3 ms·

Not sure how much frontier math you follow, but probabilistic arguments are extremely popular (particularly in, weirdly enough, number theory), especially for f

by dvt 3mo ago

Not sure how much frontier math you follow, but probabilistic arguments are extremely popular (particularly in, weirdly enough, number theory), especially for fiddling with the bounds on things, or getting closer to full coverage of various theorems. So this idea that doing math is some kind of fully deterministic & mechanistic process is a bit misleading.

adamddev1 3mo ago
Right, programmers also use randomly generated info from property based testing for example? But I was referencing the analogy to the abacus, calculator, logarithms, analysis, and higher level languages.
luke5441 3mo ago
Is that kind of argument something like where you count the number of cranks claiming P=NP and the number of cranks claiming P!=NP and then if you get 95% papers claiming P!=NP that one wins?
- dvt 3mo ago
  What? Not at all. I'm referring to things like discussing distributions of certain things or probabilities of things as we go towards infinity, etc. These are proper papers, not surveys.
  - luke5441 3mo ago
    But if a LLM writes such a paper, how do you know there aren't any issues in it that cause wrong probabilities/distributions?
    - dvt 3mo ago
      You don't, that's why you review it (just how you would handle a real human submitting a paper). The main issue with LLM papers is that they tend to be very dense/circuitous or—because LLMs don't truly understand what they're doing—have the wrong focus. An LLM might spend pages on a trivial result, but quickly gloss over a truly remarkable finding. Terry Tao talks about this challenge in some of his blog posts and interviews, it's pretty interesting.
      - luke5441 3mo ago
        That was adamddev1s point. It's a unreliable tool. You cannot copy & paste its results into a paper as proof. You could do this with e.g. Lean. To review what it writes you need to understand the topic to such an extend that you could have written it yourself (at least that is how it is for me when I review code). Yes, for inspiration or search they are great tools.
      - coldtea 3mo ago
        >You don't, that's why you review it Review enough of those without doing the proving yourself, and you'll soon lose the ability to review. And have LLMs do the course work for you at math school, and you might never acquire such ability to begin with anyway.

by dvt 3mo ago

adamddev1 3mo ago

Right, programmers also use randomly generated info from property based testing for example? But I was referencing the analogy to the abacus, calculator, logarithms, analysis, and higher level languages.

luke5441 3mo ago

Is that kind of argument something like where you count the number of cranks claiming P=NP and the number of cranks claiming P!=NP and then if you get 95% papers claiming P!=NP that one wins?

dvt 3mo ago
What? Not at all. I'm referring to things like discussing distributions of certain things or probabilities of things as we go towards infinity, etc. These are proper papers, not surveys.
- luke5441 3mo ago
  But if a LLM writes such a paper, how do you know there aren't any issues in it that cause wrong probabilities/distributions?
  - dvt 3mo ago
    You don't, that's why you review it (just how you would handle a real human submitting a paper). The main issue with LLM papers is that they tend to be very dense/circuitous or—because LLMs don't truly understand what they're doing—have the wrong focus. An LLM might spend pages on a trivial result, but quickly gloss over a truly remarkable finding. Terry Tao talks about this challenge in some of his blog posts and interviews, it's pretty interesting.
    - luke5441 3mo ago
      That was adamddev1s point. It's a unreliable tool. You cannot copy & paste its results into a paper as proof. You could do this with e.g. Lean. To review what it writes you need to understand the topic to such an extend that you could have written it yourself (at least that is how it is for me when I review code). Yes, for inspiration or search they are great tools.
    - coldtea 3mo ago
      >You don't, that's why you review it Review enough of those without doing the proving yourself, and you'll soon lose the ability to review. And have LLMs do the course work for you at math school, and you might never acquire such ability to begin with anyway.