Poetry and music related to mathematics can stimulate or soothe feelings, painting is pleasing to the eye, poetry can touch people's hearts, philosophy can make people gain wisdom, science and technology can improve material life, but mathematics can provide all of the above. We want to turn boring mathematics learning into an aesthetic process of appreciating and discovering beauty, which can completely infiltrate some poems related to mathematics and even guide students to create. I have listened to the classes and teaching and research activities of teachers in Qingdao No.2 Middle School, and I am surprised by the ability and talent of their students in this respect. Obviously, to believe that students' creativity and imagination far exceed our imagination, what we can do is to give them an inspiration and build a platform. Attached below are some math-related poems I have accumulated. I. Poems related to the chapters in the textbook Chapter 1, Collection, Mapping and Function: Flowers and fruits are fragrant at sunset, and things change for stars to see vicissitudes. Causal changes are related, and a good strategy is to break the chaos? The basic theory of set is rigorous, and the mapping function is light yellow. Look at the chart to discuss the ups and downs, and Kehai has a plan to sail. Chapter 2 "Exponential Function, Logarithmic Function, Power Function": Morning fog blocks traffic, and mushroom clouds cover the sky; The age of fossils is calculated skillfully, and the sentences of Wen Haisuo are as fast as the wind. Explain infinite things, and the three families of functions make great achievements. Second, the mathematical problems of poetry Zhu Shijie's "Meeting with the Source" and "Or Asking Songs" have twelve mathematical problems, all of which are put forward in the form of poetry. For example, the first question: "There is a square pool today, which stops at every square foot. The sides of the reef are getting bigger and bigger, and water comes out 30 inches. There is a cattail on the east coast, and there is no zero on the water. " The dock is slightly flush with the water. How to determine the three types (water depth, pier length and pier length)? "In the Yuan Dynasty, there was a calculation book about the method of measuring fields," Detailed Algorithm ":"The ancients measured fields for a long time and drew quantities by rope ruler. Although there is a form of universal law, only Tian Fang's law is easy to elaborate. If the vortex is oblique and concave,
2. Poems about mathematics include:
First, the "mountain village"
Author: Shao Yong (Northern Song Dynasty)
At first glance, it is two or three miles away, and mist hangs over four or five families.
The pavilions are six or seven, and the flowers bloom in eighty or ninety.
Translation:
At first glance, two or three miles away, mist enveloped four or five families.
There are six or seven pavilions beside the village, and many flowers are in full bloom.
Appreciation: The poet used the method of "counting primary schools" to bring beautiful villages together, which is easy to understand, as if the picture was in front of him.
Second, "Qiu Jiang's solo fishing map"
Author: Wang Shizhen (Tang)
A boat with a hat, a silk and an inch-long hook.
Sing a song, drink a bottle of wine, and catch a river alone.
Translation:
Sitting on the boat, wearing a hat and a hemp fiber, the fishing line is one foot long and the hook is one inch long.
Sing a fishing song loudly, drink a bottle of wine, and fish on the river alone this autumn.
Iii. Ode to Snow
Author: (Qing)
One, two, three or four, five, six, seven or eight.
Thousands of pieces are always missing when they fly into plum blossoms.
Translation:
Snowflakes fall from the sky one after another, and the whole world is white.
The falling snowflakes fall into the reeds and blend with the white reeds, which is difficult to distinguish.
Appreciation: People use numbers mainly to show the beauty and elegance of the snow scene, and show a scene of heavy snow in front of people, as if the snow scene is in front of readers, making people feel immersive.
Fourth, "quatrains"
Author: Du Fu (Tang)
"Two orioles sing green willows, and egrets cover the sky."
My window framed the snow-covered western hills. My door often says "goodbye" to ships sailing eastward.
Translation:
Two orioles are singing among the green willows, and a row of egrets are flying in the blue sky.
The scenery of Xiling Snow Mountain seems to be embedded in the window, and ships coming and going to Soochow are parked by the door.
Five, "Xijiang Moonlight Walking on the Yellow Sand Road"
Author: Xin Qiji (Song)
The moon on the horizon rose to the top of the tree, scaring away the magpies perched on the branches. The cool evening breeze seems to have spread to cicadas in the distance.
In the fragrance of rice and flowers, people talk about the harvest of a year, and frogs croak in their ears, as if in a bumper harvest year. In the old days, Maodian was near the forest, and the road turned to the stream bridge.
Translation:
The bright moonlight swept the branches, scaring the magpies away from them, and the cool evening breeze seemed to hear cicadas chirping in the distance. In the fragrance of rice flowers, people are talking about the harvest year, and there are bursts of frogs in their ears.
The sky is cloudy and starry, flickering, and there is a light rain in front of the mountain. The old thatched cottage is still next to the Woods of the earth temple. When the road turns the source of the stream, it suddenly appears in front of you.
Appreciation: The author described the beautiful summer night in the countryside with his specific feelings in Night on Huangsha Road. The image is vivid and vivid, the feelings are cordial and delicate, and the brushwork is light and lively, which makes people feel realistic.
3. Sion's music about the kingdom of mathematics is very similar to algebra. Hardenbergh
It is wrong to insist that there is no beauty in mathematical science. The main forms of beauty are order, symmetry and clarity. -Aristotle
Feel the beauty of mathematics, the harmony of numbers and shapes and the elegance of geometry. This is the true feeling of beauty that all real mathematicians know. -Poincare
The beauty of mathematics is naturally and clearly laid out. Halmos
In my opinion, it is correct to say that the main criterion for a mathematician to choose a subject and judge his success is aesthetic standard.
Von Neumann
My job always tries to combine truth with beauty, but when I have to choose one of them, I usually choose beauty. Will
In the evaluation of mathematical theorems, aesthetic standards are more important than logical standards and practical standards: whether the proportion of beauty and elegance is rigorous and correct is much more important than whether it is useful. -Sting
Pure mathematics can be practical and useful, and applied mathematics can also be elegant and elegant. Halmos
It is only because the existing proof lacks the charm of beauty that we make further research on the theorem that has been correctly recognized for a long time and explore its new proof. -Klein
Mathematicians, like painters or poets, are creators of style. . Mathematicians' style, like that of painters or poets, must be beautiful ... ugly mathematics has no permanent place. Thomas Hardy
A strange beauty dominates the kingdom of mathematics. It is not as similar as the beauty of art and the beauty of nature, but it deeply infects people's hearts and arouses people's appreciation of her, which is very similar to the beauty of art. -Como
Can't music be described as sensory mathematics and mathematics as rational music? In this way, musicians feel mathematics, mathematicians think of music-music is a dream, mathematics is a lifetime's work-and both sides achieve perfection through each other. At that time, the perfect model of human wisdom will be dazzling under the praise of a future Mozart-Dirichlet or Beethoven-Gauss. This combination has been clearly predicted in Helmholtz's genius and works. -Silver Foster
4. Mathematical beauty is the product of human creative practice and the perceptual expression of human essential strength.
Usually, what we call beauty exists in the form of natural beauty, social beauty and artistic beauty and scientific beauty on this basis. Mathematical beauty is the objective reflection of natural beauty and the core of scientific beauty.
In short, mathematical beauty is a wonderful, regular and pleasant thing in mathematics. Many scholars and mathematicians in history vividly expounded the beauty of mathematics from different aspects.
Plocque Ras has long asserted: "Where there is mathematics, there is beauty." Aristotle once said: "Although mathematics does not explicitly mention goodness and beauty, goodness and beauty cannot be completely divorced from mathematics.
Because the main forms of beauty are "order, symmetry and certainty", these are the principles of mathematical research. Hua, a famous mathematician in China, said: "As far as mathematics itself is concerned, it is magnificent, colorful and fascinating ... People who think that mathematics is boring only see the rigor of mathematics, but they don't realize the inner beauty of mathematics."
Mathematician Xu Lizhi said: "Mathematics, as a scientific language, has the beauty of ordinary language and art, that is, mathematics also has its own beauty in content, structure and method, which is the so-called beauty of mathematics. The meaning of mathematical beauty is rich, such as the simplicity and unity of mathematical concepts, the coordination and symmetry of structural relations, the generality, typicality and universality of mathematical propositions and mathematical models, and the singularity in mathematics. "
As can be seen from the above discussion, mathematics is full of beautiful factors. Mathematical beauty is the perceptual and rational presentation of the essential strength of mathematical science. It is not illusory and unpredictable, but has its definite objective content. Mathematical beauty is different from other beauty. It has no bright colors, pleasant sounds and dynamic pictures, but it is a unique beauty.
Klein, a German mathematician, once described the beauty of mathematics as follows: "Music can stimulate or soothe feelings, painting can make people pleasing to the eye, poetry can impress people, philosophy can make people gain wisdom, science and technology can improve material life, but mathematics can provide all of the above." The difference between mathematical beauty and other beauty lies in the beauty contained in it.
For example, everyone must feel this way. Most students are interested in the aesthetic feeling of sound and body, but not in mathematics. I think there are two main reasons for this: first, the beauty expressed by the beauty of sound and body is explicit, which makes it easier for students to feel, know and understand; Although some beauty in mathematics is manifested in the appearance of mathematical objects, such as exquisite graphics, beautiful formulas and ingenious solutions. Generally speaking, the beauty in mathematics is deeply hidden in its basic structure, and this inner rational beauty is often difficult for students to feel, know and understand, which is one of the main characteristics that distinguish mathematics from other disciplines.
Second, for a long time, our mathematics textbooks have overemphasized the logical system and logical deduction, ignoring the role of mathematical aesthetics and mathematical intuition. In the long run, students equate mathematics with logic. Paying attention to the logic of mathematics and ignoring the beauty of mathematics itself will make you feel dull and uninterested in the process of learning.
Most mathematicians will get aesthetic pleasure from their work and general mathematics. They express this joy by describing that mathematics is beautiful.
Sometimes, mathematicians will describe mathematics as an art form, or at least as a creative activity. Usually compared with music and poetry.
The beauty of mathematics also lies in its accurate expression of life and perfect deduction of logic. It can be said that it is this precision that has made a good life in modern society.
Bertrand Russell described his feelings about the beauty of mathematics in the following words: To treat mathematics correctly is not only the possibility of truth, but also the supreme beauty-a cold and Austrian beauty, just like sculpture, which has no attraction to our weaker nature, without the gorgeous decoration of painting or music, but extremely pure, and can achieve strict perfection that only the greatest art can show. The true spirit of happiness, excitement, transcending human feelings, is the touchstone of the highest Excellence, which can be found in mathematics, just like in poetry. Mathematical research, mysticism and logic, and other papers, ch. 4. London: Longmans, Green, 19 18. Mathematics, if viewed correctly, has ... supreme beauty-just like the beauty of sculpture, it is a kind of cold and serious beauty. This beauty is not the weak aspect that attracts our nature. It has no ornate decoration of painting or music. It can be pure to sublime, and only the greatest can achieve it strictly. A real spiritual pleasure, a spiritual excitement, a sense of superiority-these are the standards of perfection and beauty, which can be obtained in poetry and mathematics.
Study mathematics, mysticism and logic, and other papers, induction. 4. London: Romantic Bookstore, green, 19 18. )
Erd?s· Parr described his unspeakable views on mathematics. He said, "Why are numbers beautiful? It's like asking why Beethoven's Ninth Symphony is so beautiful. If you don't know why, no one can tell you why.
I know these numbers are beautiful. If they are not beautiful, nothing in the world is beautiful. "
The best thing about it is that it makes your mind agile invisibly. When considering things, it is not so extreme and not so single. As a citizen, not knowing is another matter. At least we should not deny it, especially students. Let's look at the following formula first:1x 8+1= 912x8+2 = 98123x8+3 = 9871234x8+4 = 9876544. 023456 x 8+6 = 987654 1234567 x 8+7 = 9876543 12345678 x 8+8 = 98765432 123456789 x 8+9 = 98765432 1 1 x 9+2 = 1654
5. Ask for poems about mathematics ~ ~ There are many poems that urgently express mathematical ideas and concepts.
For example, the new high school mathematics textbook edited by Academician Zhang Jingzhong (experimental textbook of new curriculum standard of Hunan Education Press) has a poem in each chapter. For example, the first chapter, "Collection, Mapping and Function", talks about the sunset, flowers and fruits, and the vicissitudes of life.
Causal changes are related, and a good strategy is to break the chaos? The basic theory of set is rigorous, and the mapping function is light yellow. Look at the chart to discuss the ups and downs, and Kehai has a plan to sail.
In the second chapter, "Exponential Function, Logarithmic Function and Power Function", I said: the morning fog blocked the traffic, and the mushroom cloud covered the sky; The age of fossils is calculated skillfully, and the sentences of Wen Haisuo are as fast as the wind. Explain infinite things, and the three families of functions make great achievements. After studying these two chapters, read them carefully and don't feel anything.
Secondly, the mathematics of poetry is abstract and boring. How to make mathematics easy to understand and loved by people? In this respect, Chinese ancient mathematicians made many attempts, among which ballads and formulas were one, which made people feel the charm of poetry while answering mathematical questions. Starting from Yang Hui in the Southern Song Dynasty, Zhu Shijie, Ding Ju and Jia Heng in the Yuan Dynasty, Liu Shilong and Cheng Dawei in the Ming Dynasty all put forward various algorithms in the form of verse, or put forward various mathematical problems in the form of poetry.
There are twelve mathematical problems in Zhu Shijie's "Meeting with the Source" and "Or Asking Songs", all of which are put forward in the form of poems. For example, the first question: "There is a square pool today, which stops at every square foot.
The sides of the reef are getting bigger and bigger, and water comes out 30 inches. There is a cattail on the east coast, and there is no zero on the water.
The pier is slightly flush with the water, so how to determine the three types (water depth, pier length and pier length)? "In the Yuan Dynasty, there was a calculation book about the method of measuring fields," Detailed Algorithm ":"The ancients measured fields for a long time, and all of them were measured by rope ruler. Although there is a form of universal law, only Tian Fang's law is easy to elaborate.
If you see the vortex inclined downward, you must make up for it. However, millet is actually a field product, and the method of dividing two acres or four acres is very strong.
"Cheng Dawei's Algorithm Summary of Ming Dynasty is a popular and practical mathematical work, and also a masterpiece of digital poetry. Seventeen volumes of Algorithmic Tongzong, which was widely circulated in the late Ming and early Qing Dynasties, made outstanding contributions to the popularization of folk mathematics knowledge.
It took Cheng Dawei nearly 20 years to finish this book. At first, he was a businessman. When he was in business, he collected books on arithmetic and writing from all over the country and compiled them into ballads, turning boring math problems into wonderful poems, which made people catchy and strengthened the affinity of mathematics popularization. Cheng Dawei also has a similar drinking mathematical poem with a binary linear equation: "There are many drinkers in restaurants, and the name of thin wine is thick and mellow.
One bottle of good wine makes three people drunk, and three bottles of thin wine make one drunk. * * * drank 19 times, and all 33 guests were drunk.
I want to ask Gao Ming to learn. How much alcohol is there? "The main idea of this poem is that a bottle of good wine can drunk three guests; Three bottles of thin wine can get the guests drunk. 33 guests were drunk and always drank 19 bottles of wine.
How many bottles of good wine and thin wine are there? There is a problem of "I don't know the number of things" in Sun Tzu Shu Jing. The original text of this calculation is: "Today, there are countless things, three and three numbers leave two, five and five numbers leave three, and seven and seven numbers leave two. What is the geometry of things? Answer 23.
"This problem has spread to later generations, and many interesting names have appeared, such as' Guigu Calculation' and' Han Xin Point Soldiers'. Cheng Dawei wrote a mathematical solution in the form of a poem in "Arithmetic Unity": "Three people walk in seventy miles, five trees and twenty-one plum blossoms, and seven children reunite in the middle of the month. Divide by 105 and you will know.
This poem contains the famous "remainder theorem". That is, the remainder is divided by 3 times 70, the remainder is divided by 5 times 2 1, and the remainder is divided by 7 times 15. If the result is greater than 105, reduce the multiple of 105.
The result of the above problem is: (2 * 70)+(3 * 21)+(2 *15)-(2 *105) = 23. In the works of Indian scholar Bashgaro, there is also such a mathematical poem: "Jasmine fragrance attracts bees to collect honey."
Bustling and countless, a group flew into the flowers. How many people are there in this group? And analyze the conditions: half of all square roots, the other two are added together; A few ninth of the total, wandering outside playing games.
"If unreasonable equation operations are listed, it can be concluded that this group of bees is 72. In addition, there is a mathematical poem about lotus: "Pingping Lake is crystal clear, and red-violet is born on a half-foot stone;" "Out of the mud but not stained, clean and graceful, suddenly blown to the clear water.
The fisherman looked at it and hurried forward. The flowers were two feet away from their original position. Please solve the problem. How do you know the depth of this lake? "What a poetic algebraic problem this is! You see, the red lotus growing in the lake is half a foot long and has been blown aside by the wind. The distance between the flowers on the top of the red lotus and the original water surface is 2 feet. How deep is this lake? According to Pythagoras theorem, the depth of this lake is 3.75 feet. Third, the number of poems: the most common number of poems is one.
Although "one" is a numerical concept, in fact, if the word "one" is used properly in poetry, it will produce beautiful artistic effects. For example, the poet Chen in Qing Dynasty wrote a poem "One Picture of Qiu Jiang Fishing Alone": "One sail, one paddle, one boat, one fisherman, one hook, one bow, one smile, one bright moon and one Qiu Jiang.
"In the Five Dynasties, when Li Yu, the queen of the Southern Tang Dynasty, was in office, she wrote an inscription for the painting" Fishing in the Spring River "by the court painter Wei Xian:" The waves are full of snow, and the peaches and plums are silent; A pot of wine, a club, how many people are there in the world? " "A spring breeze, a boat, a cocoon and a light hook; Flowers are full of Zhu, wine is full of Europe, and you are comfortable in the waves.
"The image of a free and easy fisherman is vividly portrayed. Another example is the poem "The Wild Goose Falls to Win" in Yuan Dynasty: "One old year, one day, one autumn after another, one generation urges another, one gathers and one leaves, one suffers and one grieves.
Lying on the couch, I will find an acquaintance in my dream all my life. He will know each other for a while, and we will all know each other, play once and sing once. The 22 words "one" in the poem are repeated constantly, reflecting the illusory bitterness of life.
His writing is strange, but he wins with slang. Some poems will embed one to ten numbers in the poem.
Shao Kang, a philosopher in the Song Dynasty, said: "When you go twenty or thirty miles, there are four or five smoke villages, six or seven pavilions, and eighty or ninety flowers." The beauty of this poem is that it is embedded in ten cardinal numbers in turn, and a few words describe a quiet and elegant pastoral scenery, which evokes people's endless feelings and longings.
6. Essay on Seeking the Beauty of Mathematics 1000 words Mathematics is the foundation of all sciences, and its role is well known.
Entering modern civilization, we have long been used to living in the ocean of numbers and have basic communication with 1, 2, 3, 4. However, contrary to its huge social function, few people really love mathematics, really indulge in mathematical research and explore the deep beauty of mathematics.
People often say "don't judge a book by its cover". Mathematics, as a subject that speaks with numbers and figures, is like Cinderella in science fairy tales. Beneath its dull and boring appearance, there is the most touching and beautiful place hidden.
First of all, I think the beauty of mathematics lies in mystery. A simple symbol can outline endless natural truths.
Newton's three laws of motion can cover the laws of motion of the vast universe with only a few simple mathematical formulas. For everyone who is willing to seek truth, mathematics can be said to be their best tourist destination.
Groups of figures and figures interweave into the most touching scenery here. This landscape is continuous, but very different. When you wander in the ocean of mathematics, you will never feel "lonely at the top" or indulge in "one Ma Pingchuan and Ren Woxing". You will only be interested in exploring and admiring the truth of nature.
Even Chen Jingrun, the most famous mathematician in China, still walks cautiously on the road of mathematical research with the feeling of pilgrimage after taking off the pearl in the crown of mathematics. Secondly, I think the beauty of mathematics lies in its application.
"Gold and jade are beyond, but they are defeated" is often used by us to belittle those superficial people and things. It can be seen that the standard for us to evaluate beauty is not only because of its internal and external beauty, but more importantly, whether it has practical value. The sentence "Mathematics is the mother of many sciences" fully embodies the value of mathematics in all fields of social life.
The application of mathematics in shopping, the development of computer software, the design of a city traffic route and the network construction of the whole earth are all inseparable from mathematics. Even in the field of art, there is mathematics; Numbers arranged in different pitches are melodious music scores; Which has the golden section law of mathematics, sculpture or painting? The Forbidden City has a watchtower without nails, and the Forbidden City with double eaves and arches cannot do without rigorous mathematical knowledge. It is no exaggeration to say that it is mathematics that builds the ladder of continuous progress of human society with numbers and graphics.
The beauty of mathematics is like beautiful and harmonious music, unique paintings and magnificent buildings, which will also make mathematics learners have passion. With such efforts and achievements, can we still say that mathematics is not beautiful? Finally, I think the beauty of mathematics lies in the success after repeated challenges.
The acquisition of this aesthetic feeling is often at the expense of long-term hard thinking and monotonous calculation. We must accept repeated failures and mistakes, and we must accept the loneliness brought by boring study. Repeated battles and defeats, repeated defeats and battles, and finally you may be suddenly enlightened when taking a shower or brushing your teeth, as if the music suddenly sounded and the problem seemed to be solved at once.
At that time, I often had a feeling of being on cloud nine in the mountains. This kind of beauty is incomparable.
This is the simple and charming mathematics in my eyes. As a strange gem in the field of science, it will shine brilliantly in the new era and guide us to move forward with its unique beauty.
7. Who will help me write a poem praising mathematics? The better I write, the more I like it.
You come from ancient times,
Strict steps can't catch dust;
Your clothes are simple and beautiful,
Shining with the light of wisdom more precious than jewelry;
You cover the sacred glume with silk curtains,
How many outstanding men are attracted to look for color,
You dance to the notes of the universe,
Our hearts, jump with you;
Pure language is so precise,
That heart can't kill more than,
In the long years,
Despite the baptism of dust,
Beauty remains the same.
Your charm can only be shown to the wise,
Those fools can't count on it,
You are a goddess,
The key to the wisdom chest,
Call those who can see you and those who appreciate you.
Get the power of life,
Yes, your beauty,
I can only sing in the most beautiful poems.
8. Mathematical beauty of famous mathematical sentences Mathematics is indeed a wonderful masterpiece, just like the creation of a painter or poet-it is the synthesis of ideas; Like the synthesis of colors or words, there should be internal harmony.
For mathematical concepts, beauty is her first touchstone; There is no deformed and ugly math in the world. -G.H. Hardy Music can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can touch the soul, philosophy can make people gain wisdom, science can improve material life, but mathematics can give all of the above.
-F klein Where there are numbers, there is beauty. -Proklose Mathematicians are as happy as seeing statues, beautiful scenery and beautiful tunes when deducing equations and formulas.
This is the advantage of a well-structured language, and its simplified symbols are usually the source of abstruse theories. -Laplace (-1827) Social progress is the crystallization of human pursuit of beauty.
-K.Max Mathematics, if viewed correctly, has not only truth, but also supreme beauty. -B. Russell mathematics can promote people's understanding of the characteristics of beauty-value, proportion, order, etc.
-Aristotle Beauty is contained in volume and order. -Hegel A mathematician who is not a poet will never be a complete mathematician.
-Karl Weisstras (18 15- 1897) Pure mathematics, in essence, is a poem of logical thinking. -Einstein Mathematics, like music or poetry, obviously does have aesthetic value.
-jacoby Mathematics is a creative art because mathematicians have created beautiful new concepts; Mathematics is a creative art because mathematicians live, speak and act like artists. Mathematics is a creative art because mathematicians think so. -halmos music is very similar to algebra.
-Hardenbergh's insistence that there is no beauty in mathematical science is wrong. The main forms of beauty are order, symmetry and clarity.
-Aristotle The beauty of mathematics is naturally and clearly displayed. -halmos I think this is correct. When a mathematician chooses a subject, the main criterion for judging his success is aesthetic standards.
Von Neumann: My job always tries to combine truth with beauty, but when I have to choose one of them, I usually choose beauty. In the evaluation of mathematical theorems, aesthetic standards are more important than logical standards and practical standards: in the evaluation of mathematical ideas, whether the proportion of beauty and elegance is rigorous and correct is much more important than whether it is useful.
-Steen Pure mathematics can be practical and useful, and applied mathematics can also be elegant. -halmos made further research on the theorem that has been correctly recognized and explored its new proof, just because the existing proof lacks the charm of beauty.
-Klein Mathematicians, like painters or poets, are all makers of style.
Mathematicians' style, like that of painters or poets, must be beautiful ... ugly mathematics has no permanent place. -Hardy A strange beauty rules the kingdom of mathematics. It is not as similar as artistic beauty and natural beauty, but it deeply infects people's hearts and arouses people's appreciation of her, which is very similar to artistic beauty.
Cuomo, can't music be described as mathematics of feeling and mathematics as rational music? In this way, musicians feel mathematics, mathematicians think of music-music is a dream, mathematics is a lifetime's work-and both sides achieve perfection through each other. By then, the wisdom of human beings has reached a perfect model, which will be dazzling under the praise of Mozart Dirichlet or Beethoven Gauss in the future. This alliance has been clearly predicted in Helmholtz's genius and works.
Generally speaking, I prefer to regard mathematics as an art rather than a science. Because we can say that the mathematician's activities, when he is guided by the external rational world, rather than controlled, constantly carry out creative activities, which are similar to those of an artist and a painter, with real similarity, rather than illusory.
Mathematicians' rigorous deductive reasoning in this respect can be compared with painters' painting skills in that respect. Just as a person without certain skills cannot be a good painter, a person without certain precise reasoning ability cannot be a good mathematician.
However, although these are their basic characteristics, they are not enough to make a painter or mathematician worthy of the name. To tell the truth, drawing skills and reasoning ability are not the most important factors after all. Much more sensitive, because both are the main features. Imagination is the only way to make an outstanding artist or mathematician.
We can expect that with the development of education and entertainment, more people will like music and painting. However, few people can really appreciate mathematics.
-Bell In reality, there is no such thing as mathematics, which has lasted for thousands of years and is really so beautiful now. -Sullivan.