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And this is exactly the point of the Statement. The process is more important than the solution itself. Most problems in mathematics don’t have immediate value

by ozgung 23d ago

And this is exactly the point of the Statement. The process is more important than the solution itself. Most problems in mathematics don’t have immediate value or applications to the real world. AI’s solutions are like the answers section to practice problems at the back of a textbook. Answer is 42, so what?You have to attempt the problem yourself, that’s the whole point of the exercise. As an engineer I’m happy to use AI for math. If I publish a paper that way, very common these days, I think it’s still problematic. My paper would include something I didn’t come up with and I don’t really understand. I think this is a good time to properly discuss these things because AI is coming for everything. Mathematics and Software were just the first two.

eru 23d ago
Then instead of publishing a paper, just upload your AI result to github. Same advancement of the state of the art. Papers are overrated here.
- pegasus 23d ago
  You don't seem to have grasped Terry Tao's (and others') criticisms. Basically they are saying that the advancement you get is illusory. Most of the time, it doesn't give you any new capabilities or deep understanding, instead you get an inhibiting of human exploration and ensuing expansion of our real understanding in that particular (sub)field. It's non-intuitive, since from a purely logical standpoint you've only added another set of known truths to the ones we already knew about before. The issue only becomes apparent when one considers the larger context of human collective truth and meaning making.
  - eru 22d ago
    Of course, you get new capabilities. Why wouldn't you? Yes, you might not get new human capabilities. But your applications still work better.
    - pegasus 22d ago
      All you get is a new, likely to be useless fact, together with the opaque proof of that fact. There are no known or forseeable applications to the finding that there are singularities in the idealized flow. What you lose OTOH, are the many deep mathematical insights humans motivated by the search would have stumbled upon on the way to that fact and which are much more likely to lead to real-world applications. It's these insights that are truly productive, not settling mathematical points, however iconic these might be. I think the error you're making is that you're assuming these systems have the same mathematical capability as humans (or better). But that's not the case, nor would an informed prediction be that they surely will get there soon enough if technological evolution keeps apace. That would be akin to believing a hiker will reach the moon if they will just keep ascending the mountain. "But look, they are making such good progress!"

by ozgung 23d ago

eru 23d ago

Then instead of publishing a paper, just upload your AI result to github. Same advancement of the state of the art. Papers are overrated here.

pegasus 23d ago
You don't seem to have grasped Terry Tao's (and others') criticisms. Basically they are saying that the advancement you get is illusory. Most of the time, it doesn't give you any new capabilities or deep understanding, instead you get an inhibiting of human exploration and ensuing expansion of our real understanding in that particular (sub)field. It's non-intuitive, since from a purely logical standpoint you've only added another set of known truths to the ones we already knew about before. The issue only becomes apparent when one considers the larger context of human collective truth and meaning making.
- eru 22d ago
  Of course, you get new capabilities. Why wouldn't you? Yes, you might not get new human capabilities. But your applications still work better.
  - pegasus 22d ago
    All you get is a new, likely to be useless fact, together with the opaque proof of that fact. There are no known or forseeable applications to the finding that there are singularities in the idealized flow. What you lose OTOH, are the many deep mathematical insights humans motivated by the search would have stumbled upon on the way to that fact and which are much more likely to lead to real-world applications. It's these insights that are truly productive, not settling mathematical points, however iconic these might be. I think the error you're making is that you're assuming these systems have the same mathematical capability as humans (or better). But that's not the case, nor would an informed prediction be that they surely will get there soon enough if technological evolution keeps apace. That would be akin to believing a hiker will reach the moon if they will just keep ascending the mountain. "But look, they are making such good progress!"