The famous mathematician Mr. Chen Shengshen once said more than once: "Mathematics is beautiful." The beauty of mathematics is now in all aspects. Perhaps the beauty lies in that she is the starting point for exploring the laws of world phenomena, in the simplicity of some information that she can express with a few letters and symbols, in the great combination of her bold assumptions and strict arguments, in the wonderful feeling that she has achieved the same goal by arguing a problem, in the perseverance of mathematicians who have spent their whole lives arguing theorems, and in her extensive application in almost all disciplines.
And the beautiful mathematics, in China, which has been advocating poetry and calligraphy since ancient times, is also full of books. China's long history has accumulated literary heritage, which has given China's mathematics a dazzling color. This is the literary talent of mathematics.
natural beauty
Liu Xie's Wen Xin Diao Long thinks that the value of the article is still natural. Articles are mirrors reflecting life, and literature divorced from life is empty and useless. The same is true of mathematics.
The significance of the existence of mathematics lies in rationally revealing some phenomena and laws of nature and helping people to understand and transform nature. It can be said that mathematics is used in life. The earliest origin of mathematics is probably the knotting notes from the ancients, one by one, which firmly tied the roots and life of mathematics from the beginning. Later, notation appeared to meet the needs of livestock breeding or commodity trading, and ancient geometry was produced to measure land. Many mathematical works in ancient China (such as Nine Chapters Arithmetic) are almost all about the exploration and popularization of a specific problem.
In China, mathematics originated from life, while in foreign countries, mathematicians in past dynasties followed the patriarchal clan system. Archimedes' mathematical achievements were used in military, architecture, engineering and many other scientific fields at that time. Newton thought of mathematics when he saw something, that is, he created calculus. Fermat and Euler's pioneering invention of variational method was also caused by exploring natural phenomena.
Beauty of simplicity
No matter how complicated the world is, add, subtract, multiply and divide;
Although the universe is vast, it is full of points, lines and surfaces.
This poem sums up the simplicity of mathematics in a few words. Mathematics, like poetry, has a unique beauty of simplicity.
As we all know, the simplicity of poetry creates a broad imagination space for readers with a few words, which is probably the charm of poetry.
The famous American psychologist L? L. Bloomfield said: "Mathematics is the highest level that language can reach." If the conciseness of poetry is freehand brushwork and the blank space in China's ink painting, then the implication of mathematical language is realistic, concise, accurate, abstract and standardized, which is the embodiment of rigorous scientific attitude. The simplicity of mathematics can not only enable people to grasp the essence of theory more quickly and accurately, but also promote the development of their own disciplines, and also make mathematics disciplines have strong versatility. At present, mathematics, as the language and tool of natural science, has become the language and tool of all sciences, including social science.
The most typical example is the application of binary in computer field. Imagine that any complex instruction is translated into an integer string of 0 1. What a great idea. It can be said that without the simplification of mathematics, there would be no era when the Internet extended in all directions and information technology developed rapidly.
symmetric beauty
China's literature pays attention to symmetry, which can be seen from the centuries-old couplet culture. A better symmetry is palindrome. Su Shi has a famous seven-tune "You Jin Shan Temple", which is a masterpiece in this respect:
Visit Jinshan Temple
Tides rise and fall, dark wave snow-capped mountains, fishing boat and moon in Pu Yuan. /The loose path from the bridge to the Temple Gate is small, and the sill is as bright as the spring eye of shi bo. /all the way to the green trees, the river is dawn, and the sunset glow is red and clear. /Looking into the distance, there are clouds and water on all sides, and there are thousands of gulls in Bifeng.
It's not hard to see that turning it upside down is still a complete seven-meter poem:
There are thousands of light gulls, and the water meets clouds and smoke, looking in all directions. /Sunny sunset red, Xiaotian river trees green. /Qingbo Shiyan Spring is the sill, opposite the Songmen Temple Bridge. /Yue Ming fishing boats fishing in Puyuan, pouring mountains, snowing waves and dark tides.
This palindrome poem, whether read forward or backward, is a good poem with a blend of scenes, freshness and readability. Similarly, there is another example: "Xiang Lian's clear water is moving and refreshing, while the water is moving and refreshing and the summer is long. In the long summer, the cool wind moves the water, and the cool wind moves the water and smells fragrant. " These poems are cleverly conceived and give people a wonderful feeling. Every time they are read, readers will secretly exclaim.
In mathematics, there are many palindromes, such as:
12× 12= 144,2 1×2 1=44 1;
13× 13= 169,3 1×3 1=96 1;
102× 102= 10404,20 1×20 1=4040 1;
103× 103= 10609,30 1×30 1=9060 1;
9+5+4=8+7+3,92+52+42=82+72+32。
The more general symmetry in mathematics is reflected in the symmetry and geometric figures of function images. The former provides convenience for us to explore the essence of function, while the latter gives people endless aesthetic feeling after being applied in the fields of architecture and art.
Suspense beauty
Novels in literature are good at setting suspense. At first, they throw fascinating pictures, unexpected events, worrying contradictions, worrying suspense and thought-provoking questions, and then describe, tell, unfold, answer and think step by step. Or leave an ending without an ending, no matter what, there is no answer, and the ending has no ending, so that readers can imagine, verify, ask and experience for themselves. According to Milan? Kundera said: The cleverness of novelists lies in turning all certainty into doubt and teaching readers to understand the world as a problem.
This phenomenon is by no means uncommon in mathematics. Many mathematical problems begin with an equation that doesn't show any clue, and are solved step by step by various methods, and finally a clear conclusion is drawn. The fun of mathematics lies in people's attitude of seeking truth, their curious solution process and the joy when the truth finally comes out. This is similar to the feeling when people read mystery novels. No wonder some people say that the world itself is an unknown, and literature itself is an equation to explore the mysteries of the world.
Imagery beauty
The most profound relationship between poetry and mathematics is the combination of mathematical concepts or images with poetry.
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. (Xin Qiji)
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. (Shao Yong)
A sail, an oar, a fishing boat, a fisherman and a hook. A bow and a smile, a bright moon and an autumn. (Ji Xiaolan)
A farewell, the two places are hung together, only in March and April, but in 56, the lyre was unintentionally played, the eight-part essay could not be passed on, and the nine-chain was never interrupted. I saw through the Shili Pavilion, and I had a lot of thoughts, but I called it a maid helplessly. I'm tired of complaining about lang. I see the lonely geese in Chongyang in 1999, and the Mid-Autumn Festival in August is not round. In July and a half, I burned incense and lit candles to worship my ancestors. In the dog days of June, everyone shakes my heart. In May, pomegranates are like fire, and the flowers fall after the rain. April loquat is not yellow, I am lazy. Peach blossoms are blown away by the wind in March! Lang Lang, I wish you were a woman. I am a man in the second century. (Zhuo Wenjun)
After reading these poems, we can clearly feel that the artistic conception of poems comes from those numbers. No matter whether numbers are used alone, repeatedly or circularly, seemingly uninfected numbers can show lonely, cheerful, indifferent or sad thoughts and feelings.
Abroad, the works of Dante (1265 ~ 132 1) and G Chaucer (1342 ~ 1400), the two greatest poets in medieval Europe, are full of mathematical knowledge. 17th century, John, a famous British metaphysical poet? John Donne (1572 ~ 163 1) and Andrew? Andrew Marvell (1621~1678) analogized love through mathematical concepts such as compasses and parallel lines in Euclidean geometry. The latter's definition of love is particularly interesting:
Like a straight line, love is also inclined/they can intersect at every angle/but our love is really parallel/although infinite, they never meet.
Love has always been a noun that is difficult to express clearly in words. With the help of familiar parallel lines and rich mathematical images, the author skillfully and accurately conveys his meaning to readers.
Logical beauty
When it comes to logic, we can't help but mention A Dream of Red Mansions, one of China's four classical novels. The complicated relationship between characters and the meticulous storyline have attracted a large number of scholars to do lifelong research and enjoy it.
The charm of A Dream of Red Mansions lies in the fact that it begins with a poem at the front of the volume and develops chapter by chapter. Beautiful mathematics is also expressed concisely and powerfully under a macro concept through rigorous argumentation.
Like a dream of red mansions, mathematical laws are expressed elegantly and clearly from some basic theorems. Most math papers are difficult to understand, but some can make people linger. Newton's three laws are simple, but they can explain very complicated phenomena, such as the laws of celestial bodies. This is the taste of mathematicians. If it is not rigorous enough to withstand scrutiny, it will not be eye-catching.
Mathematics and literary works not only pay attention to strict logical argumentation, but also follow the development law from local structure to large-scale structure.
Very similar to the literature, the development from local structure to large-scale structure is also the process of modern mathematics development. Literature from local to large-scale is often treated by contrast: that is, there are different feelings about things, and the same thing or the same thing can produce different chants. When people have different feelings about things, they often refer to them in a comparative way. For example, "beauty" has multiple meanings, not only referring to beauty, but also referring to monarch. Qu Yuan's Nine Chapters: "Speak with a little affection and be right with a beautiful husband." It can also refer to a person with good moral character, The Book of Songs? Gao Feng: "Who is thinking in the clouds, western beauty." Su Shi's Red Cliff Fu: "Looking at the beauty of heaven." Both geometry and number theory have this history. Algebraic geometricians study singularities by explosion, which is like focusing the whole world on one point. The singularity seen by differential geometry and general relativity is more complicated than algebraic manifold, but it is also hoped that the whole structure can be understood gradually from the local point of view. When studying the local structure, number theory experts use the modular method of prime numbers to turn arithmetic manifold into geometry over a finite field, and then compare it with a large range of arithmetic geometry, and get rich results. In addition, mathematicians will put forward many different proofs for some important theorems. For example, Pythagorean theorem has many different proofs of 10, isoperimetric inequality has five or six proofs, and Gauss gives six different views on the dual law of number theory. Different proofs let us understand the same fact from different angles, which often leads to different development of mathematics. This is also an example from a local to a large scale.
In a word, mathematics is not as boring as some people think. It is not the accumulation of long theorems and formulas, but a beautiful subject. Under the background of China's literature, mathematics also shines with different brilliance.
Perhaps, with a netizen's article "Qin Yuanchun? The ending of the article "Mathematics" is perfect:
"Qinyuanchun? mathematics
Several gardens are fragrant, prosperous and immortal for thousands of years.
Reading "Nine Chapters of Arithmetic" is wonderful, and "Elements of Geometry" is very meaningful.
Complex function, general theory, magnificent;
Prosperous times, taking advantage of the warmth of spring and tomorrow, learn to be magnificent.
Problems are flying all over the sky, attracting countless talents to study them in detail;
Yang cangluo Fahrenheit, group theory, Chen theorem, smiling proudly;
A generation of tianjiao, one? Wiles, the first time to verify Fermat;
Look up at the development of mathematics, there is no limit!