2. Mathematics is the king of science.
3. Start with the simplest.
Mathematics is an infinite science.
5. Problem is the core of mathematics.
6. God is a mathematician.
Imagination is more important than knowledge.
8. Mathematics is more than just solving problems.
9. Mathematics is symbol plus logic.
10, less is better than less.
1 1, where there are numbers, there is beauty.
12, thinking begins with doubt and surprise.
13, the more detached a mathematician is, the better.
14, beauty is contained in volume and order.
15, mathematics is gymnastics to exercise the mind.
16, the essence of mathematics is its freedom.
17. Mathematics is the key to science.
18, mathematics is a variety of proof skills.
19. Pure mathematics is a magician's real wand.
Please do the examples in the book yourself.
2 1, genius Please look at my elbow.
22. Mathematics is a clever art. ..
23. Mathematics is the theory of studying abstract structures.
24. Mathematics is the symbol that God describes nature.
The only way to learn mathematics is to do it.
26. Cleverness comes from diligence, and genius lies in accumulation.
27. Mathematics is the highest form of all knowledge.
28, learning mathematics, there will never be excessive efforts.
29. Mathematics is one of the most precious research spirits.
30. Mathematics is an evolving culture.
3 1, mathematics is the highest achievement of human thinking.
32. The beauty of mathematics is naturally and clearly displayed.
33. The great actions of nature are written in mathematical symbols.
34. Mathematics is the judge and master of law and theory.
35. Just because you can use mathematical formulas doesn't mean you can do mathematics.
36. Mathematics is the brightest pearl in the crown of human wisdom.
37. Social progress is the crystallization of human pursuit of beauty.
38. One of the best ways to learn to solve problems is to study examples.
39. The art of education is to make students like what you teach.
40. The first is mathematics, the second is mathematics, and the third is mathematics.
4 1, the secret of learning mathematics is to solve the problem, solve the problem, and then solve the problem.
42. Mathematics is the queen of science and number theory is the queen of mathematics.
43. Mathematicians are fascinated by nature. Without infatuation, there is no math.
44. God created integers, and the rest are man-made.
45. I would rather have less, but also better. Half a proof is equal to 0.
46. History makes people wise, poetry makes people witty, and mathematics makes people careful.
47. Specialization and generalization are important sources of useful auxiliary problems.
48. Please pay attention to the details of the problem-solving mistakes and remind yourself before the exam.
49. The scientific level of a country can be measured by the mathematics it consumes.
50. One of the values of a good question is that it can lead to other good questions.
5 1, the main goal of mathematics is the public interest and the explanation of natural phenomena.
Mathematics, like music or poetry, obviously has aesthetic value.
Please find some exercises and use the problem-solving methods learned in books!
54. In mathematics, the main tools for us to find truth are induction and simulation.
55. What pleases me most about mathematics is what can be proved.
If I can see farther, it is because I stand on the shoulders of giants.
57. It is one of your best accumulations to keep all the exercises you have solved.
58. The motive force of mathematical invention is not reasoning, but imagination.
59. Mathematics is the study of quantitative relations and spatial forms in real life.
Never think that you have solved enough problems at any time.
6 1, the big structure of the universe now begins to appear as a pure mathematician.
62. Non-mathematical induction plays an indispensable role in mathematical research.
63. No subject can clarify the harmony of nature more clearly than mathematics.
64. New mathematical methods and concepts are often more important than solving mathematical problems themselves.
65. Observation may lead to discovery, and observation may reveal some laws, patterns or rules.
66. Infinite! No other problem has touched the human mind so deeply.
67. No subject can clarify the harmony of nature more clearly than mathematics.
68. I always try my best to get rid of that heavy and monotonous calculation.
Please read carefully the examples you can understand. Please bite the bullet and don't understand examples.
70. Mathematics can promote people's understanding of the characteristics, value, proportion and order of beauty.
7 1, every problem I solve becomes the law of solving other problems in the future.
72. Mathematics, if viewed correctly, has not only truth, but also supreme beauty.
In the field of mathematics, the art of asking questions is more important than the art of answering questions.
74. Stimulating original expression and the pleasure of seeking knowledge is the highest secret of being a teacher.
75. To gain wisdom, science can improve material life, but mathematics can give all the above.
76. A mathematician who is not a poet will never be a complete mathematician.
77. In mathematics, it is very important to know what is important and what is not.
In the field of mathematics, the art of asking questions is more important than the art of answering questions.
79. Don't expect to remember and master anything the first time you read this book. Please read the second and third times.
80. Don't leave out any exercises in the book. Please complete it all and record the solution ideas.
The simple combination of 8 1 and integers has been the source of new life in mathematics for centuries.
82. Pure mathematics can be practical and useful, and applied mathematics can also be elegant and elegant.
83. Mathematics is a rational spirit, which enables human thinking to be applied to the most perfect degree.
84. When learning mathematics, you should do more exercises and think while doing it. Predict what it is and then know why.
85. Instead of talking about novel problem-solving methods, it is better to keep the conventional problem-solving methods in mind.
86. Mathematical knowledge is the purest logical thinking activity and the most advanced aesthetic embodiment of intelligence and vitality.
Any branch of mathematics, no matter how abstract, will be applied to the real world one day.
88. A science can only be truly perfect when it successfully applies mathematics.
89. If you want to learn to swim, you must go into the water. If you want to be an expert in problem solving, you must solve problems.
90. I owe my success to careful thinking. Only by thinking constantly can I reach the other side of discovery.
9 1, teachers don't teach people with the results they get, the most important thing is to teach people how to get the results.
In the mathematical world, what matters is not what we know, but how we know it.
93. Work hard before you know wisdom. Diligence is good training. Work hard for one minute.
94. Give me five coefficients and I will draw an elephant. Give me six coefficients and the elephant will wag its tail.
In the field of mathematics, the art of asking questions is more important than the art of answering questions.
96. Educating children should focus on stimulating interest and love, otherwise it is just spoon-feeding and meaningless.
97. It is found that every new group is mathematical in form, because we can't have other guidance.
98. Always review the problems solved before, try new solutions and apply the new knowledge you have learned.
99. Anyone who doesn't know that the diagonal side of a square is an incommensurable quantity is not worthy of this title.
100, pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit.
10 1, learning knowledge should be good at thinking, thinking and thinking again. That's how I became a scientist.
102, the number is not intuitive when it is invisible, and it is difficult to be nuanced when it is small. Numbers and shapes are interdependent. How can we divide them into two sides?
103. Learn mathematics as a language, learn the usage of every term, and be familiar with the meaning of every symbol.
104, the human brain is such a computer, which works very reliably at a fairly low accuracy level.
105, mediocre teachers are preaching, good teachers are dispelling doubts, better teachers are demonstrating, and excellent teachers are inspiring.
106, genius is unreliable, cleverness is unreliable, and it is unimaginable to pick up great scientific inventions conveniently.
107, remember: the concepts and objects in mathematics are not unique to mathematics, so don't forget to use mathematics in other disciplines.
108, countable belongs to the world that rules the whole quantity, and the four operations can be regarded as all the equipment of mathematicians.
109, knowledge is eaten as food. We don't live to know, just as we don't live to eat.
1 10, the incomparable eternity and omnipotence of mathematics and its independent effect on time and cultural background are the direct consequences of its essence.
1 1 1. There is no such thing as mathematics in reality. It has lasted for thousands of years and it is really so beautiful.
1 12, don't stay in the cradle of basic problems, learn to treat basic problems as comprehensive problems made up of parts.
1 13, pay attention to the observation of special cases, and you can get general mathematical results and inspire general proof methods.
1 14. Mathematics is a tool of knowledge and the source of other knowledge tools. All the sciences that study order and measurement are related to mathematics.
1 15, which is a reliable rule. When the author of mathematics or philosophy works writes in vague and abstruse words, he is talking nonsense.
1 16, don't think that some words in mathematics have exactly the same meaning just because they look the same as those in natural language.
1 17. Some beautiful theorems in mathematics have such characteristics: it is easy to sum up from facts, but the proof is extremely profound.
Mathematical methods permeate and dominate all theoretical branches of natural science. It has increasingly become the main symbol of measuring scientific achievements.
1 19, the size of the universe, the tiny particles, the speed of rockets, the cleverness of chemical industry, the change of the earth, the mystery of biology, the complexity of daily life, and mathematics are everywhere.
120, don't let go of any seemingly simple examples, they are often not that simple, or can lead to many knowledge points.
12 1, problem solving is a practical skill, just like swimming, skiing or playing the piano, it can only be learned through imitation, practice and study.
122, number theory is the oldest branch of human knowledge, but some of his deepest secrets are closely related to his most ordinary truth.
123, knowledge itself does not tell people how to use it, and the methods used are outside books. This is a skill that cannot be learned without experiment.
124. It is only because the existing proofs lack 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 method.
125. For teenagers, the most important thing is to be curious from an early age and ask questions whenever they encounter problems. This spirit is more important than getting good grades in exams.
126, elementary mathematics is one of the most representative creations of modern thought, which is characterized by linking theory with practice through direct channels.
127, don't follow some unfamiliar problem-solving norms just because the topic is "small". Good habits are cultivated and can't be remembered at once.
128. Only with the vigorous development of mathematics can a country show its national strength. The development and perfection of mathematics are closely related to the prosperity of the country.
129. Mathematicians are as happy as seeing statues, seeing beautiful scenery and hearing beautiful tunes when deducing equations and formulas.
130, time is a constant, but for diligent people, it is a variable. People who count time in minutes spend 59 times more time than those who count time in hours.
13 1. Find a chess player. Only if you are not afraid to expose your weaknesses in front of the Almighty, can you make continuous progress and learn by yourself. If you are not afraid of a low starting point, you are not afraid of the end.
132, mathematics has a high reputation, and another reason is that mathematics makes natural science theorem, which endows natural science with certain reliability.
133. 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.
134. Every time you learn a math difficulty, try to explain it to others so that they can understand it. Only when you can explain it clearly can you really understand it.
135, history makes people wise, poetry makes people wise, mathematics makes people precise, philosophy makes people profound, ethics makes people cultivated, logic and rhetoric make people able to contend.
136, in learning, we should dare to do subtraction, that is, subtract the parts that have been solved by our predecessors to see what problems have not been solved and need us to explore and solve them.
137, a person is like a score, his actual ability is like a numerator, and his evaluation of himself is like a denominator. The larger the denominator, the smaller the value of the fraction.
138, "in learning, we should dare to do subtraction, that is, subtract the parts that have been solved by predecessors and see what problems have not been solved and need us to explore and solve them.
139, don't think of mathematics as difficult, stubborn, annoying and contrary to common sense. It's just something that gives common sense spirituality.
140, feel the beauty of mathematics, feel the harmony between number and shape, and feel the elegance of geometry. This is the true feeling of beauty that all real mathematicians know.
14 1. Mathematics has made an important contribution to observing nature. It explains the simple primitive elements in the regular structure, with which celestial bodies are built.
142, every goal, I want to keep it in front of my eyes, from the first dawn, keep it, and slowly spread out until the whole earth is bright.
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.
144, this book ("Elements of Geometry") is beneficial, which can make the reader float on the surface and practice seriously; Learners make their own rules and make their own smart ideas; Therefore, there is no one in the world who is not learning correctly.
145, pursuing that goal in the best time of life, the book has been written. It doesn't matter whether modern people read it or future generations read it. It may take a hundred years to get readers.
146, most mathematical creations are the result of intuition, and a little direct perception or quickness of facts is understanding, which has nothing to do with any lengthy or formal reasoning process.
147, math problems must be done, but learning math is not just about solving problems. There are too many problems, and there is no point in not thinking: think about the problems and how to change them after thinking.
148, pursue that goal in the best time of my life ... The book has been written. It doesn't matter whether modern people read it or future generations read it. It may take a hundred years to get readers.
149, I have heard people say that I am an opponent and an enemy of mathematics, but no one respects mathematics more than I do, because it has made achievements that I have never achieved.
150, philosophers should also learn mathematics, because he must jump out of the vast phenomenon and grasp the real essence. And because it is a shortcut for the soul to transition to truth and eternity.
15 1. History makes people wise, poetry makes them elegant, mathematics makes them noble, natural philosophy makes them profound, morality makes them steady, and ethical rhetoric makes them able to contend.
152, it is not intuitive when missing numbers, and it is difficult to be nuanced when missing numbers. It is also said that there are two necessary processes to lay a good foundation of mathematics: one is to learn and accept "from thin to thick"; Digestion and refining "from coarse to fine".
153, music can stimulate 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.
154, what gives me the greatest happiness is not knowing knowledge, but learning constantly; Not what you already have, but what you keep getting; Not the height that has been reached, but the constant climbing.
155, it is not intuitive when missing numbers, and it is difficult to be nuanced when missing numbers. It is also said that there are two necessary processes to lay a good foundation of mathematics: one is to learn and accept "from thin to thick"; Digestion and refining "from coarse to fine".
156, mathematicians, like painters or poets, are all makers of styles. Mathematicians' style, like that of painters or poets, must be beautiful ... ugly mathematics has no permanent place.
157, the economic principle of thinking has been highly developed in mathematics. Mathematics is the highest form of science achieved by various sciences in its high development, and all natural disciplines frequently turn to it for help.
158, "Take some time to think about what you did during the day, whether it was a plus sign or a minus sign. If it was a plus sign, you will make progress; If it is'-',we must learn from it and take measures.
159, mathematics is more respected than all other sciences. One reason is that his proposition is absolutely reliable and indisputable, while other sciences are often in danger of being discovered by newly discovered facts.
160, another reason why mathematics is highly respected is that it is mathematics that provides an unquestionable and reliable guarantee for accurate natural science. Without mathematics, they can't achieve such reliability.
16 1. When talking about the secret of success, the greatest scientist in modern times wrote down a formula: a = x+y+z y+z. He explained that a stands for success, x stands for hard work, y stands for the correct method, and z stands for less empty talk.
162, people have financial resources but are careless, that is, financial resources are useless; People who are talented and thoughtful are useful; Being able to learn geometry is very detailed. Therefore, it is the right way to lead the world to practicality.
163, mathematics is a deductive thing, not a sudden appearance. Usually, training is very important. If you look at it from a height, change the situation, change the conditions, or look at it from a higher level, it is all new things.
164. After modern high-energy physics reaches quantum physics, many experiments can't be done at all. It is not far from what mathematicians think, so mathematics has incredible power in physics.
165 whenever there is nothing to think about in my mind, I like to re-verify the theorems I already know. There is no purpose in doing this, just to give yourself a chance to fully enjoy the fun of concentrated thinking.
166. When a question is raised, we should be able to see immediately whether it is more beneficial to study some other questions first, what are these other questions and in what order.
167. When you are halfway through a problem-solving idea and find that your method is poor, please don't throw it away at once, at least come back and re-analyze the previous idea after solving the problem with a new and better method.
168, a strange beauty rules the kingdom of mathematics. This beauty 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.
169, no problem can touch people's emotions as deeply as infinity, and few other concepts can stimulate reason to produce rich thoughts as infinity, but no other concepts can be clarified as infinity.
170, when I listen to others explain some math problems, I often find it difficult or even incomprehensible. At this time, I thought, can we simplify the problem? Often finally figured it out, in fact, it is just a relatively simple question.
17 1. 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.
172. Mathematics is advancing freely along its own path, not because it has various licenses that are not bound by law, but because mathematics has a freedom that is determined by its essence and consistent with its existence.
173, mathematics is the queen of science and number theory is the queen of mathematics. Gauss music can inspire or soothe feelings, painting can make people pleasing to the eye, poetry can impress people, philosophy can make people gain wisdom, science can improve material life, but mathematics can give all of the above.
174. If you can't solve this problem, look around and find a suitable related problem. Auxiliary questions can provide methodological help. It may prompt the method of the solution, the outline of the solution, or prompt us which direction to start working, and so on.
175. For us, the value of mathematical knowledge is not only that it is a powerful tool, but also that mathematics itself is perfect. In the internal or external development of mathematics, we have seen the purest logical thinking activities and the most advanced aesthetic embodiment of wisdom and vitality.
176, mathematics is indeed a wonderful masterpiece, just like the creation of a painter or poet, it is a 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. ;