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Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
In Raphael's fresco The School of Athens, Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of music theory on a lyre above a drawing of the sacred tetractys.