Mathematics and the scientific method

Mathematics is essential to many sciences. One important function of mathematics in science is the role it plays in the expression of scientific models. Observing and collecting measurements, as well as hypothesizing and predicting, often require mathematical models and extensive use of mathematics. Mathematical branches most often used in science include calculus and statistics, although virtually every branch of mathematics has applications, even "pure" areas such as number theory and topology. Mathematics is most prevalent in physics, but less so in chemistry, biology, and some social sciences.

Some thinkers see mathematicians as scientists, regarding physical experiments as inessential or mathematical proofs as equivalent to experiments. Others do not see mathematics as a science, since it does not require experimental test of its theories and hypotheses, although some theorems can be disproved by contradiction through finding exceptions. (More specifically, mathematical theorems and formulas are obtained by logical derivations which presume axiomatic systems, rather than a combination of empirical observation and method of reasoning that has come to be known as scientific method.) In either case, the fact that mathematics is such a useful tool in describing the universe is a central issue in the philosophy of mathematics.

Further information: Eugene Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences