There is a famous saying: Mathematics is much bigger than science because it is the language of science. This view was first put forward by the great natural scientist Galileo about 400 years ago. He is the first person in the world to express the free-falling motion in the mathematical language: v=32t (where 32 means 32 feet, which is equivalent to 9.76m, close to the value of the acceleration g of gravity), and profoundly reveals the inherent law of the free-falling motion in the gravity field from the quantitative relationship. Mathematics, summed up by human beings in their long-term practice, is inherent in human rational instinct and occupies no less position in human characteristics and human history than language, art or religion. Especially today, mathematical methods and science and technology have been "inseparable" and are having an earth-shaking impact. In modern cognitive and practical activities, people talk about the role of mathematics more and more strongly, and call our era "the mathematization of knowledge". Some physicists claim that in their knowledge and activities, mathematics is not only a tool for calculation, but also it is impossible to understand the production process without mathematics. In contemporary times, mathematics has become the productive force of society. Now, those fields that only make qualitative analysis without applying mathematical research methods, such as natural phenomena, economics, medical and health care, organizational production, management and so on, are rapidly seeking quantitative laws and widely applying strict mathematical methods.

The mathematization of today's knowledge does not mean that all knowledge should be simplified into a logical and computational schema, nor does it mean that experiments and direct observation are prohibited. The purpose of mathematicization is:

Based on the premise of accurate enumeration, logical results are obtained, including those obtained by direct observation; Turn an extremely complicated process that usually deposits many secondary influences into a process that can be analyzed logically and mathematically; In addition to the established facts, the new law is determined by mathematical analysis; It is possible to predict the process of phenomena by calculation, which is consistent with the actual process of phenomena not only in quality but also in quantity.

In a word, the mathematization of knowledge lies not only in using the existing mathematical methods and results, but also in creating a unique mathematical way, which can accurately and completely describe the real world around us and apply the obtained results to practical activities. Mathematics originates from practice and is tested in practice; Both knowledge and practical activities depend on the help of mathematics, a powerful tool. When people made urgent and profound research on mechanical motion at the beginning of18th century, Newton and others were prompted to establish a grand mathematical analysis system, which became the basis for the amazing progress of natural science and engineering science in the past 200 years. At the beginning of this century, when the research on the transformation of thermal, magnetic and electrical phenomena made the establishment of wave optics mature, the old mathematical tools could not describe this transfer and transformation relationship, which led to the establishment of a new mathematical language-mathematical physical equations. Today, mankind has entered a new stage of rapid development of natural science and serious renewal of engineering thinking. A large number of urgent mathematical problems have been put forward in new research and practical activities: electronic optics, aerospace engineering, atomic energy utilization, computer and information technology engineering, biological engineering, system engineering and so on. The old mathematical tools have become powerless, and some new mathematical tools have emerged. For example, cybernetics and optimization ideas have entered mathematics, and conventional mathematics has turned to "abnormal mathematics". Non-standard analysis, catastrophe theory and fuzzy mathematics that have appeared in recent 20 years all belong to this category. And so on, it can be seen that practice promotes the development of mathematics and mathematics guides the perfection of practical activities. With the mathematization of knowledge and practical activities, it will inevitably lead to the mathematization of thinking, even if people's thinking is accurate, making their views and conclusions more logical.