What's the word that means "I'm assuming this for the time being and upon using the assumption, if I get the correct answer, then it proves that the assumption is true" Our teacher regularly assumes stuff and use them in a formula and if the result is correct then we know that the assumtion we made is true. He uses a word that sounds something like 'Asphases' but turns out it's not a word as per dictionary so can anyone tell me what he actually means when he says that or if there is another word which has same meaning that would be also great.
I think the word you're looking for (which sounds similar to your asphases) is hypothesis:
1 a : an assumption or concession made for the sake of argument
b : an interpretation of a practical situation or condition taken as the ground for action
2 : a tentative assumption made in order to draw out and test its logical or empirical consequences
3 : the antecedent clause of a conditional statement
In particular, it's sense 2 in your case.
If your description is accurate, it's a case of circular reasoning. You can't prove something by assuming it's true and conclude there is no contradiction. This is mathematics, not a sudoku... The opposite, assuming the negation of the original assumption and reaching a contradiction works and this technique is called proof by contradiction.
It's likely that your professor starts with certain statements called axioms, for example the Peano axioms for natural numbers. But these are foundations of mathematics and reasonings shouldn't try to prove them.