How widely used is this method? Is it the most popular proof technique? All it takes it to find a condradiction or counter example in order to prove something which is often much simpler than listing all the cases (not to mention if there are infinte of them to start with) or directly proving something. i.e To prove A=>B Proof by contradiction works by showing ~B=>~A So if A is true than B must be true which is what we set out to prove. When doing undergrad abstract algebra, I am finding that I am using this method a lot. Is this good? Wasn't this Godfrey Hardy's favouriate proof technique?