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. There are many areas of mathematics , which include number theory ( the study of numbers) , algebra (the study of formulas and related structures), geometry (thestudy of shapes and spaces that contain them), analysis (the study of continuous changes), and the set theory (presently used as a foundation for all mathematics).