New era，What kind of talents do we need? "De、Zhi、Body、Mei、Labor "comprehensive development，Lack of one cannot。Mathematics education in moral education、The value of intellectual education is beyond doubt，It also makes mathematics the basic compulsory discipline of the next generation of successors in various countries and ethnic groups。In fact，The value of mathematics is also irreplaceable in other disciplines。

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Plato wrote in the "Daedi Az"，Socrates and Hippias are the question of "what is beauty"，The history of Western aesthetics research。"Daisi Az" is the development of ancient Greek philosophy to the Plato era，The first special discussion on the issue of "What is Beauty"，Dialectics of Socrates，Plato has a clear question and defense of what is beautiful: "Grasp the beauty from the beauty itself is the real beauty"。

Western classical aesthetics began in ancient Greek philosophy，and ancient Greek philosophy blended with science (natural science)，Philosophy is "metaphysics after" after "Physics"。Ancient Greek aesthetics to answer，is the fundamental question about "beauty"，The nature of beauty and the law of beauty。The spirit of rationality of mathematics formed in the history of Western civilization，Play an important role in its aesthetics。Harmony、Form logic interpretation，Form a certainty、logic、Structural research goals and methods，All reflected in Western aesthetic research。Western music、Arts and other art disciplines have strong mathematical aesthetics characteristics。The important reason is that Western aesthetics belongs to Western philosophy，and Western philosophy exactly show the rational spirit of mathematics everywhere。

Mathematics as a culture，In nature science in human history、The impact of bet365 Play online games social science and humanities and arts is very far -reaching。Science seeking truth，Humanities and Good，Art Zhenmei。Mathematics should be natural science plus humanities，It is a combination of science and art。Pure mathematics is a science，It is also an art。Mathematics has the aesthetic characteristics of common language and art，In terms of content structure and method, they have their own mathematics beauty。Generally speaking，Simple、Unity、symmetry、neat、Strangeness、Specifications, etc. are the main features of the beauty of mathematics。Due to the relationship between mathematics and philosophy in Western culture、The relationship between philosophy and aesthetics，So mathematics aesthetics has received high attention。

The pursuit of the beauty of mathematics，It has always been the direction of the hard work of mathematicians' own research。Ancient Greek philosopher、Mathematician Prieklas once thought，"Where can I count，Where is the beauty "。Russell thinks，"Mathematics not only has the truth，And has the supreme beauty -cold and simple beauty，Like the beauty of sculpture "。Hardy thinks，"Beauty is the primary standard，Not beautiful mathematics cannot find a permanent place in the world，Maybe it is difficult to find a educated person's charm of the charm of mathematics. "。von Norotan thinks，"Mathematicians whether they choose the subject matter or the criteria for judging success are mainly aesthetic，Whether mathematicians succeed or not and his efforts are worthy of subjective standards，is very self -sufficient、Aesthetic，Influence of unwillingness (or near) experience "。Poncale thinks，"The beauty of mathematics、The sense of harmony of the number and shape、Geometric elegance，This is the aesthetic sense that all the real mathematicians know ... It is this special aesthetic sense，Play the delicate screening effect I have said ... The person who lacks this aesthetic sense will never become a real creator "。

　　Mathematics provides aesthetic standards for science

In the history of science，"Aesthetic Standards" of scientific truth or even "mathematics aesthetic standards"，From the "celestial music" of Bidorlas to Einstein's general theory of relativity。The role of aesthetic standards in scientific theory and its truthful judgment，Research that has caused valuable scientists。Scientific theory should be simple in form、Consistency，Harmony in the content、Self -ties，This is not only the aesthetic requirements of the scientist itself，More importantly because it meets the general characteristics and basic laws of the research object。Caldin compares the beauty of science and mathematics，Explaining the characteristics of science beauty is a harmony、Diversity in unity。"It is different from the beauty of pure mathematics。The unity of mathematics is only due to logic strictness: it is the unity of the proposition，Propositions reliably derived without whether they are consistent with the facts。But the unity of science is not only due to the logic of the theoretical interpretation; it also includes experimental observations uniformly with the logical system，The interpretation of this system is consistent with the observation。The works of the United States in science are complete and complete work，The facts do some generals or theoretical examples。Unity in science is not as perfect as unity in mathematics，But as far as it contains a further harmonious type，It is a richer unity，That is a set of logical related propositions and a set of independent observation materials "。The difference between the beauty of mathematics and science is，"Mathematics beauty does not need to be in real new contact，No need to be consistent with observation and experimental information "。

Mathematics is exactly because of its simple form of abstraction but widely used in Da Mei。"Everything in Bida" from ancient Greek Bidorlas，Until the later "Okham Razor"，Simple, especially bet365 best casino games mathematical simplicity, has always been pursued by science and beauty。Copernicus establishes the theoretical system on the basis of pursuing the theoretical simplicity of mathematics。and Capler pointed out when explaining the reason why he supports the September,，"I prove from the deepest part of the soul to be true，​​I appreciate its beauty with the joyful mood of hard to believe，And this is because Copernicus's system has greater mathematics simplicity and harmony "。Newton pointed out in its "Mathematics Principles of Natural Philosophy"，"Naturally don't do nothing in vain，Explanation is more vain，Simplicity of words to see the true meaning; because naturally I like simplicity，Mulberry talks that will not respond to the cause of excess "。

Einstein is also the only reliable source of seeking truth in the simplicity of mathematics，Establishing his relativity system。Haisenburg once wrote to Einstein，"I believe that the simplicity of the law of nature has an objective feature，It is not just the result of thinking。If nature leads us to an extremely simple and beautiful mathematical form -what I am talking about is hypothesis、Axioms and so on, an unanimous system -the form that is not seen by the people who has not seen，We have to think that these forms are 'true'，They are the real features of nature。I frankly admit，The simplicity and beauty of the mathematical system I have shown to us by nature attracted it.。You must also have this feeling: the almost shocking simplicity and integrity of these relationships in front of us suddenly in front of us "。Einstein said to Heisenburg's reply，"You will oppose the aesthetic standards that I introduce the truth from the simplicity and beauty，I frankly admit，The simplicity and beauty of the mathematical system I have shown to us by nature attracts it strongly "。

Maxwell also pointed out，He always regards mathematics as the best form and dimension of things; this not only refers to the most practical bet365 live casino games and economical，More mainly refers to the most harmonious and most beautiful。Dirac believes，"Theoretical physicists regard the requirements of mathematics beauty as the behavior of faith。There is no reason to make people believe，But the past has proven that this is a useful goal。For example，Relative theory is so commonly recognized，The main reason is its mathematics beauty。This kind of appreciation for beauty is dominated by all our jobs。This is our creed，I believe that the equation describing the basic laws of nature must have a significant beauty of mathematics，This is a religion for us。Pursuing this religion is very useful，It can be regarded as the foundation of many of our success "。

These great physicists，Use the beauty of simple mathematics as a criterion or even a scientific belief。Mathematicians Er Er evaluation to，"In the law of nature，As I will later be established more，Simple nature is essential。If we do not add a statement that is dominated by simple laws in mathematics，So the assertion that is naturally dominated by strict laws lacks all content。This incident is similar to the double -ratio law in chemistry: Unless we add a combination of combination with a small integer with a relatively atomic weight，Otherwise it will lose all content "。Labnitz pointed out in the "On Method"，"When an arbitrary complexity，The concept of the law becomes empty。So，Simple nature becomes a working principle in natural sciences "。

　　Mathematics education should pay attention to aesthetic value

For a long time，People pay too much attention to the function of the "metaphysical" (metaphysical "(level level) of mathematics for the development of human civilization，Often ignores its "metaphysical" (spiritual level) function，Ignore mathematics as a tool、Thought、The spiritual temperament and aesthetic value contained in the method。Mathematics education has gradually stayed away from the profoundness and rational wisdom of mathematics culture itself，Bet365 lotto review increasingly lost the cultural meaning and aesthetic value of mathematics，People’s mathematical views gradually gathers instrumentalism，Mathematics becomes thought、Pronouns of Methods and Technology。Mathematics is not so beautiful in the eyes of students，Mathematics education has almost lost the powerful humanistic characteristics and aesthetic functions contained in its history。Many people's mathematical education concepts and practical behaviors have a big problem，Often focused on knowledge instills、Problem Solution Skills Training，Ignoring the spiritual education and personality training in the process of mathematics education，Don't pay much attention to guiding students to seek the meaning and value of life through mathematics learning，Student's thinking、Creative、The imagination is also depressed by boring mathematics，Students' morality、Aesthetic sense is difficult to get enlightenment through mathematics learning，Mathematical education is difficult to cultivate outstanding talents、Topped talents and innovative talents。

"Reason" and "Sensory" like two rounds of car、Bird's two wings，It is very important for the comprehensive development of people。Mathematics education should not only cultivate students' rational spirit，can cultivate students' perceptual ability。Mathematics education in the new era should be realized "educate people，The goal of a cultural person，Through the learning of mathematics, students can develop the feelings of beauty，Cultivate students' emotional experience for the beauty of the United States，Form the correct aesthetic ability and ability to express beauty。Mathematics teachers should improve their own aesthetic cultivation，During the teaching process, be good at using mathematical aesthetic emotions to "infection" and cultivate students' "beauty"，Improving students' learning interest through mathematical aesthetics，bet365 best casino games Improve the enthusiasm of learning、Activity and creativity。In short，Let students learn through mathematics，Feeling that mathematics is beauty，The process of mathematics learning should be pursuing beauty、The process of feeling beauty and creation，Let mathematics education truly restore its historical humanities and aesthetic meaning。

　　(Author Unit: School of Mathematics, Jilin Normal University)