Highly specialized
Nowadays, society has entered a stage of highly division of labor, and what people do is more and more confined to a certain field, even within a small scope of a certain field. People are getting longer and longer education, and the questions are getting smaller and deeper and more abstract. It is almost impossible to create a generalist nowadays, mainly because many subjects were relatively shallow in the past, and many achievements that now seem simple can be recorded in history. The most impressive is Von Neumann. If you want to know more, you can see the genius of the pioneers.
Branch of mathematics
Similarly in the field of mathematics, starting with the ancient simple geometry of counting arithmetic, then modern mathematics based on analytic geometry of calculus, to modern mathematics based on set theory and axiom. There are so many branches of mathematics today, the whole structure is so complex, so deep and so abstract that many theories are beyond the comprehension of most people. Mathematics has rigorous logic, but the development of mathematics can not blindly profound abstraction, but also should make mathematics more widely used, modern mathematics is also divided into two categories, namely pure mathematics and applied mathematics.
Set theory
Set theory was created by The German mathematician Cantor. At first set was built on the set of numbers and points, and later extended to any set of elements, be it a set of functions or a set of geometry. Because of its abstraction, it can be used in other branches of mathematics, and set theory has become the foundation of mathematics. A collection is a population of objects that can be finite or infinite.
axiomatic
Said to axiomatic was first discovered by the ancient Greek mathematician Euclid and use, such as the well-known “geometry originally is the application of the axiomatic method, of which five postulate and five axioms as the foundation, put forward the article 119 of the 465 definitions and propositions and has been proved that the established first in the history of mathematics axiom system. Of course, Euclid’s axiomatic system was not perfect, and later the German mathematician Hilbert redefined the modern axiomatic method. He is also known as the Alexander of mathematics, and in 1900 put forward 23 mathematical problems at the International Congress of Mathematicians, pointing out the direction of the development of mathematics in the 20th century.
abstract
Let’s start with the concept of abstraction. The English word for it is abstract, which we often see at the beginning of papers. So the abstraction is actually the abstract, and what the abstract does is abstracts the summary. Abstraction is a concise and accurate description extracted from nature, the world and things. Based on set theory and axiomatic methods, mathematics has also moved towards more abstraction, such as function theory, functional analysis, topology, and abstract algebra.
Mathematics and Physics
Mathematics is a powerful tool that penetrates into physics, and the reason why it can be used to describe physics is that mathematics can express the laws of physics in a concise and clear way through symbols. In the 18th century it was mainly classical mechanics and mathematics, in the 19th century it was electromagnetism, and in the 20th century it was relativity and quantum mechanics. Einstein’s special theory of relativity found a perfect description through mathematics, the basic principles of physical theory through mathematical models to express the logical structure. Mathematics helped physics form a unified system, and in turn physics’ new need for mathematical tools drove mathematics.
Mathematics and Computers
Computer science is the same, every big development of the computer is inseparable from mathematics, and the continuous development of the computer also promotes the research of mathematics. Belongs to one of the branch of computer science of artificial intelligence, for example, although now artificial intelligence has been hyped, and can defeat human in go, but still has a lot of math problems not solve, artificial intelligence is only in the field of mathematics has the theoretical breakthrough will have more development, the nature of mathematics also obtained the development in the process. Mathematician Von Neumann developed the idea of storing programs, and the idea of processing and storing data in parallel, which greatly influenced the development of computer science. The Turing computer model, proposed by mathematician Alan Turing, uses the language of mathematical logic to design computers, abstracting the process of people using pen and paper to perform mathematical operations. He was also one of the first to study how to make computers capable of thinking and came up with the famous Turing test for artificial intelligence. Shannon’s introduction of Boolean’s logical operations into computers, and his theory of information, all related to mathematics.
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