Is inductive reasoning superior to contradictory reasoning?

There are two methods of proof in maths and I assume it's the same for philosophy: induction and contradiction. To me contradiction is the impulse of everyone who engages in an argument, whereas inductive reasoning requires patience and thought and often leads to more significant discoveries of fact. Do you agree or disagree?

Is math induction? Induction never leads to fact.

Induction (via science) has made discoveries, and I don't think the other one has?

Maths uses induction and contradiction as methods of proof. That doesn't make it either of them as much as it doesn't make me a spoon to use a spoon.

So it seems that discovery (about the natural world) is most important to you. But there are areas of science that will never be discovered due to ethics, which is a philosophical concept. Therefore science is constrained by philosophy. It seems that we should deal ourselves with the constraint and discover its causes before we engage in the art of discovery (science).

Discovery has made a larger contribution to survival.

Discovery has made a larger contribution to survival.

survival is meaningless, there is no point to existence anymore unless we thrive. chickens, sheep, cows all survive - i'd not like to be any of them.

That wasn't the question however.

There seems to be some confusion about mathematical induction vs inductive reasoning. Mathematical induction is actually a form of deductive reasoning. Science uses inductive reasoning based on empirical evidence.

If OP meant mathematical induction versus proof by contradiction, then that's a different question, but there isn't so much overlap with philosophy.