• @smeg@feddit.uk
    link
    fedilink
    English
    61 month ago

    This is what happens when the mathematicians spend too much time thinking without any practical applications. Madness!

    • tate
      link
      English
      191 month ago

      The idea that something not practical is also not important is very sad to me. I think the least practical thing that humans do is by far the most important: trying to figure out what the fuck all this really means. We do it through art, religion, science, and… you guessed it, pure math. and I should include philosophy, I guess.

      I sure wouldn’t want to live in a world without those! Except maybe religion.

    • rockerface 🇺🇦
      link
      fedilink
      English
      101 month ago

      Just like they did with that stupid calculus that… checks notes… made possible all of the complex electronics used in technology today. Not having any practical applications currently does not mean it never will

      • @smeg@feddit.uk
        link
        fedilink
        English
        31 month ago

        I’d love to see the practical applications of someone taking 360 pages to justify that 1+1=2

        • @bleistift2@sopuli.xyz
          link
          fedilink
          English
          51 month ago

          The practical application isn’t the proof that 1+1=2. That’s just a side-effect. The application was building a framework for proving mathematical statements. At the time the principia were written, Maths wasn’t nearly as grounded in demonstrable facts and reason as it is today. Even though the principia failed (for reasons to be developed some 30 years later), the idea that every proposition should be proven from as few and as simple axioms as possible prevailed.

          Now if you’re asking: Why should we prove math? Then the answer is: All of physics.

          • rockerface 🇺🇦
            link
            fedilink
            English
            11 month ago

            The answer to the last question is even simpler and broader than that. Math should be proven because all of science should be proven. That is what separates modern science from delusion and self-deception

        • xigoi
          link
          English
          2
          edit-2
          1 month ago

          It lays the foundations for automated proof verification, which is going to help with the development of new theorems as well as automated reasoning about computer programs.

          • @smeg@feddit.uk
            link
            fedilink
            English
            21 month ago

            But like… what does the proof even entail? I feel if you asked a child (or maybe me) what the proof was they’d say “well the definition of those two numbers, and the definition of plus means that 1+1=2”. What else is there?

            • xigoi
              link
              English
              11 month ago

              Proving it from the definition is quite easy. The hard part is to build up all the concepts that you need to define the numbers and the operation in the first place. What exactly that entails depends on what axiom system and system of logic you are using. For example, here is the Metamath proof of 1 + 1 = 2, where you can click to see all the axioms, definitions and theorems involved.

              • @smeg@feddit.uk
                link
                fedilink
                English
                11 month ago

                I don’t even know where to start with that page. I feel like the curtain has really been pulled back today!