Biography should not only describe the facts, but also explain them. Why did Cantor get sick? Why hasn't he recovered? Is it a physiological accident or an inevitable result caused by the environment? People can only give some guesses and can't prove the reason. These analyses can be found in Hu Zuoxuan's Philosopher and Scientist-Cantor: The Golden Apple Causing Disputes (Hu Zuoxuan, The Golden Apple Causing Disputes-Cantor, Hunan Education Press, 1993) (translated by Bell, Xu Yuan, Mathematical Elite, Commercial Press, 19 1). In the process of expounding the facts, the biographer also expressed his different views.
The first is the attack of Kroneck and others. After the publication of Cantor's research results, it was severely criticized by some famous mathematicians at that time, including French mathematician Poincare, German mathematicians Weil and Klein, among which German mathematician Kroneck was the one with the fiercest words and the longest attack time. Kroneck was a born skeptic. His basic mathematical view is that "God created integers, and all other numbers are man-made". His mathematical achievements were achieved by attacking Wilstrass, a master of mathematical analysis. Some people think that Kroneck attacked others because of his height. "If Kroneck were six or seven inches taller, maybe he wouldn't feel compelled to make a fuss and overemphasize his opposition to analytical research." Because the content of the theory of * * * is quite different from his ideas, Kroneck has reached an intolerable level, and 10 has been attacking Cantor for years. Cantor has been teaching at Haller University with a low salary. He tried several times to get a higher salary and a more prestigious professorship in Berlin, but he failed because of the influence of Kroneck. Cantor wanted to seek a professorship in another famous university-University of G? ttingen, but he failed because of the opposition of Schwartz, a mathematician who was his friend but was later hostile to the theory of * * *. Despite repeated setbacks in his position, Cantor also has many academic bosom friends, including German mathematicians Hurve, Wilstras, Mittag Leffler, Emile, Hilbert and so on. It should be said that his theory of * * * achieved initial success before and after Cantor went crazy. This explanation highlights the conflict between conservatives and innovators in the scientific community.
Secondly, his personality weakness. Cantor is neurotic by nature, easily excited, with a strong color of * * *, and takes others' criticisms too seriously, so it is difficult to deal with objections from an academic point of view. "Kroneck may have been severely criticized for Cantor's tragedy; His attack is just one of many reasons. Not being recognized makes the person who believes that he has taken the first step-and the last step-to the theory of infinite rationality indignant, and depression makes him suffer from depression and irrationality. " Any new idea may be doubted and opposed by others. These doubts and objections are not unreasonable and play an important role in clarifying the vague concepts of new ideas. It is disgraceful for Kronel to insult Cantor in front of his students, but he sometimes shows gentlemanly and scholarly manners, that is, he objectively resolves disputes through academic articles. For example, since Cantor's articles are mainly published in the Journal of Mathematics edited by Mittag Leffler, Kroneck also hopes to publish a short article here to explain his views on some mathematical concepts. But Cantor was afraid of Kroneck's prestige and that Kroneck's article would occupy his own territory, so he told Mittag Lefler that if an article signed by Kroneck was published, he would withdraw his article. Although Kroneck didn't publish an article in the end, Cantor's sensitivity can be seen. Later, because Mittag Leffler rejected an article by Cantor with too many new terms and philosophical flavor, Cantor's relationship with his most supportive friend was also alienated. This explanation highlights the role of individual personality factors in scientific research.
The third is the problem of science itself. The weakness of personality led to Cantor's failure in scientific debate. "Kroneck is the most capable warrior in scientific debate; Cantor is one of the most incompetent soldiers. " But "Kroneck's strong hostility towards Cantor is not entirely personal, but at least partly scientific and unbiased." Cantor emphasized the infinite theory of reality, while Kroneck recognized natural numbers and what they constructed through finite steps, and opposed the proof of infinite reality and non-structure. This is a basic problem in mathematics, and there have always been great differences. Different mathematicians belong to different camps. With the success of * * * theory in dealing with the logical basis of real number theory, although the external hostile forces are weakening, Cantor has been puzzled by two major problems arising from * * * theory, one is the internal contradiction of * * * theory, and the other is the continuum hypothesis and good order theorem of * * * theory. Cantor has neither the ability to solve these problems nor the ability to get rid of them. For example, although Cantor repeatedly claimed or promised to give an accurate proof of the continuum hypothesis, he never succeeded, which made his theory of * * * unstable and in danger of being destroyed at any time, so he has always been worried about it. When a mathematician announced the failure of the continuum hypothesis, he was pale and trembling with anger. This explanation means that the formation of scientific concepts is gradual, and the existence of conflicts is inevitable from the beginning.
Finally, the defect of thinking method. Unable to find a solution to academic and work problems, Cantor turned to theology and Platonism. Cantor even applied to the university authorities to change his position as a professor of mathematics to a professor of philosophy, trying to gain a place in the debate between theology and philosophy. He believes that his theory of * * * is inspired by God, and that God can not only solve the problem of continuum hypothesis, but also ensure the objectivity and concreteness of all real cardinality. He regards the theory of * * * as a "metaphysical theory" and thinks that infinite * * * actually exists "both concretely and abstractly". Of course, it is impossible for Cantor to convince those opposing forces in this way of thinking. On the contrary, it exposed some weak links in the development of * * * theory and gave opponents more attack points. When Cantor's inner world based on religion and philosophy is also impacted and shocked, it is even more difficult to maintain mental normality. This explanation gives the personal philosophical point of view and the influence of the inner world on scientific research.