Mathematics

Data from the famous Michelson–Morley experiment
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 extensive use of mathematics and mathematical models. Calculus may be the branch of mathematics most often used in science[citation needed], but virtually every branch of mathematics has applications in science, including "pure" areas such as number theory and topology. Mathematics is fundamental to the understanding of the natural sciences and the social sciences, many of which also rely heavily on statistics.
Statistical methods, comprised of mathematical techniques for summarizing and exploring data, allow scientists to assess the level of reliability and the range of variation in experimental results. Statistical thinking also plays a fundamental role in many areas of science.
Computational science applies computing power to simulate real-world situations, enabling a better understanding of scientific problems than formal mathematics alone can achieve. According to the Society for Industrial and Applied Mathematics, computation is now as important as theory and experiment in advancing scientific knowledge.[13]
Whether mathematics itself is properly classified as science has been a matter of some debate. 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. In practice, 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 general, mathematics is classified as formal science, while natural and social sciences are classified as empirical sciences.