What is Deductive Reasoning?
Both inductive and deductive reasoning are valid and both are subject to error. Not having found an error leads us to believe that any given hypothesis is valid and correct, but not having found the error does not preclude it's existence. That is why I said "philosophically speaking". Not having found, ever, a four sided triangle or a distance between two points whose shortest distance is not measured by a straight line or the square of a hypotenuse that was not equal to the sum of the other two squares, we accept these as facts. But other dimensions may exist where these axioms fail. The future is unknown.Deductive reasoning is one of the two basic forms of valid reasoning. While inductive reasoning argues from the particular to the general, deductive reasoning argues from the general to a specific instance. The basic idea is that if something is true of a class of things in general, this truth applies to all legitimate members of that class. The key, then, is to be able to properly identify members of the class. Miscategorizing will result in invalid conclusions.
Math, dear sir, remains as "unproven" and "unprovable" as anything else from the ontological standpoint.