6 ms·

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 th

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 still moved the field forward in my own small ways. I still did respectable work. So, will these LLMs make us completely obsolete? Or will there still be room for those of us who can dot the "i"?--if only for the fact that LLMs don't have infinite time/resources to solve "everything." I don't know. Maybe I'm whistling past the graveyard.

deepsun 2y ago
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.
- Radim 2y ago
  > 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.
  - bongodongobob 2y ago
    Eugenics and vitamin C as a cure all.
    - lern_too_spel 2y ago
      If Pauling's eugenics policies were bad, then the laws against incest that are currently on the books in many states (which are also eugenics policies that use the same mechanism) are also bad. There are different forms of eugenics policies, and Pauling's proposal to restrict the mating choices of people carrying certain recessive genes so their children don't suffer is ethically different from Hitler exterminating people with certain genes and also ethically different from other governments sterilizing people with certain genes. He later supported voluntary abortion with genetic testing, which is now standard practice in the US today, though no longer in a few states with ethically questionable laws restricting abortion. This again is ethically different from forced abortion. https://scarc.library.oregonstate.edu/coll/pauling/blood/narrative/page35.html https://scarc.library.oregonstate.edu/coll/pauling/blood/nar...
      - bongodongobob 2y ago
        From what I remember, he wanted to mark people with tattoos or something.
        lern_too_spel 2y ago
        This is mentioned in my link: "According to Pauling, carriers should have an obvious mark, (i.e. a tattoo on the forehead) denoting their disease, which would allow carriers to identify others with the same affliction and avoid marrying them." The goal wasn't to mark people for ostracism but to make it easier for people carrying these genes to find mates that won't result in suffering for their offspring.
      - voltaireodactyl 2y ago
        FWIW my understanding is that the policies against incest you mention actually have much less to do with controlling genetic reproduction and are more directed at combating familial rape/grooming/etc. Not a fun thing to discuss, but apparently a significant issue, which I guess should be unsurprising given some of the laws allowing underage marriage if the family signs off. Mentioning only to draw attention to the fact that theoretical policy is often undeniable in a vacuum, but runs aground when faced with real world conditions.
  - deepsun 2y ago
    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.
    - red75prime 2y ago
      > Linus's harmful and evil promotion of Vitamin C Which is "harmful and evil" thanks to your afterknowledge. He had based his books on the research that failed to replicate. But given low toxicity of vitamin C it's not that "evil" to recommend treatment even if probabilistic estimation of positive effects is not that high. Sloppy, but not exceptionally bad. At least it was instrumental in teaching me to not expect marvels coming from dietary research.
pfisherman 2y ago
I used to do bench top work too; and was blessed with “the golden hands” in that I could almost always get protocols working. To me this always felt more like intuition than deductive reasoning. And it made me a terrible TA. My advice to students in lab was always something along the lines of “just mess around with it, and see how it works.” Not very helpful for the stressed and struggling student -_- Digression aside, my point is that I don’t think we know exactly what makes or defines “the golden hands”. And if that is the case, can we optimize for it? Another point is that scalable fine tuning only works for verifiable stuff. Think a priori knowledge. To me that seems to be at the opposite end of the spectrum from “mess with it and see what happens”.
- busyant 2y ago
  > blessed with “the golden hands” in that I could almost always get protocols working. Very funny. My friends and I never used the phrase "golden hands" but we used to say something similar: "so-and-so has 'great hands'". But it meant the same thing. I, myself, did not have great hands, but my comment was more about the intellectual process of conducting research. I guess my point was that: * I've already dealt with more talented researchers, but I still contributed meaningfully. * Hopefully, the "AI" will simply add another layer of talent, but the rest of us lesser mortals will still be able to contribute. But I don't know if I'm correct.
vouaobrasil 2y ago
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 precisely that it was a journey of human intellect. As I said elsewhere, my friends used to ask me why something was true and it was fun to explain it to them, or ask them and have them explain it to me. Now most will just use some AI. Soulless, in my opinion. Pure mathematics should be about the art of the thing, not producing results on an assembly line like it will be with AI. Of course, the best mathematicians are going into this because it helps their current careers, not because it helps the future of the subject. Math done with AI will be a lot like Olympic running done with performance-enhancing drugs. Yes, we will get a few more results, faster. But the results will be entirely boring.
- zmgsabst 2y ago
  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.
  - ndriscoll 2y ago
    Even current people will feel differently. I don't bemoan the fact that Lean/Mathlib has `simp` and `linarith` to automate trivial computations. A "copilot for Lean" that can turn "by induction, X" or "evidently Y" into a formal proof sounds great. The the trick is teaching the thing how high powered of theorems to use or how to factor out details or not depending on the user's level of understanding. We'll have to find a pedagogical balance (e.g. you don't give `linarith` to someone practicing basic proofs), but I'm sure it will be a great tool to aid human understanding. A tool to help translate natural language to formal propositions/types also sounds great, and could help more people to use more formal methods, which could make for more robust software.
nyrikki 2y ago
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.
- ComplexSystems 2y ago
  "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." - what do you mean by this? Counting the number of 1's in a bitstring and determining if it's even or odd?
  - nyrikki 2y ago
    Yes, in this case PARITY is determining if the number of 1s in a binary input is odd or even It is an effect of the complex to unpack descriptive complexity class DLOGTIME-uniform TC0, which has AND, OR and MAJORITY gates. http://arxiv.org/abs/2409.13629 http://arxiv.org/abs/2409.13629 The point being that the ability to use parity gates is different than being able to calculate it, which is where the union of the typically ram machine DLOGTIME with the circuit complexity of uniform TC0 comes into play. PARITY, MAJ, AND, and OR are all symmetric, and are in TCO, but PARITY is not in DLOGTIME-uniform TC0, which is first-order logic with Majority quantifiers. Another path, if you think about symantic properties and Rice's theorem, this may make sense especially as PAC learning even depth 2 nets is equivalent to the approximate SVP. PAC-learning even depth-2 threshold circuits is NP-hard. https://www.cs.utexas.edu/~klivans/crypto-hs.pdf https://www.cs.utexas.edu/~klivans/crypto-hs.pdf For me thinking about how ZFC was structured so we can keep the niceties of the law of the excluded middle, and how statistics pretty much depends on it for the central limit and law of large numbers, IID etc... But that path runs the risk of reliving the Brouwer–Hilbert controversy.
TheRealPomax 2y ago
What part do you think is going to become obsolete? Because Math isn't about "working out the math", it's about finding the relations between seemingly unrelated things to bust open a problem. Short of AGI, there is no amount of neural net that's going to realize that a seemingly impossible probabilistic problem is actually equivalent to a projection of an easy to work with 4D geometry. "Doing the math" is what we have computers for, and the better they get, the easier the tedious parts of the job become, but "doing math" is still very much a human game.
- busyant 2y ago
  > What part do you think is going to become obsolete? Thank you for the question. I guess what I'm saying is: Will LLMs (or whatever comes after them) be _so_ good and _so_ pervasive that we will simply be able to say, "Hey ChatGPT-9000, I'd like to see if the xyz conjecture is correct." And then ChatGPT-9000 just does the work without us contributing beyond asking a question. Or will the technology be limited/bound in some way such that we will still be able to use ChatGPT-9000 as a tool of our own intellectual augmentation and/or we could still contribute to research even without it. Hopefully, my comment clarifies my original post. Also, writing this stuff has helped me think about it more. I don't have any grand insight, but the more I write, the more I lean toward the outcome that these machines will allow us to augment our research.
  - TheRealPomax 2y ago
    As amazing as they may seem, they're still just autocompletes, it's inherent to what an LLM is. So unless we come up with a completely new kind technology, I don't see "test this conjecture for me" becoming more real than the computer assisted proof tooling we already have.
hyhconito 2y ago
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 existing working methodology we have. And on top of that the verification of any output can take considerably longer than just doing it yourself in the first place, particularly where it goes off the rails, which it does all the time. I mean it was 3 months ago I was arguing with a model over it not understanding place-value systems properly, something we teach 7 year olds here? But the abstract problem is at a higher level. If it doesn't become a general utility for people outside of mathematics, which is very very evident at the moment by the poor overall adoption and very public criticism of the poor result quality, then the funding will dry up. Models cost lots of money to train and if you don't have customers it's not happening and no one is going to lend you the money any more. And then it's moot.
- binarymax 2y ago
  This is a great point that nobody will shoot you over :) But the main question is still: assuming you replace an undergrad with a model, who checks the work? If you have a good process around that already, and find utility as an augmented system, then get you’ll get value - but I still think it’s better for the undergrad to still have the job and be at the wheel, and does things faster and better when leveraging a powerful tool.
  - hyhconito 2y ago
    Shot already for criticising the shiny thing (happened with crypto and blockchain already...) Well to be fair no one checks what the graduates do properly, even if we hired KPMG in. That is until we get sued. But at least we have someone to blame then. What we don't want is something for the graduate to blame. The buck stops at someone corporeal because that's what the customers want and the regulators require. That's the reality and it's not quite as shiny and happy as the tech industry loves to promote itself. My main point, probably cleared up with a simple point: no one gives a shit about this either way.
peterbonney 2y ago
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.
- blagie 2y ago
  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.
  - rafaelmn 2y ago
    If AI reaches this level socioeconomic impact is going to be so immense, that choosing what subject you study will have no impact on your outcome - no matter what it is - so it's a pointless consideration.
    - blagie 2y ago
      That's just about the silliest thing I've read in a long time. We've had changes before, the most recent one being the rise of computers and then the internet, and before that, manufacturing automation. In all cases, some people were better prepared for change, and some less so. The general consensus is that diverse skills and foundational skills (e.g. math, communication) best prepare people for transitions, relative to specialized skills (e.g. one technology). In addition, many careers are likely to be less impacted, such as plumbing.
bawolff 2y ago
I doubt it. Most likely AI will be good at some things and not others, and mathematicians will just move to whatever AI isn't good at. Alternatively, if AI is able to do all math at a level above PhDs, then its going to be a brave new world and basically the singularity. Everything will change so much that speculating about it will probably be useless.
ykonstant 2y ago
> I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". (｡•́︿•̀｡)
- busyant 2y ago
  > (｡•́︿•̀｡) Don't cry for me, (Argentina). When "God" tells you that you're merely dotting "i"s and crossing "t"s ... he's kind of correct. But I was arrogant enough to believe that I was still a good researcher. I just wasn't "God."
ccppurcell 2y ago
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.
jvvw 2y ago
Another PhD in maths here and I would say not to worry. It's the process of doing and understanding mathematics, and thinking mathematically that is ultimately important. There's never been the equivalent of the 'bench scientist' in mathematics and there aren't many direct careers in mathematics, or pure mathematics at least - so very few people ultimately become researchers. Instead, I think you take your way of thinking and apply it to whatever else you do (and it certainly doesn't do any harm to understand various mathematical concepts incredibly well).
qnleigh 2y ago
Highly recommend this lecture by a working mathematician shared above (https://www.youtube.com/watch?v=vYCT7cw0ycw 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.
- busyant 2y ago
  Thank you.

deepsun 2y ago

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.

Radim 2y ago
> 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.
- bongodongobob 2y ago
  Eugenics and vitamin C as a cure all.
  - lern_too_spel 2y ago
    If Pauling's eugenics policies were bad, then the laws against incest that are currently on the books in many states (which are also eugenics policies that use the same mechanism) are also bad. There are different forms of eugenics policies, and Pauling's proposal to restrict the mating choices of people carrying certain recessive genes so their children don't suffer is ethically different from Hitler exterminating people with certain genes and also ethically different from other governments sterilizing people with certain genes. He later supported voluntary abortion with genetic testing, which is now standard practice in the US today, though no longer in a few states with ethically questionable laws restricting abortion. This again is ethically different from forced abortion. https://scarc.library.oregonstate.edu/coll/pauling/blood/narrative/page35.html https://scarc.library.oregonstate.edu/coll/pauling/blood/nar...
    - bongodongobob 2y ago
      From what I remember, he wanted to mark people with tattoos or something.
      - lern_too_spel 2y ago
        This is mentioned in my link: "According to Pauling, carriers should have an obvious mark, (i.e. a tattoo on the forehead) denoting their disease, which would allow carriers to identify others with the same affliction and avoid marrying them." The goal wasn't to mark people for ostracism but to make it easier for people carrying these genes to find mates that won't result in suffering for their offspring.
    - voltaireodactyl 2y ago
      FWIW my understanding is that the policies against incest you mention actually have much less to do with controlling genetic reproduction and are more directed at combating familial rape/grooming/etc. Not a fun thing to discuss, but apparently a significant issue, which I guess should be unsurprising given some of the laws allowing underage marriage if the family signs off. Mentioning only to draw attention to the fact that theoretical policy is often undeniable in a vacuum, but runs aground when faced with real world conditions.
- deepsun 2y ago
  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.
  - red75prime 2y ago
    > Linus's harmful and evil promotion of Vitamin C Which is "harmful and evil" thanks to your afterknowledge. He had based his books on the research that failed to replicate. But given low toxicity of vitamin C it's not that "evil" to recommend treatment even if probabilistic estimation of positive effects is not that high. Sloppy, but not exceptionally bad. At least it was instrumental in teaching me to not expect marvels coming from dietary research.

pfisherman 2y ago

I used to do bench top work too; and was blessed with “the golden hands” in that I could almost always get protocols working. To me this always felt more like intuition than deductive reasoning. And it made me a terrible TA. My advice to students in lab was always something along the lines of “just mess around with it, and see how it works.” Not very helpful for the stressed and struggling student -_- Digression aside, my point is that I don’t think we know exactly what makes or defines “the golden hands”. And if that is the case, can we optimize for it? Another point is that scalable fine tuning only works for verifiable stuff. Think a priori knowledge. To me that seems to be at the opposite end of the spectrum from “mess with it and see what happens”.

busyant 2y ago
> blessed with “the golden hands” in that I could almost always get protocols working. Very funny. My friends and I never used the phrase "golden hands" but we used to say something similar: "so-and-so has 'great hands'". But it meant the same thing. I, myself, did not have great hands, but my comment was more about the intellectual process of conducting research. I guess my point was that: * I've already dealt with more talented researchers, but I still contributed meaningfully. * Hopefully, the "AI" will simply add another layer of talent, but the rest of us lesser mortals will still be able to contribute. But I don't know if I'm correct.

vouaobrasil 2y ago

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 precisely that it was a journey of human intellect. As I said elsewhere, my friends used to ask me why something was true and it was fun to explain it to them, or ask them and have them explain it to me. Now most will just use some AI. Soulless, in my opinion. Pure mathematics should be about the art of the thing, not producing results on an assembly line like it will be with AI. Of course, the best mathematicians are going into this because it helps their current careers, not because it helps the future of the subject. Math done with AI will be a lot like Olympic running done with performance-enhancing drugs. Yes, we will get a few more results, faster. But the results will be entirely boring.

zmgsabst 2y ago
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.
- ndriscoll 2y ago
  Even current people will feel differently. I don't bemoan the fact that Lean/Mathlib has `simp` and `linarith` to automate trivial computations. A "copilot for Lean" that can turn "by induction, X" or "evidently Y" into a formal proof sounds great. The the trick is teaching the thing how high powered of theorems to use or how to factor out details or not depending on the user's level of understanding. We'll have to find a pedagogical balance (e.g. you don't give `linarith` to someone practicing basic proofs), but I'm sure it will be a great tool to aid human understanding. A tool to help translate natural language to formal propositions/types also sounds great, and could help more people to use more formal methods, which could make for more robust software.

nyrikki 2y ago

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.

ComplexSystems 2y ago
"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." - what do you mean by this? Counting the number of 1's in a bitstring and determining if it's even or odd?
- nyrikki 2y ago
  Yes, in this case PARITY is determining if the number of 1s in a binary input is odd or even It is an effect of the complex to unpack descriptive complexity class DLOGTIME-uniform TC0, which has AND, OR and MAJORITY gates. http://arxiv.org/abs/2409.13629 http://arxiv.org/abs/2409.13629 The point being that the ability to use parity gates is different than being able to calculate it, which is where the union of the typically ram machine DLOGTIME with the circuit complexity of uniform TC0 comes into play. PARITY, MAJ, AND, and OR are all symmetric, and are in TCO, but PARITY is not in DLOGTIME-uniform TC0, which is first-order logic with Majority quantifiers. Another path, if you think about symantic properties and Rice's theorem, this may make sense especially as PAC learning even depth 2 nets is equivalent to the approximate SVP. PAC-learning even depth-2 threshold circuits is NP-hard. https://www.cs.utexas.edu/~klivans/crypto-hs.pdf https://www.cs.utexas.edu/~klivans/crypto-hs.pdf For me thinking about how ZFC was structured so we can keep the niceties of the law of the excluded middle, and how statistics pretty much depends on it for the central limit and law of large numbers, IID etc... But that path runs the risk of reliving the Brouwer–Hilbert controversy.

TheRealPomax 2y ago

What part do you think is going to become obsolete? Because Math isn't about "working out the math", it's about finding the relations between seemingly unrelated things to bust open a problem. Short of AGI, there is no amount of neural net that's going to realize that a seemingly impossible probabilistic problem is actually equivalent to a projection of an easy to work with 4D geometry. "Doing the math" is what we have computers for, and the better they get, the easier the tedious parts of the job become, but "doing math" is still very much a human game.

busyant 2y ago
> What part do you think is going to become obsolete? Thank you for the question. I guess what I'm saying is: Will LLMs (or whatever comes after them) be _so_ good and _so_ pervasive that we will simply be able to say, "Hey ChatGPT-9000, I'd like to see if the xyz conjecture is correct." And then ChatGPT-9000 just does the work without us contributing beyond asking a question. Or will the technology be limited/bound in some way such that we will still be able to use ChatGPT-9000 as a tool of our own intellectual augmentation and/or we could still contribute to research even without it. Hopefully, my comment clarifies my original post. Also, writing this stuff has helped me think about it more. I don't have any grand insight, but the more I write, the more I lean toward the outcome that these machines will allow us to augment our research.
- TheRealPomax 2y ago
  As amazing as they may seem, they're still just autocompletes, it's inherent to what an LLM is. So unless we come up with a completely new kind technology, I don't see "test this conjecture for me" becoming more real than the computer assisted proof tooling we already have.

hyhconito 2y ago

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 existing working methodology we have. And on top of that the verification of any output can take considerably longer than just doing it yourself in the first place, particularly where it goes off the rails, which it does all the time. I mean it was 3 months ago I was arguing with a model over it not understanding place-value systems properly, something we teach 7 year olds here? But the abstract problem is at a higher level. If it doesn't become a general utility for people outside of mathematics, which is very very evident at the moment by the poor overall adoption and very public criticism of the poor result quality, then the funding will dry up. Models cost lots of money to train and if you don't have customers it's not happening and no one is going to lend you the money any more. And then it's moot.

binarymax 2y ago
This is a great point that nobody will shoot you over :) But the main question is still: assuming you replace an undergrad with a model, who checks the work? If you have a good process around that already, and find utility as an augmented system, then get you’ll get value - but I still think it’s better for the undergrad to still have the job and be at the wheel, and does things faster and better when leveraging a powerful tool.
- hyhconito 2y ago
  Shot already for criticising the shiny thing (happened with crypto and blockchain already...) Well to be fair no one checks what the graduates do properly, even if we hired KPMG in. That is until we get sued. But at least we have someone to blame then. What we don't want is something for the graduate to blame. The buck stops at someone corporeal because that's what the customers want and the regulators require. That's the reality and it's not quite as shiny and happy as the tech industry loves to promote itself. My main point, probably cleared up with a simple point: no one gives a shit about this either way.

peterbonney 2y ago

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.

blagie 2y ago
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.
- rafaelmn 2y ago
  If AI reaches this level socioeconomic impact is going to be so immense, that choosing what subject you study will have no impact on your outcome - no matter what it is - so it's a pointless consideration.
  - blagie 2y ago
    That's just about the silliest thing I've read in a long time. We've had changes before, the most recent one being the rise of computers and then the internet, and before that, manufacturing automation. In all cases, some people were better prepared for change, and some less so. The general consensus is that diverse skills and foundational skills (e.g. math, communication) best prepare people for transitions, relative to specialized skills (e.g. one technology). In addition, many careers are likely to be less impacted, such as plumbing.

bawolff 2y ago

I doubt it. Most likely AI will be good at some things and not others, and mathematicians will just move to whatever AI isn't good at. Alternatively, if AI is able to do all math at a level above PhDs, then its going to be a brave new world and basically the singularity. Everything will change so much that speculating about it will probably be useless.

ykonstant 2y ago

> I even had a Nobel Laureate once tell me that my research was simply "dotting 'i's and crossing 't's". (｡•́︿•̀｡)

busyant 2y ago
> (｡•́︿•̀｡) Don't cry for me, (Argentina). When "God" tells you that you're merely dotting "i"s and crossing "t"s ... he's kind of correct. But I was arrogant enough to believe that I was still a good researcher. I just wasn't "God."

ccppurcell 2y ago

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.

jvvw 2y ago

Another PhD in maths here and I would say not to worry. It's the process of doing and understanding mathematics, and thinking mathematically that is ultimately important. There's never been the equivalent of the 'bench scientist' in mathematics and there aren't many direct careers in mathematics, or pure mathematics at least - so very few people ultimately become researchers. Instead, I think you take your way of thinking and apply it to whatever else you do (and it certainly doesn't do any harm to understand various mathematical concepts incredibly well).

qnleigh 2y ago

Highly recommend this lecture by a working mathematician shared above (https://www.youtube.com/watch?v=vYCT7cw0ycw 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.

busyant 2y ago
Thank you.