the person who hires the director.

didibus 2y ago

I think I'm missing your point? You still want to enjoy doing math yourself? Is that what you are saying? So you equate "Can AI do math in my place?" with "Can AI drink and watch TV in my place?"

bubble12345 2y ago
AI will not do math for us, but maybe eventually it will lead to another mainstream tool for mathematicians. Along with R, Matlab, Sage, GAP, Magma, ... It would be interesting if in the future mathematicians are just as fluent in some (possibly AI-powered) proof verifying tool, as they are with LaTeX today.
- bufferoverflow 2y ago
  AI can already do a bunch of math. So "AI will not do math for us" is just factually wrong.
  - fooker 2y ago
    Your idea of ‘do math’ is a bit different from this context. Here it means do math research or better, find new math.
  - vlovich123 2y ago
    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 years? Very likely. 100 years? None of us here will be alive to be proven wrong but I’ll venture that that’s a certainty.
    - khafra 2y ago
      This is a pretty strong position to take in the comments of a post where a mathematician declared the 5 problems he'd seen to be PhD level, and speculated that the real difficulty with switching from numerical answers to proofs will be finding humans qualified to judge the AI's answers. I will agree that it's likely none of us here will be alive to be proven wrong, but that's in the 1 to 10 year range.

amanda99 2y ago

> 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 time would a good researcher be confidently wrong in a way that ChatGPT is often. In other words, ChatGPT completely lacks the meta-layer of "having a feeling/knowing how confident it is", which is so useful in research.

portaouflop 2y ago
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 2y ago
  [deleted]
- rednerrus 2y ago
  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."
- amanda99 2y ago
  I think you are imagining a different class of "questions". To clarify, I was doing research on applied math. My field is not analysis, but I needed to prove some bounds on certain messed up expressions (involving special functions, etc), and analyze an ODE that's not analytically solvable. I used the COT model a fair bit. I would ask ChatGPT for hints/ideas/direction in proving various bounds, asking it for theorems or similar results in literature. This is exactly the kind of thing where a researcher would go "yeah this looks like X" or "I think I saw something like this in (book/article name)", or just know a method; or alternatively say they have no clue. ChatGPT most often will confidently give me a "solution", being right 10% of the time (when there's a pretty standard way to do it that I didn't see/know). On the whole it was quite useful.

heresie-dabord 2y ago

> Talking to fellow <humans> can be frustrating, and so is talking with AI, but AI conversations go faster and can take place in the middle of the night. I made a slight change to generalise your statement, I think you have summarised the actual marketing opportunity.

eleveriven 2y ago

The analogy with self-driving cars is spot on

deleted 2y ago

[deleted]

pontus 2y ago

I agree. I think it comes down to the motivation behind why one does mathematics (or any other field for that matter). If it's a means to an end, then sure have the AI do the work and get rid of the researchers. However, that's not why everyone does math. For many it's more akin to why an artist paints. People still paint today even though a camera can produce much more realistic images. It was probably the case (I'm guessing!) that there was a significant drop in jobs for artists-for-hire, for whom painting was just a means to an end (e.g. creating a portrait), but the artists who were doing it for the sake of art survived and were presumably made better by the ability to see photos of other places they want to paint or art from other artists due to the invention of the camera.

goalieca 2y ago

> 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. Improved tooling and techniques have given humans the free time and resources needed for arts, culture, philosophy, sports, and spending time to enjoy life! Fancy telecom technologies have allowed me to work from home and i love it :)

rfurmani 2y ago

Absolutely agree. There's some interesting articles in a recent [AMS Bulletin](https://www.ams.org/journals/bull/2024-61-02/home.html?active=allissues 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 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.