(1) mode of thinking

The outstanding feature of mathematics is that things in objective reality are abstracted into mathematical concepts from the quantitative side through the brain, and reasoning activities are carried out with the help of concepts, so concepts are accurate, concise and vague.

The characteristic of art is to think with the help of subjective images or representations or intentions, which requires images or representations or intentions to be vivid, vivid and rich.

(2) Thinking process

Mathematics uses mathematical concepts to judge and reason, forms propositions, conjectures and proofs, forms theorems, formulas and rules, and explains and applies them through analysis and comprehensive induction into a theoretical system. It can also be abstracted step by step to establish a more perfect and universal theoretical system. It is a process from concrete to general, and then from general to concrete.

Art is a process of continuous analysis, concentration and comprehensive generalization by using subjective images or representations or intentions. It is a process from concrete to concrete and from individual to individual. By enriching, refining and casting the perceptual subject image that reflects the world, we can shape the artistic image with typical significance and grasp the essence of things.

(3) the result of thinking

Mathematical achievements are abstract mathematical concepts, theorems, laws and formulas, and are a complete mathematical theoretical system.

The artistic result is a typical aesthetic artistic image and artistic conception.

(4) Value judgment of works

The evaluators of mathematical works are almost unanimous in their opinions, rigorous in logic, concise in expression and widely used.

There is no consistent standard for the value of artistic works, and their appreciation opinions often move with the wind.

(5) historical development process

Mathematics is cumulative, and mathematical activities are often modified, supplemented, perfected and expanded on the basis of previous achievements.

Art is individual, and a new generation of artists should start from scratch in addition to the inheritance of style and the continuation of techniques.

(6) Theory

Mathematical theory can be replaced. Under certain conditions, there is only one unified mathematical invention. Calculus, for example, if Newton and Leibniz don't create calculus, other mathematicians will.

Art is irreplaceable. For example, Da Vinci's Mona Lisa.

similar

(1) From the perspective of the law of cognition, both mathematics and art should go through the process from phenomenon to essence and from sensibility to rationality under the guidance of a certain world outlook, so that they can understand the essence of things and actually transform them.

(2) From the goal of pursuing, they all use their own specific symbols to express nature, portray society and reveal the soul, thus promoting social development and human civilization, promoting the all-round development of people and cultivating new generations.

(3) From the perspective of creative activities, they have greater freedom in the topics they choose; They accompany and permeate the subject's aesthetic emotion when determining the topic; Their creative activities can be regarded as a combination of some basic elements. Painters combine color and form, musicians combine the sound of music, poets compose music, and mathematicians combine some mathematical symbols and concepts.

The role of mathematics in art

(1) is conducive to artistic creation.

In 600 BC, the Pythagorean school studied the vibration of strings by mathematical methods and established a theory about music.

The perspective principle based on mathematics is a milestone in the history of art development.

In the 20th century, Kolmogorov, a Soviet mathematician, used mathematical methods to study the rhythm organization law of poetry, and created the art metrology.

(2) The tie function of mathematics

Sound comes down to sine function, and current can also be described by sine function, so sound waves can be converted into current, further converted into electromagnetic waves, and finally the speaker vibrates to produce sound waves.

(3) used to identify works of art.

Statistical linguistics. From 65438 to 0980, the signature plays of the British Library were all works by Shakespeare. The last forty chapters of A Dream of Red Mansions were not written by Cao Xueqin.

The role of art in mathematics

(1) Provide new topics and expand the field of mathematics.

During the Renaissance, the real world became the goal of painting, and it was necessary to depict objects in three-dimensional space on two-dimensional canvas, which led to the establishment of perspective. Then there is projective geometry.

(2) It helps to understand and spread mathematics.

Express abstract mathematical content in simple and beautiful words. Hua expounded the method of combining numbers and shapes in the form of poems; Academician Zhang Jingzhong's representative work of mathematics science popularization; Goldbach conjecture of Xu Chi reportage.

(3) change temperament and cultivate sentiment

Mathematics research activities, it is necessary to think hard for a long time, but also to relax. The most active relaxation is reading literary classics and listening to elegant music.