[barmar]

I think the right answer is a middle ground between just knowing how to use math and understanding how it works at a deep level. Do most people need to be able to prove the Pythagorean Theorem? I don't think so. But should they understand the general principle of mathematical proofs? While it may not come up much in their day-to-day life, I still think it's a good idea because it improves logical thinking and understanding. Similarly, you don't need to actually BE a scientist to get value from understanding the scientific method -- this helps you judge statements made by and about scientists, which is important for making decisions in the real world.

[kenberg]

 barmar, on 2015-March-15, 10:19, said:

I think the right answer is a middle ground between just knowing how to use math and understanding how it works at a deep level. Do most people need to be able to prove the Pythagorean Theorem? I don't think so. But should they understand the general principle of mathematical proofs? While it may not come up much in their day-to-day life, I still think it's a good idea because it improves logical thinking and understanding. Similarly, you don't need to actually BE a scientist to get value from understanding the scientific method -- this helps you judge statements made by and about scientists, which is important for making decisions in the real world.

I agree with this, probably no surprise there. The Pythagorean Theorem can be something of a metaphor. By itself it is hard to see any useful purpose. to it. But the idea that we can form abstract ideas and logically follow where they lead us? That's another matter.

it is often noted that the existence of 3-4-5 right triangles was known long before Pythagoras. True enough. But the full theorem, together with a logical demonstration of its truth, does, at least I think that it does, belong to the ancient Greeks even if not to Pythagoras. And that's a big step up from a 3-4-5 right triangle.