Mathematics is essential to the 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.algebra ,geometry ,calculus etc for example, are all essential to physics . every branch of mathematics has applications in science, including "pure" areas such as number theory and topology .
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 of industrial and applied mathematics , computation is now as important as theory and experiment in advancing scientific knowledge.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 an experimental test of its theories and hypotheses.
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