For me, studying mathematics is as natural as breathing. ----- Erdos
Because the structure of the universe is the most perfect and most wise creation of God, therefore, if there is not some law of great or minimal in the universe, Then nothing will happen at all. -----Euler
What gives me the greatest happiness is not the knowledge I have acquired, but the continuous learning. It is not something that already exists, but something that is constantly acquired. Not the height already reached, but the continued climb. -------Gauss
The numbers in late sequence are not magical, they are tangible and can be detected, and they can be deduced numerically. ------Zu Chongzhi
Mathematics is the most powerful knowledge tool left behind by human knowledge 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
Later numbers are not miraculous, they are tangible and detectable, and they can be deduced by counting. ------Zu Chongzhi
Mathematics is the most powerful knowledge tool left behind by human knowledge 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
Hua Luogeng Scientific achievements are accumulated bit by bit. Only long-term accumulation can the bits and pieces merge into a sea.
Hua Luogeng It is best for us to regard our own life as the continuation of the lives of our predecessors, as a part of the same life today, and at the same time as the beginning of the lives of future generations. If this continues, science will become more brilliant day by day, and society will become more beautiful day by day.
Hua Luogeng (China) A strong man fights to the death in battle, even with a few scars, fighting against a thousand-year-old demon and fighting for the new style of EMI. Be generous with yourself.
Hua Luogeng (China) In the long march of seeking truth, only by learning, continuous learning, diligent learning, and creative learning can we cross mountains and ridges.
Hua Luogeng Although Jincheng is happy, it is better to return to my hometown; although Paradise is good, it is not a place to stay for a long time. Come back.
Hua Luogeng studies hard but does not know enough, and humility comes from insufficient knowledge. False modesty can only win mediocre applause, but cannot achieve real progress.
Hua Luogeng Although Jincheng is happy, it is better to return to my hometown; although Paradise is good, it is not a place to stay for a long time. Come back.
Hua Luogeng When people help me, I will never forget it; when I help others, I won’t forget it.
Hua Luogeng The value of people lies in their ability to think creatively.
Hua Luogeng All the more accomplished scientific workers are, without exception, experts at utilizing time, and they are also people who are determined to invest a lot of time in a lot of work.
Hua Luogeng Time is made up of minutes and seconds. Only those who are good at utilizing sporadic time will achieve greater results.
Mathematics is advancing unfettered along its own path, not because it has any license to be exempted from legal constraints, but because mathematics inherently has a Freedom determined by and consistent with its existence.---Hankel, Hermann
Geometry, theoretical arithmetic, and algebra, these subjects have no other principles than definitions and axioms, and no other principles than deduction. But in this process, simplicity, complexity, rigor and generality have been integrated. This characteristic is not possessed by other disciplines. ---Whewell, W.
Mathematical knowledge has three main characteristics that are different from other knowledge: first, mathematical knowledge makes its results more truthful than other knowledge; second, mathematical knowledge is It is the necessary first step to obtain other correct knowledge; third, the acquisition of mathematical knowledge does not depend on other knowledge. ---Schubert, H.
Mathematicians pay no attention to statements or conjectures. They deduce everything based solely on definitions and axioms, using arguments and reasoning.
In fact, it is incorrect to call those theories that are only based on conjectures or hypotheses as science, because conjectures often resort to certain opinions or claims, and therefore they cannot produce knowledge from them. ---Reid, Thomas
No subject can illustrate the harmony of nature more clearly than mathematics. ---Carus, Paul
"Chinese scientist Wang Juzhen has a motto when it comes to experimental failure, which is: "If you keep doing it, there is a 50% chance of success, but if you don't do it, it will be a 100% failure." "
" A person is like a fraction, his actual talent is like a numerator, and his valuation of himself is like a denominator. The larger the denominator, the smaller the value of the fraction. "----Tolstoy
"The essence of mathematics lies in its freedom."----Cantor
"In the field of mathematics, The art of asking questions is more important than the art of answering them." ---- Cantor
"No question can touch people's emotions as deeply as infinity, and few can touch people's emotions as deeply as infinity. No other idea stimulates the intellect to such fruitful thoughts as infinity, but no other concept demands so much elucidation as infinity."----Hilbert
" Mathematics is an infinite science" ---- Hermann Weyl
"Problems are the heart of mathematics" ---- P.R. Halmos
"As long as a branch of science can ask A large number of problems makes it full of vitality, while the lack of problems heralds the termination or decline of independent development." ----Hilbert
"Some beautiful theorems in mathematics have such characteristics: they are extremely It is easy to summarize from the facts, but the proof is extremely hidden."----Gauss
"Time is a constant, but for those who are diligent, it is a 'variable'. People who measure time in minutes have 59 times more time than those who measure time in hours. ” ---- Rybakov
“We must dare to make subtractions in learning, that is, subtracting the parts that have been solved by predecessors to see which problems are still unresolved and need us to explore and solve them. "----Hua Luogeng
"Genius = 1% inspiration and 99% blood and sweat. "----Edison
"Use your time to think about what you did during the day, whether it is a 'positive sign' or a 'minus sign'. 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 represents hard work, y represents the correct method, and Z represents less empty words.
” ——Einstein
“Mathematics is an infinite science.” ——Hermann Weyl
“Some beautiful theorems in mathematics have such characteristics : They are easily summarized from facts, but the proofs are extremely hidden. Mathematics is the king of science." --- Gauss
"In the field of mathematics, the art of asking questions is more important than solving them. The art of asking questions is more important." ----Kampohl
"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 end of independent development or the failure of independent development.
"In the world of mathematics, what matters is not what we know, but how we know it." --- Hilbert ——Pythagoras
“A science can only achieve true perfection when it successfully uses mathematics.” ——Marx
“A country The level of science can be measured by the mathematics it consumes." --- Rao
"Mathematics is 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
"Without the 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
"There is no king of geometry! " ---- Euclid
"A mathematician is actually a fascination. Without fascination, there would be no mathematics. " ---- Novalis
"Without bold guesses, great discoveries cannot be made. "---- Newton
"Numbers rule the universe. "----Pythagoras
"Mathematics, the queen of science; number theory, the queen of mathematics. "——Gauss
"God created 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, a science 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
"The discovery of every new group is mathematical in form, because we can have no other guidance. "---Darwin
"The great architecture of the universe now begins 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 and the same sides are incommensurable quantities, then he does not deserve the title of human being. "——Plato
"The simple composition of whole numbers 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. "----Newton
"The reason why I can see farther than Descartes is because I stand on the shoulders of giants. " --- Newton
"No traveler can go far without personally examining the soundness of every part of the bridge. Even in mathematics some things are risky. "
" Go forward, go forward, you will have faith. "——-D'Alembert
"Read Euler, read Euler, he is the teacher of all of us. " --- Laplace
"If I inherit a considerable fortune, I may not have much value mathematically. ”——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. "
" The greatest benefit of astronomical science is to eliminate the errors caused by neglecting 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. "
" Sometimes, you fail to get the simplest and most beautiful proof at the beginning, but it is this kind of proof that can deepen 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
"Exquisite arguments are often not achieved overnight, but are the accumulated results of people's long-term discussions." I also learned it slowly, and I have to continue to learn. " ————-Abel
"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
"The discovery of every new group is mathematical in form, because we can have no other guidance. "---Darwin
"The great architecture of the universe now begins 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 and the same sides are incommensurable quantities, then he does not deserve the title of human being. "——Plato
"The simple composition of whole numbers 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. "----Newton
"The reason why I can see farther than Descartes is because I stand on the shoulders of giants. " --- Newton
"No traveler can go far without personally examining the soundness of every part of the bridge. Even in mathematics some things are risky. "
" Go forward, go forward, you will have faith. "——-D'Alembert
"Read Euler, read Euler, he is the teacher of all of us. " --- Laplace
"If I inherit a considerable fortune, I may not have much value mathematically. ”——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. "
" The greatest benefit of astronomical science is to eliminate the errors caused by neglecting 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.
"
" Sometimes, you fail to get the simplest and most beautiful proof at the beginning, but it is this kind of proof that can deepen 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
"Exquisite arguments are often not achieved overnight, but are the accumulated results of people's long-term discussions." 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 by 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 "tast". This word is not easy to translate, and some translate it into taste and love. If a person wants to achieve great achievements, he must have a very clear "tast". "----Yang Zhenning
"Mathematics is the king of science."---Gauss
cedbed\" is the king of science. There is certainty only in the evidence of feeling, and that would be 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 convinced that science is making great progress if he is adding many new terms to it and leaving the reader to study the wonderful and indescribable things that lie before them. "---Cauchy
"Mathematics is a deductive science. From a set of postulates, through logical reasoning, a conclusion is obtained. "——Chen Shengshen
"Science requires experiments. But experiments cannot be absolutely accurate. If there is a mathematical theory, it all depends on inference, which is completely correct. This is why science cannot be separated from mathematics. Many basic concepts of science often require mathematical concepts to represent them. Therefore, it is natural that mathematicians can make a living but cannot win Nobel Prizes. "
" There are no Nobel Prizes in mathematics, which is probably a good thing. The Nobel Prize is too high-profile and distracts mathematicians from focusing on their own research. "
"We appreciate mathematics, we need mathematics. "——Chen Shengshen
"The purpose of a mathematician is to understand mathematics. Historically, mathematics has progressed in two ways: increasing understanding of known materials, and extending the scope. "
" Although we are not allowed to see through the secrets of the nature of nature and thus understand the true causes of phenomena, such a situation may still occur: certain fictional assumptions enough to explain many phenomena. "——Euler
"Because the structure of the universe is the most perfect and wise creation of God, therefore, if there is no certain maximum or minimum law in the universe, Then nothing will happen at all. "---Euler"
"The numbers in late sequence 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 and origin, and they only originate from one end. The principles are analyzed in words and dissected with diagrams. The common people can also summarize and understand, and they are clear but not obscuring. Those who have read it have thought more than half of it. "----Liu Hui
"Imaginary numbers are 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. The one who clears the way for the master. ”----Sylvester
“Perhaps I may not unduly claim the title of mathematical Adam, for I believe that the creation of mathematical rationality is named by me (already popularly universal) rather 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
Reference: Baidu Library 1|Comments (1)
Report|2011-11-01 19: 20304483711|First Class Love Einstein said: "One of the reasons why mathematics is respected above all other sciences is because its propositions are absolutely reliable and indisputable, while other sciences are constantly in danger of being overturned by newly discovered facts. …. Another reason why mathematics has a high reputation is that mathematics enables natural science to achieve theoremization and gives natural science a certain degree of reliability. "
Qiu Chengtong said: "After modern high-energy physics reaches quantum physics, there are many experiments that cannot be done at all. You can use paper and pen to calculate at home. This is not far from what mathematicians think, so mathematics is in It has incredible power in physics."
Roentgen said: "The first is mathematics, the second is mathematics, and the third is mathematics."
Hua Luogeng said: "The universe is so big, the particles are so big." Micro, the speed of rockets, the ingenuity of chemical engineering, the changes in the earth, the mysteries of biology, the complexity of daily life, mathematics is used everywhere. "
Von Neumann said: "Mathematical methods penetrate and dominate all theoretical branches of natural science. It has increasingly become the primary measure of scientific achievement. "
Pillo (Canadian biologist) said: "Ecology is essentially mathematics."
Kepler said: "Mathematics makes an important contribution to the observation of nature. , it explains the simple primitive elements in the regular structure, and the celestial bodies are built with these primitive elements."
Fourier said: "The main goal of mathematics is the public interest and the explanation of natural phenomena."
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Lobachevsky said: "No matter how abstract any branch of mathematics is, it will one day be applied to the real world."
Leibniz said: "Use One, everything can arise from nothing."
Aristotle said: "Thinking begins with doubt and surprise."
Novales said: "A mathematician is essentially a mathematician. For those who are obsessed, there is no mathematics if you are not obsessed."
Kopnin (a former Soviet philosopher) said: "When mathematicians derive equations and formulas, it is like seeing statues, beautiful scenery, hearing beautiful tunes, etc. and get full happiness"
Russell said: "What pleases me most in mathematics are those things that can be proved."
Gauss said: "Give me the most What makes you happy is not the knowledge you already know, but the continuous learning; not the things you already have, but the continuous acquisition; not the height you have reached, but the continuous climbing."
Polya said : "Start with the simplest thing"
Gauss said: "It would be better to have less, but better" "One-half proof is equal to 0"
Hilbert said : “When I listen to others explaining certain mathematical problems, I often find it difficult or even impossible to understand. Then I thought, can the problem be simplified? Often, after you finally figure it out, it's actually just a simpler problem. "
Hirotaka Heisuke (Japanese Fields Medal-winning mathematician) said: "In mathematics, it is important to distinguish what is important and what is not important, and to know what to choose."
Hua Luogeng said: “To play chess, you need a master…. .
Only if you are not afraid of exposing your weaknesses in front of capable people can you continue to make progress." "Self-study is not afraid of a low starting point, but it is afraid of not reaching the end."
Newton said: "If I can see further, it is because I Standing on the shoulders of giants"
"My success is attributed to careful thinking. Only by constant thinking can we reach the other side of discovery."
Newton said: "Every goal, I want it to stay in front of my eyes, from the first to the first dawn, keep it, slowly unfold, until the whole earth is bright."
Einstein said: "Whenever my mind When I have no problems to think about, I like to re-verify the theorems I already know. There is no purpose in doing this, it is just to give myself the opportunity to fully enjoy the pleasure of concentrating on thinking."
Hua Luogeng said: "When the number is missing, it is less intuitive, and when the shape is missing, it is difficult to understand the subtleties." He also said, "It is necessary to There are two necessary processes to lay a good foundation in mathematics: first learn and accept "from thin to thick"; then digest and refine "from thick to thin""
Su Buqing (Mathematician from Mainland China) said: "Learning In mathematics, you should do more exercises and think while doing them. Predict what is happening, and then know why it is happening."
Rama Nujan (the national treasure of mathematics in India) said: "Genius? Please look at my elbows."
Karagiodori (Greek mathematician of functional theory) said: "When studying mathematics, you will never work too hard."
Einstein said: "The inside of the circle represents the knowledge I have learned now. There is still infinite blank space outside the circle, and as the circle becomes larger and larger, the blank space touched by the circle becomes larger and larger." Between genius and diligence, I chose diligence without hesitation, because it is the catalyst for all achievements in the world." "I thought about it over and over for months and years; ninety-nine times I was wrong, and the first I was right a hundred times."
Newton said: "I have no extraordinary intelligence, all I have is the energy to think with disdain. Try your best to do well today, and you may be able to do better tomorrow."