Math And Logic Are Formal Sciences

Let's put Mathematics and Logic in proper relationship to Science:

"Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.^[1] Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural and social sciences by providing information about the structures the latter use to describe the world, and what inferences may be made about them." (link)

"Formal sciences – branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules." (link)

"All of science relies heavily on the existing abstract frameworks of mathematics and logic to interpret and describe the evidence it analyzes and ultimately to express its conclusions. Put simply, science uses mathematics and logic as scaffolding to construct predictive models, using empirical evidence as building materials. In this way, all branches of science are concerned with these fields, but no branch of science is directly concerned with advancing them.

"In a similar way, applied fields such as Medicine and Engineering rely heavily on the natural sciences as a framework on which to build, but are not themselves concerned with advancing those fields." (link)

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The principles underlying mathematics and logic are axiomatic.