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Contents of fifth grade mathematics manuscripts
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————Wang Juzhen

“A person is like a fraction. His actual talent is like the numerator, and his valuation of himself is like the denominator. The larger the denominator, the greater the value of the fraction. "——Tolstoy

"The essence of mathematics lies in its freedom."——Cantor

"In mathematics. In the field of science and technology, the art of asking questions is more important than the art of answering questions.”——Cantor

“No question can touch people’s emotions as deeply as infinity. Few other ideas stimulate the intellect to such fruitful thoughts as infinity, and yet no other concept demands so much elucidation as infinity.”——Hilbert

"Mathematics is the science of infinity."————Herman Weyl

“Problems are the heart of mathematics.”————P.R. Halmos

" As long as a branch of science can raise a large number of questions, it is full of vitality, while the lack of questions heralds the termination or decline of independent development." ——Hilbert

"Some beautiful theorems in mathematics. They have such characteristics: they are easily summarized from the facts, but the proof is extremely hidden.”——Karl Friedrich Gauss

“Time is a constant, but it is difficult for diligence. For readers, it is a 'variable'. People who use 'minutes' to calculate time have 59 times more time than people who use 'hours' to calculate time." --- Rybakov

" We must dare to make subtractions in our studies, which is to subtract the parts that have been solved by predecessors to see what problems remain that we need to explore and solve." ——Hua Luogeng

"Genius = 2. % inspiration + 98% blood and sweat.”——Thomas Alva Edison (Some versions are “Genius = 1% inspiration + 99% blood and sweat.”)

“Use your time. , think about what you did during the day, whether it is a 'plus' or a 'minus', if it is '+', it means progress; if it is '-', you have to learn lessons and take measures." ———— Dimitrov

"When Einstein, the greatest scientist in modern times, was talking about the secret of success, he wrote down a formula: A=x+y+z. And explained: A represents success, x It stands for hard work, y stands for the correct method, and Z stands for less empty words." --- Albert Einstein

"Some beautiful theorems in mathematics have this characteristic: they are extremely. It is easy to generalize from facts, but the proof is extremely hidden. Mathematics is the king of science.”——Gauss

“In the field of mathematics, the art of asking questions is better than the art of solving problems. more important. "——-Cantor

"As long as a branch of science can raise a large number of questions, it is full of vitality, while the lack of questions indicates the termination or decline of independent development. "---Hilbert

"In the world of mathematics, what matters is not what we know, but how we know it. " --- Pythagoras

"A science can only achieve true perfection when it successfully uses mathematics. "——Karl Heinrich Marx

"The scientific level of a country can be measured by the mathematics it consumes. " --- Rao

"Mathematics - the unshakable cornerstone of science and a rich source of advancement for human undertakings. ” ---- Barrow

“The God who rules on Mount Olympus is the eternal number. "----Jacobi

"If there is no eternal imitation of the universe created by numbers, human beings will not be able to continue to survive. "----Nietzsche

"Those who do not understand geometry are not allowed to enter. "----Plato

"Geometry has no king! " ---- Euclid

"A mathematician is actually a fascination. Without fascination, there would be no mathematics. " ---- Novalis

"Without bold guesses, great discoveries cannot be made. ” ---- Isaac Newton

“Numbers rule the universe. "----Pythagoras

"Mathematics, the queen of science; number theory, the queen of mathematics. "---Karl Friedrich Gauss

"God created the integers, and all other numbers are man-made. "----Kronek

"God is an arithmetician"----Jacobi

"A mathematician without some poetic spirit will never become a mathematician. Complete mathematician. "——Weierstrass

"Pure mathematics, in its modern stage of development, can be said to be the most original creation of the human spirit. "---Huaidehai

" Countability rules the entire world of quantity, and the four arithmetic operations can be regarded as all the equipment of a mathematician.

"——Maxwell

"Number theory is the oldest branch of human knowledge, yet some of its most profound secrets are closely connected with its most ordinary truths. "----Smith

"Infinite! No other question has touched the human heart so deeply. "---Hilbert

"Every new group discovered is mathematical in form, because we can have no other guidance. "---Darwin

"The great architecture of the universe is now beginning to appear in the face of pure mathematicians. "---Jings

"It is a reliable rule that when the author of a mathematical or philosophical work writes in vague and esoteric terms, he is talking nonsense. "----A.N. Huaidehai

"Give me five coefficients and I will draw an elephant; give me six coefficients and the elephant will shake its tail. "————Cauchy

"Pure mathematics is the magician's real magic wand. "----Novales

"If anyone does not know that the diagonals of a square on the same side are incommensurable quantities, then he is not worthy of the title of human being. "---Plato

"The simple composition of integers has been the source of new life for mathematics for centuries. "---Berkhoff

"The incomparable permanence and omnipotence of mathematics and its independence of time and cultural background are direct consequences of its essence. "——A. Ebo

"Life is only for two things, developing mathematics and teaching mathematics"——Pulson

"Use all the power of the mind, to choose the path we should follow. "---Descartes

"I don't know what people in the world will think of me; however, I think to myself, I am just like a child playing on the beach, picking up a smoother piece after a while. From the pebbles, I suddenly found a beautiful shell; but in front of me, the ocean of truth has not yet been discovered at all. "——Isaac Newton

"The reason why I can see further than Descartes is because I stand on the shoulders of giants. ————Isaac Newton

“The traveler who passes through a bridge cannot get far without personally examining the soundness of every part of the bridge.” Even in mathematics some things are risky. "

——Horace. Lamb

"Go forward, and forward will give you faith. "——-D'Alembert

"Read Euler, read Euler, he is the teacher of all of us. "----Laplace

"If I inherit a considerable amount of property, I may not have much value in mathematics. "---Lagrange

"I regard mathematics as an interesting job, rather than trying to build some monument to myself. It's safe to say that I enjoy other people's work more than my own. I am always dissatisfied with my work. "---Lagrange

"It seems to be an axiom of character that a person's contribution is strictly inversely proportional to his pride. "----Lagrange

"For the sake of God, never give up your work! This is your best medicine. "---D'Alembert

"My success depends on only two things. One is to persevere unswervingly to the end; the other is to use hands to accurately create the graphics in the mind. ”

——Monge

“The greatest benefit of astronomical science is the elimination of errors caused by neglect of our true relationship with nature. Because social order must be based on such relationships, such mistakes are all the more disastrous. Truth and justice are the eternal foundations of social order. Would that we should be freed from the dangerous maxim that it is sometimes more useful to deceive and enslave than to secure their happiness! Historical experience from all ages proves that whoever breaks these sacred laws will be punished. ”

————Laplace

“Sometimes, you fail to get the simplest and most beautiful proof at the beginning, but it is this kind of proof that can deepen your understanding. to the wonderful connections of higher arithmetic truths. This is what motivates us to continue research and what best enables us to make discoveries. "----Gauss

"If someone else thinks about the truth of mathematics as deeply and persistently as I do, he will also find my discovery. "——Gauss

"People die, but the cause will last forever. " --- Cauchy

"Sophisticated arguments are often not achieved overnight, but are the result of long-term discussions among people." I also learned it slowly, and I have to continue to learn. "----Abel

"After all, it is the work of a master, extraordinary! "--- Galois

"Exceptionally abstract issues must be discussed extremely clearly. " - Descartes

"I think, therefore I am. "----Descartes

"I am determined to give up that mere abstract geometry. That is to say, stop thinking about problems that are just for thinking. I did this in order to study a different kind of geometry, one whose purpose was to explain natural phenomena. "----Descartes

"Mathematics is the most powerful knowledge tool left over from human intellectual activities, and it is the root of some phenomena.

Mathematics is immutable and exists objectively. God will build the universe based on mathematical laws. "----Descartes

"Learn directly from the masters rather than from their students. "----Abel

"Choose a definite research object and persevere. You may never reach the end, but you're bound to discover some interesting things along the way. "---Klein

"I never regard my works as a personal matter, nor do I pursue fame or praise. I am simply doing my best for the advancement of truth. Whether it's me or someone else, it doesn't matter to me. What matters is that it's closer to the truth. "——Weierstrass

"The movement form of thinking is usually like this: conscious research-subconscious activities-conscious research. "——Poincaré

"Life is a continuous struggle. If we occasionally enjoy tranquility, it is because our ancestors fought tenaciously. If our spirit, our vigilance were to let down for a moment, we would lose what our forefathers had won for us. ”——Poincaré

“If we want to foresee the future of mathematics, the appropriate way is to study the history and current situation of this subject. "——Poincaré

"We must know, we will know. "---Hilbert

"Throw them into ice water and let them learn to swim on their own, or they will drown. Many students do not try to work on their own until they have mastered everything that others have done that is relevant to their problem. As a result, very few develop the habit of independent work. "——E.T. Bell

"If a person has done outstanding mathematical work and wants to attract the attention of the mathematical community, it is really easy, no matter how humble and unknown this person is. , he only has to do one thing: send his account of the results to a leading authority. ”

————Model

“A mathematician usually discovers a theorem through intuition; the result is first likely to him, and then he sets out to create it. A proof. "---Hardy

"A scholar, in addition to learning knowledge, must also have "taste". This word is not easy to translate, but some translate it into taste and love. If a person wants to achieve great achievements, he must have a very clear "taste." --- Yang Zhenning

"If you think that necessity is only found in geometric proofs or sensory evidence, then it will is a serious mistake. Give me five coefficients and I will draw an elephant; give me a sixth coefficient and the elephant will wag its tail. One must be sure if he is adding many new terms to science. Letting readers continue to study the wonderful and indescribable things before them has made great progress in science." --- Cauchy

"Mathematics is a deductive science. Set up postulates and obtain conclusions through logical reasoning." --- Chen Shengshen

"Science requires experiments, but experiments cannot be absolutely accurate. If there is a mathematical theory, it is completely correct. This is why science cannot be separated from mathematics. Many basic concepts of science often need to be expressed by mathematical concepts, so it is natural that mathematicians can earn a living but cannot win the Nobel Prize.”

- -- Shengshen Chen

"There is no Nobel Prize in mathematics, which may be a good thing. The Nobel Prize is too eye-catching and will distract mathematicians from focusing on their own research."

----Chen Shengshen

“We appreciate mathematics, we need mathematics.”————Chen Shengshen

“The purpose of a mathematician is to understand mathematics. In the history of mathematics There are only two ways of progress: increasing the understanding of known materials and extending the scope."

——Chen Shengshen

"Although we are not allowed to see through the secrets of the nature. Thus, we can understand the real causes of phenomena, but it may still happen that certain fictional hypotheses are enough to explain many phenomena. "——Euler

"Because the structure of the universe is the most complete and the most complete. A wise creation of God, therefore, if there were not some great or minimal law in the universe, nothing would happen at all." --- Euler

"Late order. The numbers are not miraculous, they are tangible and can be detected, and there are numbers that can be deduced. "--- Zu Chongzhi

"Things are related to each other, and each has its own purpose. Therefore, although the branches are divided, they have the same origin. It's just one end. It's analyzed in words and broken down with pictures. It can be summarized and understood, and the person who understands it has already thought about it halfway."——Liu Hui

"Imaginary number. It is a wonderful human spiritual sustenance. It seems to be an amphibian between existence and non-existence."—— Leibniz

"Things that do not work will not exist. ."—— Leibniz

"After considering those few things, the whole thing boils down to pure geometry, which is an aim of physics and mechanics."—— ——Leibniz

“Geometry sometimes seems to be ahead of analysis, but in fact, geometry precedes analysis, just like a servant walking in front of his master, paving the way for his master. of.

"——Sylvester

"Perhaps I may not unduly claim the title of mathematical Adam, since I believe that mathematically rational creatures are named by me (already popular) than More than all other mathematicians of the same generation put together. "——Sylvester

"A mathematician without some poetic talent will never become a complete mathematician. "——Weierstrass

Leonhard Euler (1707-1783 AD) was born in Basel, Switzerland in 1707. He entered the University of Basel at the age of 13 Studying, he received careful guidance from the most famous mathematician at the time, Johann Bernoulli (1667-1748).

Eulerian was the most prolific and outstanding mathematician in the history of science. According to statistics, during his tireless life, *** wrote 886 books and papers, of which analysis, algebra, and number theory accounted for 40%, geometry accounted for 18%, physics and mechanics accounted for 28%, and astronomy accounted for 11%. %, ballistics, navigation, architecture, etc. accounted for 3%. The Petersburg Academy of Sciences was busy for 47 years in sorting out his works. The great 19th century mathematician Gauss (1777-1855) once said: "Studying Euler's works is always the best way to understand mathematics. "

Excessive work caused him to suffer from eye disease, and unfortunately he became blind in his right eye. He was only 28 years old at this time. In 1741, at the invitation of Peter the Great of Prussia, Euler went to Berlin to teach at the Institute of Physics and Mathematics of the Academy of Sciences. Director until 1766, when he returned to Petersburg at the sincere invitation of Tsar Catlin II. Unexpectedly, not long after, the vision in his left eye deteriorated, and finally he became completely blind. Unfortunately, things happened one after another, including the great fire of Petersburg in 1771. The disaster affected Euler's house. The 64-year-old Euler, who was sick and blind, was trapped in the fire. Although he was rescued from the flames, his study and a large number of research results were all reduced to ashes.

The heavy blow still did not make Euler fall. He vowed to regain his loss. Before he was completely blind, he could still see things dimly. He seized this last moment and wrote something on a big blackboard. He discovered the formula and then dictated its contents, which were recorded by his students, especially his eldest son A. Euler (a mathematician and physicist). After Euler became completely blind, he still fought against the darkness with amazing perseverance, relying on his memory and knowledge. He conducted research on mental arithmetic until his death, which lasted 17 years.

Euler's memory and mental arithmetic ability were rare. He was able to recite the contents of his notes in his youth. Mental arithmetic was not limited to simple calculations. Mathematics can also be done with mental arithmetic.

Euler's style is very high. Lagran corresponded with Euler from the age of 19 to discuss the general solution to the isoperiod problem, which led to the development of the calculus of variations. Birth. The isoperiod problem was a problem that Euler had painstakingly considered for many years. Lagrange's solution won Euler's warm praise. Euler maintained his abundant energy until the last moment. On the afternoon of September 18, 1783, Euler Celebrating his success in calculating the law of ascent of balloons, he invited friends to dinner. Not long after Uranus was discovered, Euler wrote out the essentials for calculating the orbit of Uranus, and even laughed with his grandson. After drinking tea, he suddenly suffered from an illness and his pipe stopped smoking. The hand fell and he murmured: "I am dead". Euler finally "stopped life and calculation".

Tao Zhexuan was born in Adelaide, Australia on July 15, 1975. , is the eldest son of the family. He is a Chinese mathematician who currently teaches in the Department of Mathematics at the University of California, Los Angeles (UCLA). He is the only Chinese-Australian mathematics professor in Australia to win the highest honor in mathematics, the Fields Medal. He was awarded the title after Yau Shing-tung in 1982. The second Chinese to receive this honor. After receiving his doctorate from Princeton University in 1996, he taught at UCLA and was appointed as a full professor at UCLA at the age of 24.

At the "Palace of Discovery" in Paris, France. The name of Zu Chongzhi is tied with the value of pi he discovered. His ancestor Chongzhi once calculated that the moon takes 27.21223 days to orbit the earth, which is almost the same as the modern accepted 27.21222 days. It is really admirable to have such a great achievement in that era. No wonder Western scientists put one of the many craters on the moon Named "Zu Chongzhi". And even in the Soviet Union, the "big brother" of the socialist communist country, among the portraits of famous scientists from all over the world inlaid with colored marble on the corridor wall of the auditorium of Moscow State University, there are also China's Zu Chongzhi and Li Shizhen. Outstanding performance, we can't help but know him a little bit.

Dr. Qiu Chengtong is an internationally renowned mathematician, an academician of the American Academy of Sciences, and a foreign academician of the Chinese Academy of Sciences. In 1982, he won the Fields Medal (known as the Nobel Prize of mathematics) for his outstanding work in geometry. In 1994, he won the internationally renowned Clifford Award from the Swedish Royal Academy. Won the U.S. National Medal of Science in 1997.

Dr. Yau Shing-tung has made outstanding achievements in scientific research and won many honors.

What is even more valuable is that he pays close attention to the development of basic research in China and closely links it with his own scientific research development. Over the years, he has been using his international influence and ability to coordinate various forces to contribute to China's development. A lot of work has been done in the development of mathematics.