Proof methods are systematic approaches used to establish the truth of mathematical statements or theorems. Common methods include direct proof, where a statement is proven by straightforward logical reasoning, and indirect proof, which involves assuming the opposite of what is to be proven and showing that this leads to a contradiction. Another important proof method is mathematical induction, often used for statements involving natural numbers. This method consists of two steps: proving the base case and then showing that if the statement holds for an arbitrary case, it must also hold for the next case. These methods are essential in mathematics for validating results.