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2022-01-05 11:19:57 | onclick: | Enlightenment of mathematics learning to psychological research

I saw an article on the "science net" about the "strange thing" of mathematical research introduced by a Chinese academician of Mathematics: many mathematicians hide their thinking process, which makes people marvel at their exquisite thinking, but they don't understand why they think and solve problems like this; However, a mathematician recorded and disclosed his thinking and problem-solving process in detail. Later, I wanted to find this article and planned to quote it in class. Who knows, after many twists and turns, I didn't find it. I deeply regret that I failed to write it down when I was studying.

Last night, I finally found the material about mathematicians' hidden thinking process on other web pages, which was originally said by academician Lin Qun. I read the corresponding materials again and again, collected the web page, and learned and experienced it again today.

Academician Lin pointed out that Gauss is a typical representative of the hidden thinking process, and Descartes is a typical representative of the whole thinking process. Academician Lin took Descartes's thinking process of solving the center of gravity of tetrahedron as an example to illustrate Descartes's thinking process, that is, compress a vertex to the bottom to form a triangle, then press one vertex of the triangle down and into the other edge to form a line segment, and the center of gravity of a line segment is at the midpoint, which is known by a farmer carrying a shoulder pole.

I was inspired to understand Descartes's methodology. I believe that Descartes' method can be adopted or used for reference in the thinking and solving of various scientific problems, including psychology, that is, to simplify continuously and systematically until the research is simple, clear and easy to understand.

Academician Lin believes that the two most important theorems of plane geometry are the sum theorem of triangle internal angle and Pythagorean theorem. The sum of the interior angles of a triangle is equal to 180 degrees, "This theorem is very surprising. In the ever-changing triangles, there is a constant, the sum of internal angles or the sum of external angles. This is very great, which shows that all kinds of data and phenomena in mathematics are chaotic on the surface, but in fact there are clear laws. This is a very beautiful law."

I think this example is also excellent for psychology. Psychological learners and researchers often emphasize the diversity and differences of human beings. It seems that it is difficult to study the psychological law, "people have evil intentions". However, the mathematical research of the triangle can make us sure that the human heart has clear laws. This can enhance our confidence in psychological research.

In recent years, through learning and thinking, I have also deeply realized that triangles and circles are excellent models or tools for mathematical research. Many problems can be expressed and handled by using the properties and theorems of triangles or circles when they are transformed into triangles or circles. When I studied circle on the third day of junior high school that year, I didn't understand the role and significance of proving the four point common circle, and I was not familiar with the relevant properties and theorems of circle, so I relatively excluded these contents. Now, I fully realize the importance of circle.

So, what models or tools do we have in psychology that are similar to triangles and circles in mathematics? To what extent has psychology explored these models or tools? To what extent can other disciplines learn from and use such models or tools? At the same time, is there a phenomenon that psychologists hide their thinking and research process in psychology?

I believe that mathematics learning has practical enlightenment and guiding significance for our psychological research.

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