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.
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
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.
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
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…
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?
This is what happens when the mathematicians spend too much time thinking without any practical applications. Madness!
We all know that math is just a weirdly specific branch of philosophy.
Physics is just a weirdly specific branch of math
Only recently
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.
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
I’d love to see the practical applications of someone taking 360 pages to justify that 1+1=2
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.
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
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…
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?