First of all, pure mathematics pays attention to theory and abstraction. It is devoted to exploring the basic concepts, principles and structures of mathematics, and pursuing the inherent beauty and logical rigor of mathematics. Pure mathematicians promote the development of mathematics by proposing new mathematical theorems, proving and discovering new mathematical laws. The study of pure mathematics often does not depend on specific practical applications, but pursues the perfection and universality of mathematics itself.
In contrast, applied mathematics pays more attention to solving practical problems and providing practical solutions. It focuses on applying mathematical methods and techniques to various fields, such as physics, engineering and economics. , to solve specific problems in the real world. Applied mathematicians usually need interdisciplinary knowledge and skills, and can combine mathematical theory with practical problems to provide effective solutions to practical problems.
In addition, pure mathematics and applied mathematics are also different in research methods and ways of thinking. Pure mathematics emphasizes logical reasoning and proof, and pays attention to abstract thinking and formal expression. Applied mathematics pays more attention to numerical calculation, model building and experimental verification, emphasizing practicality and operability.
Although there are differences in research objectives and methods between pure mathematics and applied mathematics, there are also close links and mutual promotion between them. Pure mathematics provides a solid theoretical foundation and tools for applied mathematics, and applied mathematics provides practical challenges and application scenarios for pure mathematics. Therefore, both pure mathematics and applied mathematics occupy an important position in mathematics, complement each other and develop each other.