Pure mathematics, also known as theoretical mathematics or fundamental mathematics, refers to the branch of mathematics that focuses on the exploration and development of abstract mathematical concepts and structures, often without explicit consideration of their immediate applications to the physical world. It is primarily concerned with the study of mathematical principles, properties, and relationships, as well as the development and proof of theorems within various mathematical disciplines.

Pure mathematics seeks to establish rigorous logical frameworks and formal systems, employing deductive reasoning and mathematical proof to derive new results and extend existing theories. It encompasses a wide range of areas such as algebra, analysis, geometry, number theory, topology, logic, and set theory, among others.

Unlike applied mathematics, which emphasizes the utilization of mathematical techniques to solve practical problems in fields like physics, engineering, economics, and computer science, pure mathematics is driven by a pursuit of intellectual curiosity and a desire to uncover fundamental truths about the nature of mathematics itself. It often involves exploring abstract structures, patterns, and relationships that may have no direct physical interpretation but have profound implications for understanding the underlying mathematical principles governing the universe.

In summary, pure mathematics is the discipline that investigates abstract mathematical concepts, establishes logical frameworks, and seeks to develop a deep understanding of the fundamental principles and structures of mathematics. Its focus lies in the pursuit of knowledge and the exploration of mathematical truths independent of immediate applications.

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