5 ms·

For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and a

For anyone using LLMs heavily for coding, this shouldn't be too surprising. It was just a matter of time. Mathematicians make new discoveries by building and applying mathematical tools in new ways. It is tons of iterative work, following hunches and exploring connections. While true that LLMs can't truly "make discoveries" since they have no sense of what that would mean, they can Monte Carlo every mathematical tool at a narrow objective and see what sticks, then build on that or combine improvements. Reading the article, that seems exactly how the discovery was made, an LLM used a "surprising connection" to go beyond the expected result. But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept.

cubefox 5mo ago
There is a long and interesting recent essay on that topic by a mathematician: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e...
- zem 5mo ago
  wow, that was indeed a brilliant essay. i particularly liked the framing that "solving a big conjecture was a cryptographic proof that you had come up with a genuine conceptual innovation".
- svieira 5mo ago
  > The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics. I just wanted to highlight this very correct human-centric thought about the purpose of intellection.
- toraway 5mo ago
  Thank you for sharing, that was one of the most insightful long form pieces I've read in a long time! And the writing was enjoyable to read even as a math layperson. I was going to say you should submit it but I saw you did a few days ago but it only got a few votes... If Dang sees this IMO it would be extremely deserving of the second chance pool as I wouldn't be surprised to see easily jump to the front page with a different roll of the dice.
- rf_physics 5mo ago
  Thanks for sharing this. It's unfortunate that the more honest framing about the value of mathematics that he suggests is going to be really, really hard because of all the pitfalls and agendas he mentioned here. I can only hope when the dust settles something will be left.
daishi55 5mo ago
> the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Isn't this just anthropocentrism? Why is understanding only valid if a human does it? Why is knowledge only for humans? If another species resolved the contradictions between gravity and quantum mechanics, does that not have meaning unless they explain it to us and we understand it?
- interroboink 5mo ago
  It's a bit of an "if a tree falls in the forest but nobody hears it, does it make a sound?" quandary. Sure, maybe some aliens in a distant galaxy understand quantum mechanics better than we do. That's great, but it has no bearing on our little bubble of existence. Though perhaps more to your point, if some superhuman AI is developed, and understands things better than us without telling us about it (or being unable to), it could perform feats that seem magical to us — that would concern us even if we don't understand it, since it affects us. But I think in the frame of reference of the commenter you were replying to, they're just saying that the low-level AI used in this specific case is not capable of making its results actually useful to us; humans are still needed to make it human-relevant. It told us where to find a gem underground, but we still had to be the ones to dig it out, cut it, polish it, etc.
  - nextaccountic 5mo ago
    It's less likely that aliens of distant galaxies will appreciate this rather than, you know, AI themselves We are in the birth of the AI age and we don't know how it will look like in 100 or 1000 or 10000 or 100000 years (all those time frames likely closer than possible encounters with aliens from distant galaxies). It's possible that AI will outlast humans even
- tern 5mo ago
  Do the forms etched into stone by weather over millennia in Moab matter to the wind? Certainly yes, in one sense, but not in the same sense we mean when we say things matter to us, or to animals, or even bacteria.
anon291 5mo ago
It is not only unsurprising ; it was always expected. There is no difference between programs and proofs. They are the same thing
mikert89 5mo ago
for now the LLMs will build off human understanding, eventually we will be left behind
kamaal 5mo ago
>>But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Future of code is pretty much a bunch of guys shepherding a bunch of agents to get them to your goal. I don't see how math might not go that way as well.

cubefox 5mo ago

There is a long and interesting recent essay on that topic by a mathematician: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e...

zem 5mo ago
wow, that was indeed a brilliant essay. i particularly liked the framing that "solving a big conjecture was a cryptographic proof that you had come up with a genuine conceptual innovation".
svieira 5mo ago
> The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics. I just wanted to highlight this very correct human-centric thought about the purpose of intellection.
toraway 5mo ago
Thank you for sharing, that was one of the most insightful long form pieces I've read in a long time! And the writing was enjoyable to read even as a math layperson. I was going to say you should submit it but I saw you did a few days ago but it only got a few votes... If Dang sees this IMO it would be extremely deserving of the second chance pool as I wouldn't be surprised to see easily jump to the front page with a different roll of the dice.
rf_physics 5mo ago
Thanks for sharing this. It's unfortunate that the more honest framing about the value of mathematics that he suggests is going to be really, really hard because of all the pitfalls and agendas he mentioned here. I can only hope when the dust settles something will be left.

daishi55 5mo ago

> the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Isn't this just anthropocentrism? Why is understanding only valid if a human does it? Why is knowledge only for humans? If another species resolved the contradictions between gravity and quantum mechanics, does that not have meaning unless they explain it to us and we understand it?

interroboink 5mo ago
It's a bit of an "if a tree falls in the forest but nobody hears it, does it make a sound?" quandary. Sure, maybe some aliens in a distant galaxy understand quantum mechanics better than we do. That's great, but it has no bearing on our little bubble of existence. Though perhaps more to your point, if some superhuman AI is developed, and understands things better than us without telling us about it (or being unable to), it could perform feats that seem magical to us — that would concern us even if we don't understand it, since it affects us. But I think in the frame of reference of the commenter you were replying to, they're just saying that the low-level AI used in this specific case is not capable of making its results actually useful to us; humans are still needed to make it human-relevant. It told us where to find a gem underground, but we still had to be the ones to dig it out, cut it, polish it, etc.
- nextaccountic 5mo ago
  It's less likely that aliens of distant galaxies will appreciate this rather than, you know, AI themselves We are in the birth of the AI age and we don't know how it will look like in 100 or 1000 or 10000 or 100000 years (all those time frames likely closer than possible encounters with aliens from distant galaxies). It's possible that AI will outlast humans even
tern 5mo ago
Do the forms etched into stone by weather over millennia in Moab matter to the wind? Certainly yes, in one sense, but not in the same sense we mean when we say things matter to us, or to animals, or even bacteria.

anon291 5mo ago

It is not only unsurprising ; it was always expected. There is no difference between programs and proofs. They are the same thing

mikert89 5mo ago

for now the LLMs will build off human understanding, eventually we will be left behind

kamaal 5mo ago

>>But the result has no meaning without the human intent behind the objective, human understanding to value the new pathway the AI used (more valuable than the result itself, by far) and the mathematical language (built by humans) to explore the concept. Future of code is pretty much a bunch of guys shepherding a bunch of agents to get them to your goal. I don't see how math might not go that way as well.