Peng Jiale's Mathematical Aesthetics And Methods

Henri Poincare is famous French mathematician, who is also an outstanding philosopher of science, in his math research activities, ubiquitous shadow of mathematical beauty, thus enables the Poincare became a pioneer in the field of science and aesthetics. Since ancient times, for a discussion on the relationship between truth and beauty has never been interrupted, on the contrary, with the development of the times, the progress of science, the topic has attracted more and more attention. Poincare as the pioneer of science aesthetics, we from his《Science and Method》、《The Value of Science》、《Science and Assumption》 several this works among are can see many on mathematics beauty of wonderful discusses, these discusses is incisive, but is too dispersed, and in this paper, the Poincare as the research object, from the perspective of aesthetics to explore Poincare’s creation, the Poincare’s aesthetic thoughts of the system and methods for finishing and induction, this for us to study mathematics aesthetics and science aesthetics have important enlightenment function.This paper first discusses the system about this topic research background, in the process of research, actually it’s not hard to find, there have been many predecessors to mathematical aesthetics have had more or less are theory, and this gives us the Poincare’s aesthetic thought and the method offers many reference content. Through a lot of mathematical aesthetics, scientific aesthetics reading related books, journals and academic papers, this topic make me have a more clear and systematic understanding, this project also have a deeper understanding of the current state of research. Poincare himself from reading books at the same time, and then to extract a lot about his thoughts and methods of mathematical aesthetics, through a series of arrangement and analysis, to complete the creation of this article has played a vital role. This paper argues that Poincare as a brilliant mathematician, is also a highly accomplished philosopher of science, his math and profound aesthetic thoughts, in his creating mathematics activities, everywhere can show light of mathematical beauty, he himself is also attaches great importance to the mathematics beauty. Then we analyze the Poincare thinks besides has the objective of practical purpose and philosophy, but also has beautiful purpose, he points out that the mathematical beauty lies in the nature of rational beauty at the same time, for the important role of mathematical beauty in mathematics creative activities to a high degree of affirmation, he thinks math is mathematicians selecting mathematics theory is an important standard, mathematicians are usually the significance and their associated methods and results of beauty. Not only that, but he also used many examples to prove the aesthetic factors existing in the mathematical discovery, thus summarizes the unity, simplicity, symmetry, strangeness and other features of mathematical aesthetics, especially for unity and simplicity, Poincare made a lot of paper. Besides, Poincare also good at using mathematical aesthetics to create activities, so in a subsequent stage system in this paper discusses the system in his method of mathematical aesthetics, he thought that is creating mathematics mathematical invention, the invention is a choice, and this choice is usually controlled by mathematicians aesthetic feeling, at the same time, he also emphasizes the hypothesis in mathematical creation, and the important role of intuition thinking, he cites a lot of examples to prove the hypothesis and the important position and intuition in mathematical creation activity, to assume the classification research, and warned us to dialectical view assumption, in the process of the study of intuitive thinking, he discusses the interaction of logic and intuition, reveals the intuitive thinking in mathematical creation activities play a role in various fields, and through the in-depth study of intuitive thinking, and discussed in this paper, the fourth chapter discusses the psychological mechanism of mathematical invention, Poincare which, in turn, it is concluded that the unconscious thinking in mathematics plays the important role of creation, and through him to fuchs function in the process of the invention of the experience, thus demonstrates the important role of the unconscious mind, he points out that the unconscious is laden with the complicated complex task, it can not only for us to construct a variety of combination of thinking, can also according to the researchers and aesthetic principles of making the essential choice for them.This article systematically summarized the aspects mentioned above, then analyzed and discussed, by category, for example analysis of the various aspects and aesthetics of the Poincare’s mathematical ideas and methods presented in a complete and clear attitude.Poincare’s aesthetic thoughts and methods is extensive and profound, can say in the whole of science aesthetics has played a pioneering role in history, so more are worth further study.