"The deductive method is used exclusively in mathematics, and the inductive method (it is the scientific method, after all) is used exclusively in science, right?"
As stated previously, mathematicians do not spend their days plodding along from theorem to theorem - mathematics requires insight, exploration, intuition, hypothesis, and yes, experiment. Mathematicians use inductive methods to explore mathematics.
However, what is accepted as evidence in mathematics is proof - the deductive method rules. You can (and should) use any method possible to discover new mathematics, but in order for your discoveries to be accepted, you must be able to fit them into the deductive structure of mathematics.
On the other hand, physicists use mathematics all the time. Every major physical theory of the last 400 years has been mathematical in nature - theoretical physics is mathematical physics. To explore the consequences of their theories, physicists use the tools of mathematics - deductive methods.
However, what is accepted as evidence in science is observation - the inductive method rules here. That doesn't mean that scientists never use deductive reasoning - they do, profitably and all the time - but that in order for a discovery to be accepted as a part of science, it must agree with observations of nature.
So, the statement that began this page turns out to be considerably oversimplified. Oh well, most statements about the nature of science and mathematics are, by necessity, oversimplified.
BHS -> Mr. Stanbrough -> Physics -> About Science -> this page