pure mathematics
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Pure mathematics is the study of mathematical ideas and structures for their own sake, without concern for practical applications in the real world. It matters because it develops fundamental knowledge and tools that often later find unexpected uses in science, engineering, and technology, while also expanding human understanding of abstract logical systems.
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Mathematics Portal v t e
Pure mathematics is an informal term to describe the study of the properties and structure of abstract objects, such as the Mandelbrot set. This may be done without focusing on concrete applications of concepts in the physical world. In the context of the philosophy of mathematics, pure mathematics is an informal term to describe the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but research is not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of defining new mathematical objects or working out the mathematical consequences of basic principles.