Were you to be developing a new field of mathematics then you would apply the scientific method.
Nonsense. The principle tool is logical deduction. Once enough of the base framework is developed, it is possible to use a process similar to the scientific method to launch deeper into the field, introducing tentativity and uncertainty. This is often the tactic used by mathematical physicists such as myself, and we are constantly criticised for it
Furthermore, any part of the body of work so developed is considered conjecture until it is formally connected with the foundations of the field.
Possible example: the relationship between Donaldson Theory and Seiberg-Witten Theory.
Mathematics can certainly appear scientific at times, but to claim that Mathematics is a science in the modern understanding of the word is simply wrong. In fact, I know several mathematicians who would claim that tentativity is the antithesis of mathematics.