I accept the hypothesis that the body of existing principles of mathematics is the creation of the combined efforts of persons truly called pure mathematicians. Tracing the history of the origins of specific mathematical principles can be an inaccurate effort at best. However, accepting the origins that have been assigned by mathematics historians does not violate the premise that particular mathematical principles have been created by particular pure mathematicians. It is also true that a given mathematical idea is often re-created independently by different persons. Every person involved in the study of mathematics can be called a mathematician during the time of that study.
Art is the practice of creating perceptible forms expressive of human feelings.
Science is an activity which has as its goal the formulation and understanding of a complete model of the universe. A tool is a device designed to extend human powers. Language is the symbolic representation of human perceptions. Mathematics, in its various aspects, takes on the roles of art, science, tool, and language. A Scientific Approach Set up an efficient way to spin the four coins simultaneously, and do so many times, recording the results.