The brand-new and epoch-making set theory initiated by Cantor is the first time in the history of human cognition to establish an abstract formal symbol system and definite operation for infinity since the ancient Greek era of more than 2,000 years. It reveals the characteristics of infinity in essence, makes the concept of infinity revolutionize, and permeates all branches of mathematics, fundamentally transforms the structure of mathematics, promotes the establishment and development of many other new branches of mathematics, and becomes the theory of real variable function and algebraic topology. However, Cantor's set theory is not perfect. On the one hand, Cantor is always at a loss about the "continuum hypothesis" and "well-ordered theorem". On the other hand, the Blary-Forty Paradox, Cantor Paradox and Russell Paradox discovered at the turn of19th century have made people seriously doubt the reliability of set theory. In addition, the emergence of set theory really impacted the traditional ideas and reversed many predecessors' ideas, which was difficult for mathematicians at that time to accept and was opposed by many people, among which Kroneck, one of the representatives of Berlin School and a structuralist, was the most fierce. Kroneck thinks that the object of mathematics must be constructable, and what cannot be constructed by finite steps is suspicious and should not be regarded as the object of mathematics. He opposed the theory of irrational numbers and continuous functions, and severely criticized and viciously attacked Cantor's theory of infinite set and surplus, which was not mathematics but mysticism. He said that Cantor's set theory was empty. Besides Ronic, some famous mathematicians also expressed their opposition to set theory. French mathematician Jules Henri (1854.4.29-1912.7.17) said, "I personally, and I'm not alone, think it's important not to introduce things that can't be fully defined with limited words. He described set theory as an interesting "morbid state" and predicted that "later generations will regard (Cantor's) set theory as a disease from which people have recovered". German mathematician Weil (Wey 1, Claude Hugo Herman,1885.1.9-1955.12.8) thinks that Cantor's hierarchical view of cardinality is "on the fog. Klein (Christian Felix,1849.4.25-1925.6.22) also disapproved of the idea of set theory. Mathematician H.A. Schwartz used to be a good friend of Cantor, but he broke off relations with Cantor because he opposed set theory. After the paradox of set theory appeared, they began to think that set theory was a morbid state. They developed into empiricism, semi-empiricism, intuitionism and constructivism in different ways, and formed the anti-Cantor camp in the basic war. 1884, because the continuum hypothesis has not been proved for a long time, coupled with the sharp opposition with Kroneck, his spirit was repeatedly hit. At the end of May, he couldn't support it, and he had a mental breakdown for the first time. He was depressed, unable to concentrate on the study of set theory, and was deeply involved in the debate of theology, philosophy and literature. However, whenever he returns to his normal state, his thinking always becomes unusually clear and he continues his work on set theory. Cantor's set theory has been publicly recognized and warmly praised, and it should be said that the first international congress of mathematicians held in Zurich has already begun to show signs. Professor Hurwitz (Adolf,1859.3.26-19.118) clearly pointed out in his comprehensive report that Cantor's set theory has greatly promoted. At the group meeting, the French mathematician Hadamard Jacques (1865.12.8-1963.438+00.17) also reported Cantor's important role in his work. As time goes on, people gradually realize the importance of set theory. Hilbert David (1862.1.23-1943.2.14) spoke highly of Cantor's set theory as "the best work of mathematical genius", "one of the highest achievements of human pure intellectual activities" and "the greatest work that can be boasted in this era. At the second international congress of mathematicians in 1900, Hilbert spoke highly of the importance of Cantor's work and put Cantor's continuum hypothesis at the top of 23 important mathematical problems to be solved in the early 20th century. When a series of paradoxes appeared in Cantor's naive set theory, Kroneck's successor Brouwer (1881.2.27-1966.12.2) and others made a big fuss about it. Hilbert declared to his contemporaries in firm language: "No one can drive us out of the Garden of Eden created by Cantor.