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Is mathematics a tool of science?
Since junior high school, we have been exposed to mathematics and natural science. However, the natural science research at that time did not involve advanced mathematics knowledge. At that time, the research on natural science was mostly based on simple calculation under ideal model conditions, and there was little quantitative research on real natural science phenomena. Even though the teacher showed us many experiments at that time, most of them were qualitative. Except for a few physical measurement experiments.

It was not until we came into contact with college physics experiments in university that quantitative research scientific experiments entered our field of vision for the first time. What I remember clearly is "Young's double-slit interference experiment". Just using two small holes, a light source, a panel and a ruler, we can observe that light can actually "rotate" and measure the wavelength of light, which is simply amazing. We can not only measure the wavelength, but also give its measurement error. Understanding this process is the first step into science.

Our natural science is based on the improvement of observation ability. We have expanded the scope of naked eye observation through telescopes and microscopes. However, from Copernicus's establishment of the Heliocentrism to Galileo's discovery of the laws of planetary motion on the basis of Tycho's observation data for many years, to Newton's discovery of universal gravitation, and to the experimental verification of Einstein's theory of relativity, not only observation, but also mathematical quantitative description, logical deduction and calculation methods were used, which further promoted scientific discovery.

We always say that we are in a modern society with rapid development of science and technology, but ask ourselves, do we really have scientific thinking? After studying mathematics for so many years, do I understand the difference between mathematics and science?

Keith Devlin wrote in his book Introduction to Mathematical Thinking, "In natural science, authenticity is established through empirical methods, which include observation, measurement and experiment (as the gold standard). In mathematics, authenticity is established by constructing a proof, which is a logical and reasonable argument and can establish the authenticity of a statement. "

Zhihu statphd thinks that mathematics is obviously not a natural science. Because the object of mathematical research is not nature. (Yes, I want to make it clear in bold that the research "object" of a certain discipline can best reveal the essence of a certain discipline, and all other research methods are secondary. Mathematics is a logical deduction based on a certain axiom system, rather than a study of natural phenomena themselves, although it has a wide and in-depth application in natural science. Mathematics, an ancient building, will not be overthrown directly because of the discovery of some natural phenomena, but only its own internal contradictions can be overthrown. Well, it can also be said that mathematics cannot be falsified. What is mathematics? This is a formal science. What is formal science? Baidu on its own. . . Finally, I quote a sentence from the idol Einstein: Mathematics is paid more attention than all other sciences because its theorem is absolutely certain and beyond doubt. However, other sciences are controversial because of the discovery of new facts and are in danger of being abandoned.

Wikipedia: Many philosophers think that mathematics cannot be proved by experience [22].

Therefore, it is not science as defined by karl popper.

So, what is science?

The following is the definition given by Wikipedia, Science (English: Science, Greek: ε π σ τ? μ η) is a subject that attributes phenomena (originally referred to as natural phenomena, now generally referred to as social phenomena) through empirical methods. The knowledge gained from scientific activities is clearly defined (can't be ambiguous or explained at will), can stand the test, and can't contradict the known facts in any applicable scope. Science originally only refers to the exploration and summary of the laws of natural phenomena, but humanities are increasingly called "science". People are used to dividing science into different categories according to different research objects. Traditional natural sciences mainly include biology, physics, chemistry, geology and astronomy. Logic and mathematics have a special position. They are the basis and tools of all other sciences.

Science tries to solve various concrete problems at different levels of understanding nature, emphasizing the concreteness and falsifiability of prediction results, which is different from fuzzy philosophy. Science is not the same as seeking absolute truth, but on the existing basis, constantly exploring and approaching the truth. Therefore, the history of scientific development is a history of correcting the deviation of human understanding of nature. Therefore, "science" itself requires a certain degree of doubt about the theory, so it is by no means synonymous with "correctness".

"Science" cannot be accurately defined in short words. Generally speaking, science covers three aspects:

(1) observation: devote yourself to revealing the truth of nature and fully observe or study the effects of nature (including ideological experiments), which usually means that it can be carried out by necessary methods or scientific methods-a set of procedures for evaluating empirical knowledge.

(2) Assumption: Through this process, the systematic knowledge of the organization system is assumed.

(3) Verification: To verify the reliability and validity of the research objectives.

Science includes basic science and applied science. Basic science only aims at exploring natural principles through experiments, and its achievements are generally not easy to be applied in a short time, such as physics, chemistry, biology, geology, etc. Applied science has both the motivation to explore principles and the motivation to pay attention to applications, such as medicine, pharmacy, applied optics, meteorology, science and technology archaeology, game theory and so on.