Mathematics is the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics). It involves the study of patterns, relationships, and structures through the use of symbols and logical reasoning. Key branches of mathematics include arithmetic, algebra, geometry, calculus, and statistics. Mathematicians seek to understand and solve problems related to numerical and spatial relationships, and they develop theories and techniques that can be used to model and analyze real-world situations. Mathematics is characterized by its rigorous approach to proof and logical deduction, making it a fundamental tool in various fields, including natural and social sciences, computer science, finance, and engineering.
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