Geometry can't be king! -Euclid
In the mathematical world, what matters is not what we know, but how we know it. Everything counts. Pythagoras
Although we are not allowed to see through the secrets of nature and know the real reason of the phenomenon, some fictional assumptions may still explain many phenomena. Because the structure of the universe is God's most perfect and intelligent creation, nothing will happen if there is no certain maximum or minimum law in the universe. -Euler
The essence of mathematics lies in freedom. "In the field of mathematics, the art of asking questions is more important than the art of answering questions." In the field of mathematics, the art of asking questions is more important than the art of answering questions. -Cantor
"No problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich ideas as infinity, but no other concepts need to be clarified as infinity." As long as a branch of science can raise a large number of questions, it is full of vitality, and no questions indicate the termination or decline of independent development. "Infinite! No other problem has touched the human mind so deeply. " We must know, and we will know. -Hilbert
Mathematics is an infinite science. -Will
The problem is the core of mathematics. -P.R. halmos
Mathematics is the key to science. -Bacon (British philosopher)
Mathematics is the language that God uses to write the universe. Galileo
The mathematical expression is accurate and concise, the logic is abstract and universal, and the form is flexible and changeable, which is an ideal tool for cosmic communication. Zhou Haizhong
"A science can only be truly perfect if it successfully uses mathematics". Marx
The scientific level of a country can be measured by the mathematics it consumes. -Rao
"Some beautiful theorems in mathematics have such characteristics: it is easy to sum up from facts, but the proof is extremely profound." "Mathematics, the queen of science; Number theory, the queen of mathematics. " "Sometimes, you can't get the simplest and most wonderful proof at first, but it is this kind of proof that can go deep into the wonderful connection of higher arithmetic truth. This is the driving force for us to continue our research, which can best make us find something. " If others think about the truth of mathematics as deeply and persistently as I do, they will also find my discovery. Gauss
God created integers, and the rest are man-made. -Kroneck
The God who rules Mount Olympus is an eternal number. God is a mathematician.
"Mr. Fourier believes that the main purpose of mathematics is to serve mankind and explain natural phenomena; But philosophers like him should know that the only purpose of science is for the glory of the human mind, so a question about numbers has the same meaning as a question about the universe system. " -jacoby
A mathematician who is not a poet will never be a complete mathematician. "I never regard my work as a private matter, nor do I pursue fame and praise. I just do my best for the progress of truth. It doesn't matter to me whether it is me or others. What matters is to be closer to the truth. " -Wilstras
"The science of pure mathematics can be said to be the most primitive creation of human spirit in its modern development stage." This is a reliable rule. When the author of a mathematical or philosophical work writes with vague and abstruse words, he is talking nonsense. -Baishihai
"Give me five coefficients and I will draw an elephant; Give me six coefficients and the elephant will wag its tail. " "It would be a serious mistake to think that it is inevitable only in geometric proof or sensory evidence. Give me five coefficients and I will draw an elephant; Give me the sixth coefficient and the elephant will wag its tail. People must be convinced that if he is adding many new terms to science and letting readers continue to study the wonderful and difficult things in front of them, then science has made great progress. " People will die, but their careers will continue. -Cauchy
"Try our best to choose the path we should take." "Very abstract problems must be discussed very clearly." "I'm determined to give up that only abstract geometry. In other words, stop thinking about problems that are only used to practice ideas. I did this to study another kind of geometry, that is, geometry aimed at explaining natural phenomena. " "Mathematics is the most powerful knowledge tool left by human knowledge activities and the root of some phenomena. Mathematics is immutable and exists objectively, and God will build the universe with mathematical laws. " . Descartes
"I don't know what people in the world will think of me; However, I feel like a child playing by the sea, picking up a smooth pebble and finding a beautiful shell; In front of me, the sea of truth has not been discovered at all. " "I see farther than Descartes, because I stand on the shoulders of giants." "Without bold speculation, there will be no great discovery". newton
"Imaginary number is a wonderful spiritual sustenance of human beings. It seems to be an amphibian between existence and non-existence. " "Things that don't work don't exist." "After considering several things, the whole thing boils down to pure geometry, which is a goal of physics and mechanics." -Leibniz
"Read Euler, read Euler, he is our teacher." "The greatest benefit of astronomical science is to eliminate the mistakes caused by ignoring our true relationship with nature. Because social order must be based on this relationship, such mistakes are even more catastrophic. Truth and justice are the eternal foundation of social order. I hope we can get rid of this dangerous maxim. Deception and slavery are sometimes more useful than ensuring their happiness! The historical experience of each era proves that whoever breaks these sacred laws will be punished. " Laplace
"If I inherit a considerable fortune, I may be of little value in mathematics." "I regard mathematics as an interesting job, not a monument to myself. To be sure, I prefer other people's works to my own. I am always dissatisfied with my work. " It seems to be a character axiom that a person's contribution is strictly inversely proportional to his conceit. Lagrange
"My success depends only on two. One is to persevere; The first is to accurately hand-make the graphics that emerge in your mind. " gaspard monge
"Exquisite arguments are often not achieved overnight, but the result of long-term accumulation. I learned it slowly and I will continue to learn. " Learn directly from the masters, not from their students. -Abel
"What is a masterpiece, extraordinary". -Galois
"Choose a clear research object and persevere. You may never reach the finish line, but you can certainly find something interesting along the way. " Klein
"The movement form of thinking is usually like this: conscious research-subconscious activity-conscious research." "Life is a constant struggle. If we enjoy peace occasionally, it is our ancestors who are fighting tenaciously. If our spirit and vigilance relax for a while, we will lose what our ancestors have won for us. " If we want to foresee the future of mathematics, the proper way is to study the history and present situation of this subject. -Poincare
"If a person is doing well in mathematics, it is really easy to attract the attention of the mathematics community. No matter how humble and obscure this person is, he only needs to do one thing: send his discussion of the results to the leadership authority. " Mo Deer
"Mathematicians usually first discover a theorem through intuition; The result was specious to him first, and then he set about making a proof. " -Hardy
"Science needs experiments. But the experiment cannot be absolutely accurate. If there is a mathematical theory, it is completely correct to infer. This is why science cannot be separated from mathematics. Many basic scientific concepts often need mathematical concepts to express. So it is natural for mathematicians to have food, but they can't win the Nobel Prize. " "The Nobel Prize is so compelling that mathematicians can't concentrate on their own research." "We appreciate math, and we need math." "The purpose of mathematicians is to understand mathematics. The progress of mathematics in history is nothing more than two ways: increasing the understanding and promotion of known materials. " Chen shengshen
"Intelligence lies in diligence, and genius lies in accumulation." "Dare to do subtraction in learning is to subtract what the predecessors have solved and see what problems have not been solved and we need to explore and solve them." -Hua
For centuries, the simple combination of integers has been the source of new students in mathematics. -boekhoff
"Things push each other, each has its own togeher, so although the branch knows the same thing, it only sends one end. It is also analyzed by words and disintegrated by pictures. It is also possible to make it a week, but it is not awkward. The viewer thinks that more than half. " -Liu Hui
"Geometry sometimes seems that essence precedes analysis, but in fact geometry precedes analysis, just like a servant walking in front of his master and opening the way for him." "Maybe I can't call myself Adam in mathematics inappropriately, because I believe that there are more mathematical rational creations named after me (which has become popular) than all other mathematicians in the same era put together." Sylvester
"The number of late orders is not supernatural, tangible and verifiable, and there are several that can be pushed." -Zu Chongzhi
"It is impossible for a traveler to go far without personally checking the firmness of each part of the bridge. Even in the field of mathematics, some things are risky. " -Horace Lamb