Let me paraphrase you: Knowing how to multiply two 3 digit numbers is boring. The method has been known for thousands of years, and you've got calculators that can do it for you. So why should one learn how to do that?
The answer is that it gives you intuition about how these things behave, even if you always use a calculator to come up with the correct result.
And mental back-of-the-envelope calculation is unbelievably useful in every day life; if you can't do it, I can guarantee that you're either making worse decisions for it, or wasting a lot of time optimizing your every purchase by typing it on a calculator.
Similarly, you need to practice proving and reading proofs so you actually have the right intuition about what constitutes "proof". Unfortunately, all of western culture, and american culture in particular, is so far divorced from the concept of sound logic, that it is very likely that most people don't even realize they are missing something.
It's not any of the specific proofs that matter. It's the exercise. You go to the gym to exercise your muscle; You do proofs to exercise your logic.
The answer is that it gives you intuition about how these things behave, even if you always use a calculator to come up with the correct result.
And mental back-of-the-envelope calculation is unbelievably useful in every day life; if you can't do it, I can guarantee that you're either making worse decisions for it, or wasting a lot of time optimizing your every purchase by typing it on a calculator.
Similarly, you need to practice proving and reading proofs so you actually have the right intuition about what constitutes "proof". Unfortunately, all of western culture, and american culture in particular, is so far divorced from the concept of sound logic, that it is very likely that most people don't even realize they are missing something.
It's not any of the specific proofs that matter. It's the exercise. You go to the gym to exercise your muscle; You do proofs to exercise your logic.