how mathematicians “prove” that mathematical proofs, such as the Pythagorean Theorem, are true for any input?

Question

how mathematicians “prove” that mathematical proofs, such as the Pythagorean Theorem, are true for any input?

In: 51

Answer 1

In a proof, we use previously known true statements to go from assumption to the thing which we need to prove. It basically boils down to several steps where we show if A is true, then B is has to be true also. Simplest examples to check out are probably some basic proofs in algebra/number theory, like the proof that square of every even number is even.