this post was submitted on 17 May 2024
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Some problems lend themselves to "guess-and-check" approaches. This calculator is great at guessing, and it's usually "close enough".
The other calculator can check efficiently, but it can't solve the original problem.
Essentially this is the entire motivation for numerical methods.
In my personal experience given that's how I general manage to shortcut a lot of labour intensive intellectual tasks, using intuition to guess possible answers/results and then working backwards from them to determine which one is right and even prove it, is generally faster (I guess how often it's so depends on how good one's intuition is in a given field, which in turn correlates with experience in it) because it's usually faster to show that a result is correct than to arrive at it (and if it's not, you just do it the old fashion way).
That said, it's far from guaranteed faster and for those things with more than one solution might yield working but sub-optimal ones.
Further, merelly just the intuition step does not yield a result that can be trusted without validation.
Maybe by being used as intuition is in this process, LLMs can help accelerate the search for results in subjects one has not enough experience in to have good intuition on but has enough experience (or there are ways or tools to do it inherent to that domain) to do the "validation of possible results" part.