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If math is more than proof, we need to better celebrate the rest of it

433 points · 285 comments · num42

  1. trhway · · focus · HN ↗
    It starts to sound like medieval science - "understanding" instead of proofs. And like a medieval army loosing a battle in the open field tries to retreat back into the fortress, people, facing the prospects of machine doing intelligent tasks better than humans, start to retreat into areas like intuition which supposedly aren't reachable by the machine. Some go even further starting to talk about religion. It is very Hegelian that the crown jewel achievement of our civilization starts to drive people away from the foundational principles of that civilization.
    1. card_zero · · focus · HN ↗
      Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability. But of course mathematics is all about proof, and for that reason I was wary of it for a very long time.
      1. trhway · · focus · HN ↗
        >Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability

        not really. You can consider positive proof as an experiment confirming your theory and the negative proof and counter examples as an experiment falsifying your theory.

        1. card_zero · · focus · HN ↗
          Yes, really. "Positive proof" opposes the concept of falsification. You can only have it within a system formal logic, and science can contain those, but isn't one.
          1. trhway · · focus · HN ↗
            >"Positive proof" opposes the concept of falsification.

            no. Positive proofs have nothing to do with falsification. They just tell you that there is no point in spending effort on searching for negative proofs and counter examples. They don't prevent nor prohibit you from spending that effort. They just advise you that that effort will be wasted.

            It is like nobody prevents from experiments to turn lead into gold. Of from searching for a right angled triangle violating Pythagoras.

            1. card_zero · · focus · HN ↗
              ... within a system formal logic.
      2. someguynamedq · · focus · HN ↗
        Fortunately this is not basing science on proof. It's just making it much easier to do proofs when that is what we choose to do
    2. QuesnayJr · · focus · HN ↗
      Understanding has been the point of mathematics for millenia. The idea that purpose of math is to produce machine-checkable proofs is an entirely modern idea.
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