I've been thinking about this for a few days now, and it has come to my attention, how do you prove your answer is correct?

Formulas and geometric proof put to one side; I'm talking about the answer to your problem in general.

If one ever watches the MIT math "You-Tube" videos, then you will notice how a
correction for an error that was made pop up every now and again.

Back in the day, there is no doubt i'm sure, a small error can "somehow" get magnified through cumbersome black boards full of math.

My point is, what does your answer depend upon?

Is it competence, a back-up mathemetician, double-checking your work, mathematical reasoning?

There is always room for error and somehow it happens, but back then computer software did not exist, it was purely down to competence in one respect.

 

on large scale, knowing the theory behind your problem - does your solution make sense? You should have an idea of what your expected answer will look like. There have been many times where I had lengthy problems to solve on the test and my answer made no sense often because of messed up signs in the middle of the calculation... Given time, you go through your work and double check the approach and algebra. The beauty of this approach is that software will spit out non-sense answers to problems which are correctly calculated but are invalid for other reasons, they got no critical thinking.

 

on large scale, knowing the theory behind your problem - does your solution make sense? You should have an idea of what your expected answer will look like. There have been many times where I had lengthy problems to solve on the test and my answer made no sense often because of messed up signs in the middle of the calculation... Given time, you go through your work and double check the approach and algebra. The beauty of this approach is that software will spit out non-sense answers to problems which are correctly calculated but are invalid for other reasons, they got no critical thinking.

Justtrying, you have contradicted yourself.

You should have an idea of what your expected answer will look like.

There have been many times where I had lengthy problems to solve on the test and my answer made no sense often because of messed up signs in the middle of the calculation...

 

the point is that I know my answer is wrong because it is not what I expected, then there is a reason for the mistakes - wrong application of theory or algebra problems.

ex/ calculating RMS value - your answer should be positive so if you see a negative number you already know it is wrong.

Ultimately your answer is correct if your calculations are correct

btw, it is proving

 

the point is that I know my answer is wrong because it is not what I expected, then there is a reason for the mistakes - wrong application of theory or algebra problems.

ex/ calculating RMS value - your answer should be positive so if you see a negative number you already know it is wrong.

Ultimately your answer is correct if your calculations are correct

btw, it is proving

I 100% agree.

I think a considerable viewpoint, for me anyway, is theory in general. I cannot accept the theory until I see proof.

This reminds me when I was introduced to Ohms law. Only after I had seen the math to derive V=IR, I accepted it and I have no reason why.

 

I am the same way. Seeing proofs also reinforces understanding. What is amazing is that there are still a number of theorems that have not been proven but are actually being used - Riemann Hypothesis for example, I only know of it and the fact that other theorems have been built based on it being true, but it is still unproven, but has been verified to make it usable.