Mathematics solves problems by using logic. One of the main
tools of logic used by mathematicians is deduction. Deduction is
a special way of thinking to discover and prove new truths using old
truths. Using deduction is what makes mathematical thinking different from
other kinds of scientific thinking, which might rely on experiments or on
interviews.
Logic and reasoning are used by mathematicians to create
general rules, which are an important part of mathematics. These rules
leave out information that is not important so that a single rule can
cover many situations. By finding general rules, mathematics solves many
problems at the same time as these rules can be used on other problems.