1. Mathematics is a necessary tool and language for people to make great discoveries in nature (time, space, material movement, etc.). ), society (economy, system and culture) and human thinking (philosophy, art and culture). Every field involved in mathematics embodies its importance. Major inventions and discoveries can create new branches of mathematics in the future. It will inevitably lead to or rely on a breakthrough in the foundation or essence of mathematics. 2. The rise of the modern west, especially the United States of America, found that the driving force of its scientific and technological military development was mathematics and related projects. As long as you have a copy & gt (available online). After a little statistics or analysis, we can find the law. The four ancient civilizations (ancient Egypt, ancient India, ancient Babylon and ancient China) and Greek civilization reached their peak in the> modern times19th century. Britain, France, Germany and other western European countries and China made the most important mathematical discoveries, so the richest countries in the world at that time were also these countries. In China, although there are many mathematical discoveries, it can be said that there are no important or essential discoveries like those in western European countries, and the people's awareness of prevention was not strong at that time. Suffering from the invasion and expansion of western Europe, the most striking thing is that most of the major mathematical discoveries from the 20th century to the present can be said to be a one-man show by the United States, which is consistent with its hegemonic position in the world during this period. In the first half of the 20th century, the Soviet Union also made many important discoveries, and its strength was still very strong at that time. China also made some mathematical discoveries in modern times and the 20th century. But its quantity and quality are not enough, so the economy is developing now, but this development is not enough. There are also many great discoveries in mathematics in Japan, but there are also many international awards, which also shows that although Japan is relatively developed in economy and technology, its strength is still insufficient. After entering the 2 1 century, the development direction of all countries must be planning adjustment, which is unknown to other countries, except for China, where major inventions and discoveries are patented every year. To sum up, the strength of a country at that time can be said to be almost in line with the proportion of major achievements in world mathematics. It can be said that we can list the progress brought about by the major discoveries in mathematics. This will be known after studying mathematics. Then carefully analyze the actual contents of major mathematical discoveries in different countries in different periods, and we can know how similar the mathematical contents of the discoveries are, that is, the contents of economic and cultural development at that time! I wish you good grades! !