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> Have mathematicians become "less savvy" since the invention of the abacus or calculator? The invention of logarithms or analysis? This is not a fair analogy.

> Have mathematicians become "less savvy" since the invention of the abacus or calculator? The invention of logarithms or analysis? This is not a fair analogy. Those things are like compilers, languages, and type-checkers. They are deterministic, carefully proven, hand-crafted tools, that allow people to go safely to a higher level of abstraction and still make things in a deterministic way. The jump into the fuzzy world of LLMs is a completely different thing. It's different than the jump from assembly to a higher-level language.

dvt 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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.

dvt 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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 28d 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.