A remarkable feature of pure mathematics is to temporarily put aside the specific content and study the quantitative relationship and spatial form of things in pure form. It studies the inherent laws of mathematical structure itself according to the inherent needs of mathematics or its possible future application, and has no direct connection with other disciplines seeking common ground to solve practical problems.
Applied mathematics has developed rapidly. After all, the real world is the source of mathematics development. Since17th century, social development and production demand have been the main driving forces for the development of mathematics. Mathematics can provide tools for other disciplines and make them more powerful. At the same time, the development of other disciplines will greatly promote the progress of mathematics, which is an important feature of mathematics.
Newton invented calculus to meet the needs of physics, and tycho brahe discovered Neptune by mathematical methods. Until the 20th century, the manufacture and navigation of jet planes and spaceships, medical equipment scanned by CT, and battle plans for organizing large-scale wars were all mathematical techniques in essence.