9 ms·

Mathematics in the age of AI

212 points by jonbaer 2mo ago

nadermx 2mo ago
[flagged]
tocs3 2mo ago
Maybe the Hitchhikers Guide to the Galaxy series was predictive in pointing out the problems of ill defined questions (The Answer to the Ultimate Question of Life, the Universe, and Everything).
sonicrocketman 2mo ago
Anyone else print their white papers before reading? (At least the short ones)
- magneticnorth 2mo ago
  When I was in academia and had easy access to a good printer, I always did. I miss it now that it's easier to just read on my screen.
- ivansavz 2mo ago
  Absolutely. I feel I gain at least 10 IQ points when reading something on paper. This is also the strategy I use for editing drafts of my books. I bring a printed draft to someplace nice (e.g. coffee shop or park) and read it all carefully, then I transfer the edits back to the .tex sources. I do several passes of this, until I feel the text + explanations are solid. Reading on screen just isn't the same...
  - i_am_a_peasant 2mo ago
    Oh hey I was thinking of buying your stats book! I'll do that right away.
paulpauper 2mo ago
Not using AI puts one at a huge disadvantage in a career setting. Ai can find deep references better than humans now, let alone actually doing the math. The challenge is knowing which problems to tackle given the cost limitations. If you have $10k to spend on tokens, you have to choose problems that can conceivably be solved within this budget.
highfrequency 2mo ago
Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."
- paulpauper 2mo ago
  Similar to Ai writing. Lots of bloat.
  - piker 2mo ago
    Coding, too.
- TMWNN 2mo ago
  >Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument." I noticed a long time ago, that the more people focus on trivialities like typos when arguing against someone online, the more compelling the original argument is. Basically, bikeshedding. The most compelling evidence of the compelling nature of the original argument is when the most-upvoted reply is a joke or a meme. That's when you really know that those responding have nothing else to say. It's a white flag being run up, or the dog turning over and exposing its belly.
  - jltsiren 2mo ago
    I noticed another thing a long time ago. Some academic cultures have a tradition of formal debates. They are based on the premise that an educated person should be able to argue convincingly for or against any idea, regardless of whether they believe in it. A natural corollary is that you should not let convincing arguments convince you, as the merits of the argument have little to do with the merits of the idea itself. LLMs have made the situation worse. People's ability to generate convincing arguments now greatly exceeds their ability to evaluate the value of ideas.
sonicrocketman 2mo ago
Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
- czgov 2mo ago
  I wonder what his views on the 4 color problem are. One can explain it as the computer checked a bunch of cases and all maps reduce to one of these cases. It doesn’t take an expert to state this. Properly explain is an enormous grey area. Soon, I think, there will be proofs of results that are verified in Lean that are so long that no one will be able to “properly explain”. I don’t think they should be discarded. Resolution of singularities is a famous theorem of Hironaka. Abhyankar claimed that no one truly understood the proof of the theorem. He said that he and Zariski couldn’t get through the paper with a full understanding. But everyone accepts this theorem as being correct.
  - deleted 2mo ago
    [deleted]
  - ChadNauseam 2mo ago
    > One can explain it as the computer checked a bunch of cases and all maps reduce to one of these cases. It doesn’t take an expert to state this. Hmm, doesn't it take an expert to explain why those cases are exhaustive, and why the code that checked them is correct? Tangentially, I'm not a mathematician but I wonder if one "opaque" proof that is too complicated for anyone to understand, but that we know is correct via formal verification, might end up being built on with "transparent" human-understandable proofs. For example, it's my understanding that there are many conjectures that have been proven true conditional on the riemann hypothesis being true. In that case, an opaque proof of the riemann hypothesis would enable those conjectures to be known and built upon
    - 2mo ago
rramach 2mo ago
Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress. Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only by compute/cost and a human math-world where we understand a subset of the AI math-world as a hobby (similar to Stockfish vs human chess).
- plastic-enjoyer 2mo ago
  Somehow, I feel that progress, in your understanding of what progress is, loses all meaning.
- tocs3 2mo ago
  In some sense "understanding" (understanding if it is true, if it is important, how to use it) is about the only bottleneck in math. Any theorem that you can write down or imagine is already true, false, not provable already. In some ways we can already start iterating through all the theorems. We will never get to the end (or really get very far down the line) and most all of them be trivial (I think the Busy Beaver[1] project is a fascinating example, ymmv). I am wary of AI in all aspects I am seeing it in but in many ways in mathematics seems to me the least troubling. It will change things in and the field will not be the same. Blacksmithing has not really gone away. You can still work as a farrier, if you like that sort of things. The tools that replaced a man working over a forge with a big hammer are part of a giant industry that is still producing works for the modern world. [1]: https://bbchallenge.org/8226493 https://bbchallenge.org/8226493
  - frozenseven 2mo ago
    Chasing these 'trivialities' is a good thing, imo. The Busy Beaver game has lead to a better understanding of complexity theory and automata. Also, direct "hands on" work on improving proof assistants and related tools. Btw, for those who are curious, the Busy Beaver Challenge wiki is a treasure trove of rabbit holes and curiosities: https://wiki.bbchallenge.org/wiki/Main_Page https://wiki.bbchallenge.org/wiki/Main_Page
qsera 2mo ago
If the title have said in the age of "LLMs", I might have given it a try.
- GPerson 2mo ago
  You should give it a try. Tao is a wonderful person and is trying to help humanity.
  - qsera 2mo ago
    > is trying to help humanity. That is what all marketing wants you to think...
    - GPerson 2mo ago
      It’s not marketing. This guy could have signed up for one of those hundred million dollar salaries with a phone call and did not. I know several people who have met him and everyone says he’s the genuine article. He’s actually just devoted to human mathematics. One tragic thing about all of this is that unlike almost every profession, mathematics actually has a kind of honesty. You honestly solve the problem or you don’t. The pecking order in mathematics at least used to have a grounding in actual abilities. People respect this guy because he’s actually legit.
      - qsera 2mo ago
        Legit people are used by marketing all the time.
        GPerson 2mo ago
        I think the villains who run these companies benefit from Tao’s actions because he’s a de facto thought leader of mathematics not taking a very hard anti-AI stance. However, I don’t think a very hard anti-AI stance is correct for someone in his position. Honestly, do you want a bunch of AI labs to 100% dictate the future of whatever your field is or do you want the best leaders of your field to at least try to shape how AI will change it? And if all of the legitimate people in math ignore AI entirely, then historically important parts of the field will get entirely taken over by dilettantes and AI labs. I’m all for math institutions being a safe haven for AI free math work. But I don’t want to see some space X intern solve all the most important problems on a whim and no leaders in math be aware of it. (I’m not sure the extent to which you think this is marketing. I’m operating under the assumption that you agree with his Hypothesis 4.1. If you don’t, then I’d assume you haven’t seen the long list of prominent open math problems that these systems are providing answers to. And if this doesn’t sway you about Hypothesis 4.1 I’d just halt and ask why.)
glimshe 2mo ago
Terence Tao sees a role for AI in science. I'm no genius but he basically described what I've thought all along... We don't need to be "all in" or "all out". It's the old cliche of "if you only have a hammer every problem looks like a nail". Let's not fall into the trap of thinking that our life needs to be 100% about AI or completely devoid of AI. We can really use this thing to make our lives better. Instead of wasting time on the question of whether we should use it, let's focus on HOW we'll use it. And one thing about Tao: it's really refreshing to have an influential genius "around" who isn't a egomaniacal psychopath trying to rule the world through their XYZ corporation but, instead, being a reasonable and well-balanced person. Big fan.
- GPerson 2mo ago
  I think it’s more that he seeks to preserve and promote human understanding of mathematics, and sees that grappling with this new technology is necessary. One reason is that for human mathematical practices and institutions to retain legitimacy, they need to justify their value. As Tao explains, one obvious answer to that is made less obvious now with AI.
- a2ff6eeb0 2mo ago
  I think it's impossible to be half in. AI will eventually be better at things than people, and people will simply be rocks in the gears of progress. The only thing to do is to be all in, or get run over.
  - evenhash 2mo ago
    If what you’re saying is true, what’s the use (or even meaning) of being “all in”? You’re a rock either way.
    - a2ff6eeb0 2mo ago
      It's not there yet, and every move we're currently making is towards an extremely inequitable future. Unless things change, not everyone is going to benefit from AI. What are you doing today to end up on the team that wins? Once AI starts under its own direction, human brains won't be competitive. It feels like we're a breakthrough or two away, and with trillions of funding, we'll get there. Every dollar we spend on Claude subscriptions gets us closer.
a2ff6eeb0 2mo ago
I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems. If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed. The human brain is being obsoleted, soon thinking is going to be a recreational activity like weightlifting. If you want to think as a hobby, that's fine, but most people will be free of that toil of unwanted brain labor.
- hintymad 2mo ago
  > I don't know why anyone should care about understanding the results if the AI is better at math than us This is a big if, right? AI can still generate subtle or even silly mistakes that any normal human, let alone a mathematician, wouldn't make. Besides, math is more than just getting a conclusion but to understand and to generalize new ways of solving problems. After all, mathematicians are a curious bunch. To quote Hilbert's epitaph: We must know. We shall know.
  - bayesnet 2mo ago
    It’s a bit of an ominous quote given that Hilbert’s program was dismantled shortly thereafter by Gödel…
    - pfdietz 2mo ago
      I'm reminded of the joke about the two friends who come across a bear in the woods. When one puts on running shoes, his friend chides him that he can't outrun the bear. He responds, "I don't need to outrun the bear, I just need to outrun you." AI doesn't have to implement Hilbert's vision and be able to prove everything. I just has to out-prove human mathematicians.
  - a2ff6eeb0 2mo ago
    Well, that's why we have automated proof checking. And again, I don't think humans will be able to solve problems at a commercial scale in the future. Maybe we'll have some hobbyist dabblers, but any real progress will be done by machines that skip the human.
piker 2mo ago
If you're having dinner like me and prefer to watch: https://www.youtube.com/watch?v=M0--ZH1lOzg https://www.youtube.com/watch?v=M0--ZH1lOzg
caglaroktay 2mo ago
AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is only one think will remain for humans to go for these solutions: what we value. that will be the last resort I believe and hopefully ai systems won't start manipulate us too as we are very fragile on manipulation.
- mmoll 2mo ago
  But how would „what we value“ still be relevant?
ghm2199 2mo ago
Goal 6.4 reminds me always of the numerous times AI generated n PR's for a feature and I revolted and threw my laptop because it was incomprehensible or unworkable when viewed as a process/workflow.
itissid 2mo ago
What is being made is "what are our core values?" argument. One does not need to be a mathematician to know how poorly this worked for large communities when incentives are misaligned... If a subset of mathematicians, use AI to condense timelines focusing on goal 6.2 exclusively and make rapid progress and reach a proverbial inflection point — one where value proposition of the using this new normal is too enticing to give up — everyone will ask: "This thing is so awesome. Why should I care about your values?"
deleted 2mo ago
[deleted]
efavdb 2mo ago
one thought: AI can often help us solve a problem once posed. E.g., try to prove that X is True. But formulating good conjectures is something altogether different. right now we have a backlog of interesting / good conjectures that ai can grind on. but once those are done, will we still need people to sniff out interesting new ones?
ZeroDayDreamer 2mo ago
The chess analogy doesn't quite work for me. In chess, an engine's move is useful because it helps you win. In math, a proof is useful because it helps you understand something - and from that, you can build more. If a proof is incomprehensible, it's like a chess move that only works in that one specific position. Useless. The ABC conjecture is a perfect example - Mochizuki's proof might be correct, but no one can follow it, so it's basically dead. AI proofs are going to be like that, but way more of them. Tao's essay is a great starting point
AndrewDucker 2mo ago
The talk contains references to what is clearly a subset of questions and hypotheses. Anyone got a link to somewhere with all of these?
sigbottle 2mo ago
Optimizing for the appearance rather than the underlying substance. Ahh. I know Terrence Tao didn't have the following in mind when he said those words, but oh man, the philosophy neurons are firing in my brain rn.
seanm2w 2mo ago
Math is about making new discovery as well. AI will be better at processing but humans can still generate new thoughts and ideas never been done before.
croemer 2mo ago
Here's a video of his ICM talk with the same name: https://www.youtube.com/watch?v=M0--ZH1lOzg https://www.youtube.com/watch?v=M0--ZH1lOzg

212 points by jonbaer 2mo ago

[flagged]

tocs3 2mo ago

Maybe the Hitchhikers Guide to the Galaxy series was predictive in pointing out the problems of ill defined questions (The Answer to the Ultimate Question of Life, the Universe, and Everything).

sonicrocketman 2mo ago

Anyone else print their white papers before reading? (At least the short ones)

magneticnorth 2mo ago
When I was in academia and had easy access to a good printer, I always did. I miss it now that it's easier to just read on my screen.
ivansavz 2mo ago
Absolutely. I feel I gain at least 10 IQ points when reading something on paper. This is also the strategy I use for editing drafts of my books. I bring a printed draft to someplace nice (e.g. coffee shop or park) and read it all carefully, then I transfer the edits back to the .tex sources. I do several passes of this, until I feel the text + explanations are solid. Reading on screen just isn't the same...
- i_am_a_peasant 2mo ago
  Oh hey I was thinking of buying your stats book! I'll do that right away.

paulpauper 2mo ago

Not using AI puts one at a huge disadvantage in a career setting. Ai can find deep references better than humans now, let alone actually doing the math. The challenge is knowing which problems to tackle given the cost limitations. If you have $10k to spend on tokens, you have to choose problems that can conceivably be solved within this budget.

highfrequency 2mo ago

Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."

paulpauper 2mo ago
Similar to Ai writing. Lots of bloat.
- piker 2mo ago
  Coding, too.
TMWNN 2mo ago
>Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument." I noticed a long time ago, that the more people focus on trivialities like typos when arguing against someone online, the more compelling the original argument is. Basically, bikeshedding. The most compelling evidence of the compelling nature of the original argument is when the most-upvoted reply is a joke or a meme. That's when you really know that those responding have nothing else to say. It's a white flag being run up, or the dog turning over and exposing its belly.
- jltsiren 2mo ago
  I noticed another thing a long time ago. Some academic cultures have a tradition of formal debates. They are based on the premise that an educated person should be able to argue convincingly for or against any idea, regardless of whether they believe in it. A natural corollary is that you should not let convincing arguments convince you, as the merits of the argument have little to do with the merits of the idea itself. LLMs have made the situation worse. People's ability to generate convincing arguments now greatly exceeds their ability to evaluate the value of ideas.

sonicrocketman 2mo ago

Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

czgov 2mo ago
I wonder what his views on the 4 color problem are. One can explain it as the computer checked a bunch of cases and all maps reduce to one of these cases. It doesn’t take an expert to state this. Properly explain is an enormous grey area. Soon, I think, there will be proofs of results that are verified in Lean that are so long that no one will be able to “properly explain”. I don’t think they should be discarded. Resolution of singularities is a famous theorem of Hironaka. Abhyankar claimed that no one truly understood the proof of the theorem. He said that he and Zariski couldn’t get through the paper with a full understanding. But everyone accepts this theorem as being correct.
- deleted 2mo ago
  [deleted]
- ChadNauseam 2mo ago
  > One can explain it as the computer checked a bunch of cases and all maps reduce to one of these cases. It doesn’t take an expert to state this. Hmm, doesn't it take an expert to explain why those cases are exhaustive, and why the code that checked them is correct? Tangentially, I'm not a mathematician but I wonder if one "opaque" proof that is too complicated for anyone to understand, but that we know is correct via formal verification, might end up being built on with "transparent" human-understandable proofs. For example, it's my understanding that there are many conjectures that have been proven true conditional on the riemann hypothesis being true. In that case, an opaque proof of the riemann hypothesis would enable those conjectures to be known and built upon
  - 2mo ago

rramach 2mo ago

Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress. Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only by compute/cost and a human math-world where we understand a subset of the AI math-world as a hobby (similar to Stockfish vs human chess).

plastic-enjoyer 2mo ago
Somehow, I feel that progress, in your understanding of what progress is, loses all meaning.
tocs3 2mo ago
In some sense "understanding" (understanding if it is true, if it is important, how to use it) is about the only bottleneck in math. Any theorem that you can write down or imagine is already true, false, not provable already. In some ways we can already start iterating through all the theorems. We will never get to the end (or really get very far down the line) and most all of them be trivial (I think the Busy Beaver[1] project is a fascinating example, ymmv). I am wary of AI in all aspects I am seeing it in but in many ways in mathematics seems to me the least troubling. It will change things in and the field will not be the same. Blacksmithing has not really gone away. You can still work as a farrier, if you like that sort of things. The tools that replaced a man working over a forge with a big hammer are part of a giant industry that is still producing works for the modern world. [1]: https://bbchallenge.org/8226493 https://bbchallenge.org/8226493
- frozenseven 2mo ago
  Chasing these 'trivialities' is a good thing, imo. The Busy Beaver game has lead to a better understanding of complexity theory and automata. Also, direct "hands on" work on improving proof assistants and related tools. Btw, for those who are curious, the Busy Beaver Challenge wiki is a treasure trove of rabbit holes and curiosities: https://wiki.bbchallenge.org/wiki/Main_Page https://wiki.bbchallenge.org/wiki/Main_Page

qsera 2mo ago

If the title have said in the age of "LLMs", I might have given it a try.

GPerson 2mo ago
You should give it a try. Tao is a wonderful person and is trying to help humanity.
- qsera 2mo ago
  > is trying to help humanity. That is what all marketing wants you to think...
  - GPerson 2mo ago
    It’s not marketing. This guy could have signed up for one of those hundred million dollar salaries with a phone call and did not. I know several people who have met him and everyone says he’s the genuine article. He’s actually just devoted to human mathematics. One tragic thing about all of this is that unlike almost every profession, mathematics actually has a kind of honesty. You honestly solve the problem or you don’t. The pecking order in mathematics at least used to have a grounding in actual abilities. People respect this guy because he’s actually legit.
    - qsera 2mo ago
      Legit people are used by marketing all the time.
      - GPerson 2mo ago
        I think the villains who run these companies benefit from Tao’s actions because he’s a de facto thought leader of mathematics not taking a very hard anti-AI stance. However, I don’t think a very hard anti-AI stance is correct for someone in his position. Honestly, do you want a bunch of AI labs to 100% dictate the future of whatever your field is or do you want the best leaders of your field to at least try to shape how AI will change it? And if all of the legitimate people in math ignore AI entirely, then historically important parts of the field will get entirely taken over by dilettantes and AI labs. I’m all for math institutions being a safe haven for AI free math work. But I don’t want to see some space X intern solve all the most important problems on a whim and no leaders in math be aware of it. (I’m not sure the extent to which you think this is marketing. I’m operating under the assumption that you agree with his Hypothesis 4.1. If you don’t, then I’d assume you haven’t seen the long list of prominent open math problems that these systems are providing answers to. And if this doesn’t sway you about Hypothesis 4.1 I’d just halt and ask why.)

glimshe 2mo ago

Terence Tao sees a role for AI in science. I'm no genius but he basically described what I've thought all along... We don't need to be "all in" or "all out". It's the old cliche of "if you only have a hammer every problem looks like a nail". Let's not fall into the trap of thinking that our life needs to be 100% about AI or completely devoid of AI. We can really use this thing to make our lives better. Instead of wasting time on the question of whether we should use it, let's focus on HOW we'll use it. And one thing about Tao: it's really refreshing to have an influential genius "around" who isn't a egomaniacal psychopath trying to rule the world through their XYZ corporation but, instead, being a reasonable and well-balanced person. Big fan.

GPerson 2mo ago
I think it’s more that he seeks to preserve and promote human understanding of mathematics, and sees that grappling with this new technology is necessary. One reason is that for human mathematical practices and institutions to retain legitimacy, they need to justify their value. As Tao explains, one obvious answer to that is made less obvious now with AI.
a2ff6eeb0 2mo ago
I think it's impossible to be half in. AI will eventually be better at things than people, and people will simply be rocks in the gears of progress. The only thing to do is to be all in, or get run over.
- evenhash 2mo ago
  If what you’re saying is true, what’s the use (or even meaning) of being “all in”? You’re a rock either way.
  - a2ff6eeb0 2mo ago
    It's not there yet, and every move we're currently making is towards an extremely inequitable future. Unless things change, not everyone is going to benefit from AI. What are you doing today to end up on the team that wins? Once AI starts under its own direction, human brains won't be competitive. It feels like we're a breakthrough or two away, and with trillions of funding, we'll get there. Every dollar we spend on Claude subscriptions gets us closer.

a2ff6eeb0 2mo ago

I don't know why anyone should care about understanding the results if the AI is better at math than us. It'd be like demanding that human mathematicians are banned from publishing until their cats understand the theorems. If Amazon uses AI math to come up with better routing, the cats can benefit from cheaper delivery fees just as much as humans can. No understanding needed. The human brain is being obsoleted, soon thinking is going to be a recreational activity like weightlifting. If you want to think as a hobby, that's fine, but most people will be free of that toil of unwanted brain labor.

hintymad 2mo ago
> I don't know why anyone should care about understanding the results if the AI is better at math than us This is a big if, right? AI can still generate subtle or even silly mistakes that any normal human, let alone a mathematician, wouldn't make. Besides, math is more than just getting a conclusion but to understand and to generalize new ways of solving problems. After all, mathematicians are a curious bunch. To quote Hilbert's epitaph: We must know. We shall know.
- bayesnet 2mo ago
  It’s a bit of an ominous quote given that Hilbert’s program was dismantled shortly thereafter by Gödel…
  - pfdietz 2mo ago
    I'm reminded of the joke about the two friends who come across a bear in the woods. When one puts on running shoes, his friend chides him that he can't outrun the bear. He responds, "I don't need to outrun the bear, I just need to outrun you." AI doesn't have to implement Hilbert's vision and be able to prove everything. I just has to out-prove human mathematicians.
- a2ff6eeb0 2mo ago
  Well, that's why we have automated proof checking. And again, I don't think humans will be able to solve problems at a commercial scale in the future. Maybe we'll have some hobbyist dabblers, but any real progress will be done by machines that skip the human.

piker 2mo ago

If you're having dinner like me and prefer to watch: https://www.youtube.com/watch?v=M0--ZH1lOzg https://www.youtube.com/watch?v=M0--ZH1lOzg

caglaroktay 2mo ago

AI also can replace a lot of expert attention too. Why not? What is useful or what is not useful is based on the expert's narrow opinion. An AI system can do much more and deep value comparison. It looks like if our current technological advancement continues, in the space of what is possible (or even impossible), AI can find the optimal solutions better than any human or human organizations. But I think there is only one think will remain for humans to go for these solutions: what we value. that will be the last resort I believe and hopefully ai systems won't start manipulate us too as we are very fragile on manipulation.

mmoll 2mo ago
But how would „what we value“ still be relevant?

ghm2199 2mo ago

Goal 6.4 reminds me always of the numerous times AI generated n PR's for a feature and I revolted and threw my laptop because it was incomprehensible or unworkable when viewed as a process/workflow.

itissid 2mo ago

What is being made is "what are our core values?" argument. One does not need to be a mathematician to know how poorly this worked for large communities when incentives are misaligned... If a subset of mathematicians, use AI to condense timelines focusing on goal 6.2 exclusively and make rapid progress and reach a proverbial inflection point — one where value proposition of the using this new normal is too enticing to give up — everyone will ask: "This thing is so awesome. Why should I care about your values?"

deleted 2mo ago

[deleted]

efavdb 2mo ago

one thought: AI can often help us solve a problem once posed. E.g., try to prove that X is True. But formulating good conjectures is something altogether different. right now we have a backlog of interesting / good conjectures that ai can grind on. but once those are done, will we still need people to sniff out interesting new ones?

ZeroDayDreamer 2mo ago

The chess analogy doesn't quite work for me. In chess, an engine's move is useful because it helps you win. In math, a proof is useful because it helps you understand something - and from that, you can build more. If a proof is incomprehensible, it's like a chess move that only works in that one specific position. Useless. The ABC conjecture is a perfect example - Mochizuki's proof might be correct, but no one can follow it, so it's basically dead. AI proofs are going to be like that, but way more of them. Tao's essay is a great starting point

AndrewDucker 2mo ago

The talk contains references to what is clearly a subset of questions and hypotheses. Anyone got a link to somewhere with all of these?

sigbottle 2mo ago

Optimizing for the appearance rather than the underlying substance. Ahh. I know Terrence Tao didn't have the following in mind when he said those words, but oh man, the philosophy neurons are firing in my brain rn.

seanm2w 2mo ago

Math is about making new discovery as well. AI will be better at processing but humans can still generate new thoughts and ideas never been done before.

croemer 2mo ago

Here's a video of his ICM talk with the same name: https://www.youtube.com/watch?v=M0--ZH1lOzg https://www.youtube.com/watch?v=M0--ZH1lOzg