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# Why are students of mathematics made learn proofs?

I am a maths student.

I've never understood why maths students (either in school or higher) are forced to learn off proofs of theorems.

For example, everybody knows Pythagoras' theorem, why aren't people just taught the fact that x^2 + y^2 = z^2 in a right triangle and then given problems about where to use it? What is the purpose of a student learning *why* this fact is true?

I'm completely serious about this. Yes, fair enough, some people might question the proof, but the proof should be presented as "additional reading" for people who don't believe the result at face value, students should not be required to learn it off.

Example in my case, when I first learned Pythagoras' theorem, I *was* interested in why it was true and initially thought "no way", so the proof was nice to me. When I first learned about things like "the squeeze theorem" and "the fundamental theorem of calculus" I would have been more than happy to accept these at face value (in the knowledge these facts had been proven) WITHOUT having to actually learn these off by heart.

Also, why are they called "theorems" and "lemmas"? This is needlessly pompous and intimidating to weaker students. Just call them "facts"

### 3 Answers

- ?Lv 71 month agoFavorite Answer
The idea is so that you can verify the theorem's correctness to yourself.

The process also gives you the skills you need should you find yourslef needing to prove something in the future.

- ?Lv 71 month ago
Advanced math is abstract. Construct a system not based on observation. Discard Euclid’s fifth postulate. How do you verify its correctness?

- ted sLv 71 month ago
Then YOU should go to another discipline . There have been many statements which were "proved" by people which have been found to be false { counter-exampled } . How do YOU know the "Pythagorean Theorem " is valid ? Mathematicians {good ones } never accept as valid a statement made about mathematics which has no proof.