2. God created integers, and the rest are man-made. Cloned neck
3. When you are halfway through a problem-solving idea and find that your method is poor, please don't throw it away immediately, at least after solving the problem with a new and better method, come back and re-analyze the previous idea.
4. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning.
It is better to keep the novel problem-solving methods in mind than to keep the conventional problem-solving methods in mind.
6. In mathematics class, the taste of mathematics should be more pure, and more attention should be paid to comparison from the perspective of mathematics itself, which is conducive to promoting students' reflection and thus achieving a conscious learning state.
7. The essence of mathematics is freedom. cornel
In the field of mathematics, the art of asking questions is more important than the art of answering questions. -Cantor
9. The incomparable eternity and omnipotence of mathematics, as well as its independence in time and cultural background, are the direct consequences of its essence. -Ebou
10, apply what you have learned, especially in math learning. Applying what you have learned to real life is the ultimate goal of mathematics learning.
1 1. Mathematical knowledge comes from life and serves it.
12, we find that every new group is mathematical in form, because we can't have other guidance. -Darwin
13. One of the best ways to learn to solve problems is to study examples.
14. To establish the concept of space, there must be a hands-on process. The process of hands-on operation is not only a process of practice, but also a process of trying, imagining, reasoning and reflecting.
15. Mathematics teaching activities must be based on students' cognitive development level and existing life experience, so that students can experience and explore, abstract practical problems into mathematical models and explain and apply them.
16, if anyone does not know that the diagonal side of a square is an incommensurable quantity, then he is not worthy of this title. -Plato
17, impetuous people easily ask: how should I learn? Don't ask, just learn.
18, infinite! No other problem has touched the human mind so deeply. -D. Hilbert
19, history makes people wise, poetry makes people witty, and mathematics makes people implicit. bacon
20. Give me five coefficients and I will draw an elephant. Give me six coefficients and the elephant will wag its tail. -Al Cauchy
2 1, don't follow some unfamiliar problem-solving norms just because the topic is "small"-good habits are cultivated, not remembered at once.
22. Just because you can use mathematical formulas doesn't mean you can do mathematics.
23. The biggest failure and sorrow of primary school math teachers is that some students are afraid of math because of you.
24. A mathematician who is not a poet will never be a complete mathematician. -Wilstes
25. The more detached a mathematician is, the better. anonymous
26. The best way to learn anything new is to let students discover it by themselves, because this kind of discovery is the deepest to understand and the easiest to master the internal laws and connections.
27. Don't let go of any seemingly simple examples-they are often not that simple, or they can lead to many knowledge points.
28. Pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit. -Baishihai
29. This is a reliable law. When the author of a mathematical or philosophical work writes with vague and abstruse words, he is talking nonsense. -Ann whitehead.
30. Number theory is the oldest branch of human knowledge, but some of his deepest secrets are closely related to his most common truth. A professional who is good at creating with a certain material: goldsmith | wordsmith.
3 1, pure mathematics is the magician's real wand. Novalis
32. Countability belongs to the world that rules the whole quantity, and the four operations can be regarded as all the equipment of mathematicians. Maxwell
33. It is easy for impetuous people to ask: Is it better to write on the blackboard in class or not to take notes and follow the teacher's ideas? I tell you, as long as you learn, everything will be fine.
34. Simple combinations of integers have been the source of new students in mathematics for centuries. -G.D. boekhoff
I have heard 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 made. -Goethe
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. -Bell
37. Mathematical knowledge is the purest logical thinking activity and the most advanced aesthetic embodiment of intelligence and vitality. Plinson
38. Mathematics is more than just solving problems.
39. Establish abstract mathematical knowledge of image perception and static teaching theory of dynamic experience, perception and thinking.
40. If you are not a genius, you don't want to play games if you want to learn math-you think you have done it, but your math level has not improved with your ability to pass the customs-in fact, you can always remember that learning math makes you play the big game of "life" better!
4 1, the essence of mathematics is its freedom -Cantor
42. Mathematics is the judge and master of law and theory. Benjamin
Never think that you have solved enough problems at any time.
44. Mathematics is one of the most precious research spirits. -Hua
45. 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.
46. The great architecture of the universe is now beginning to emerge as a pure mathematician. -J.H. King
47. Most mathematical creations are the result of intuition, with a little direct perception or quick understanding of facts, which has nothing to do with any lengthy or formal reasoning process. -Lucas (William Lucas)
48. Observation may lead to discovery, and observation may reveal some laws, patterns or rules. -Polya
Generally speaking, I prefer to regard mathematics as art rather than science. Because we can say that the mathematician's activities, when he is guided by the external rational world, rather than controlled, constantly carry out creative activities, which are similar to those of an artist and a painter, with real similarity, rather than illusory. Mathematicians' rigorous deductive reasoning in this respect can be compared with painters' painting skills in that respect. -Boucher
2. Engels (philosopher of dialectics of nature) said: "Mathematics is mathematics that studies the quantitative relationship and spatial form in real life.
3. Arithmetic is the oldest branch of human knowledge, perhaps the oldest branch; However, some of its deepest secrets are close to its common truth. Smith
4. Further study the theorem that has been correctly recognized and explore its new proof, just because the existing proof lacks the charm of beauty. Klein
Aristotle said, "Thinking begins with doubt and surprise."
6. Feel the beauty of mathematics, with harmonious numbers and shapes and elegant geometry. This is the true feeling of beauty that all real mathematicians know. -Poincare
7. The latest progress in mathematical science helps us to improve our ability to predict the weather, estimate the impact of environmental hazards, study the origin of the universe and plan election results. Mathematical methods have become indispensable for the real effectiveness of our technological society. Halmos
8. Queen of Mathematics and Science; Number theory, the queen of mathematics. -Gauss
9. There is no special way for king geometry. -Euclid (Euclid)
10, we must know, we will know. -Hilbert
1 1, often gives the theory of pure geometry. In many problems, it will give many simple and natural ways to gain insight into the source of truth and expose the mysterious chain connecting them, so that they can get a unique, clear and complete understanding. -Josnas
12, genius lies in accumulation, and cleverness lies in diligence. -Hua
13 Mathematics is an infinite science. Herman Weil
14. History makes people wise, poetry makes people witty, mathematics makes people thoughtful, philosophy makes people deep, morality makes people grave, logic and rhetoric make people able to contend. Bacon F.
15. Although we are not allowed to see through the secrets of nature, so as to know the real reason of the phenomenon, some fictitious assumptions may still occur to explain many phenomena. Because the structure of the universe is God's most perfect and wise creation, nothing will happen if there is no certain maximum or minimum law in the universe. -Euler
16, my works always try to combine truth and beauty, but when I have to choose one of them, I usually choose beauty. -Mm-hmm
17. Books in nature are written in mathematical language. Galileo
18, don't ignore analogy, it can lead us to discover. -Polya
19, making mathematics divorced from practical needs is like locking cows away from bulls. -Chebyshev
20. Pure mathematics is a magician's real wand. Novalis
2 1, God is always geometric. -Plato
22. 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. -Hilbert
23. Music can inspire or soothe feelings, painting can please people, poetry can impress people, philosophy can make people gain wisdom, technology can improve material life, but mathematics can provide all of the above. Klein. m
24. Mathematics is symbol plus logic. Bertrand Russell
25. When we say something is infinite, we just say that we can't perceive the end or boundary of what we mean. Hobbes
A) Newton said, "If I can see farther, it is because I stand on the shoulders of giants."
26. Mathematicians' aesthetic feeling is like a sieve. Without it, people will never become mathematicians. Adama
27. Kopnin (philosopher of the former Soviet Union) said: "Mathematicians are as happy as seeing statues, beautiful scenery and beautiful tunes when deducing equations and formulas."
28. Fourier said: "The main goal of mathematics is the public interest and the explanation of natural phenomena."
29. Geometry is the art of making correct reasoning on inaccurate figures. -Polya
The more we are ecstatic about the beauty of mathematics, the more we will regret that only a few people can enjoy our happiness. ..... Remember, 400 years ago, arithmetic was a difficult skill. Now, every child in primary school must master them. Perhaps the beauty of advanced mathematics ... will eventually be understood by all educated people. -crull
3 1, it may sound strange, but the power of mathematics lies in that it avoids all unnecessary thinking and surprisingly saves mental work. -Mach e
32. The main purpose of studying the external world is to find the reasonable order and harmony endowed by God, which is revealed to us by God in mathematical language. Kepler
33, geometry has no way to be king! -Euclid
34. Mathematics is a science that studies quantitative relations and spatial forms in real life. -Engels
35. Wittgenstein said: "Mathematics is all kinds of proof skills."
36. 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. Halmos
37. The essence of mathematics is to constantly seek simpler and simpler methods to prove theorems and solve mathematical problems. Gardner
38. God is a numerologist. -jacoby
39. All problems can be reduced to mathematical problems. Descartes
40. The endless silence in those infinite spaces scares me. pascal
4 1. Mathematics, like philosophy, cannot be separated from its history. Edward
42. Algebra is generous, and it often gives people more than people ask of her. -D'Alembert
43. I don't know what the world thinks of me. I just feel like a child playing by the sea. Sometimes I am glad to find a smooth stone or a beautiful shell, but the ocean of truth has not been discovered before me. newton
44. Mathematics is a clever art ... halmos.
45. Mathematics has made an important contribution to the observation of nature. It explains the simple primitive elements in the regular structure, with which celestial bodies are built. Kepler
46. The greatest mathematicians, such as Archimedes, Newton and Gauss, always combine theory with application impartially. Klein
47. Solving many tangled and difficult problems about infinitesimal mathematics in the past one by one today may be one of the great achievements that we must boast about in our time. Bertrand Russell
48. Mathematics is one of the main manifestations of the free creativity of human mind besides language and music, and it has become a medium to understand everything in the universe through theoretical construction. Therefore, mathematics must remain the main component of knowledge, skills and culture, while knowledge and skills must be passed on to the next generation and culture must be passed on to the next generation. -Herman Wey
49. Knowles said: "Mathematicians are fascinated by nature. Without fascination, there is no mathematics."
50. Numbers rule the universe. Pythagoras
5 1, the motive force of mathematical invention is not reasoning, but imagination. -Demonstration
52. The Queen of Mathematics and Science; Queen of arithmetic and mathematics. Gauss
A) Hua said, "If you want to find a good chess player, you can make continuous progress as long as you are not afraid to expose your weaknesses in front of others." "Self-study, not afraid of the low starting point, not afraid of the end."
B) Gauss said: "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. "
53. My job always tries to unify truth and beauty, but when I have to choose between them, I usually choose beauty. -Will
If we want to put the educational potential of mathematics into practice, we should not only pay attention to the technical level of mathematics, but also pay attention to its structure, history, creation and philosophy, and all aspects should be properly balanced. -Senizer
55. The most important achievement of modern mathematics is to truly reveal the whole picture of mathematics and its essential existence. -Bertrand Russell
56. Mathematics is the king of science. Gauss
57, mathematical proof and method
Music is very similar to algebra. Hardenbergh
59, mathematics can promote people's understanding of the characteristics of beauty-numerical value, proportion, order, etc. -Aristotle
A) Lobachevsky said, "No matter how abstract any branch of mathematics is, it will be applied to the real world one day."
60. A mathematician will never be a perfect mathematician unless he becomes a poet to some extent. -Wilstras
6 1. Mathematical methods permeate and dominate all theoretical branches of natural science. It has increasingly become the main symbol of measuring scientific achievements. Von Newman
62. Mathematics is the highest form of all knowledge. -Plato
63. Gauss said, "Less is better, but better." "Half the proof is equal to zero."
64、
65. Some teachers only ask students to solve math problems through classroom teaching. This practice will hinder the development of the original ability, lead to failure and cause fear of difficulties. -Boiani
66. Music is very similar to algebra. Novalis
67. The definition of guidance can often start with counterexamples. —— Huang (Professor of National Taiwan University)
68. Many arts can beautify people's minds, but none can decorate people's minds more effectively than mathematics. -Billingsley
69. Mathematics is gymnastics to exercise your thinking. Kalinin
70. Logic is a health care method for mathematicians to keep their brains healthy and strong. -Mm-hmm
Math motto 3 Mathematics is a kind of spirit, a kind of rational spirit. It is this spirit that inspires, promotes, inspires and drives human thinking to the most perfect degree, and it is this spirit that tries to decisively influence human material, moral and social life; Trying to answer questions about human existence; Strive to understand and control nature; Try your best to explore and establish the deepest and most perfect connotation of the knowledge you have learned. -Klein mathematics in western culture
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. Klein
The essence of mathematics lies in freedom. -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. -Hilbert (Hilbert)
Mathematics is an infinite science. Herman Weil
The problem is the core of mathematics. -P.R halmos
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. -Hilbert
Some beautiful theorems in mathematics have such characteristics: they are easy to be summarized from facts, but the proofs are extremely profound. Gauss
Philosophers should also study 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. -Plato
Gauss (Prince of Mathematics) said, "Mathematics is the king of science."
Russell said, "Mathematics is symbol plus logic."
Pythagoras said, "Numbers dominate the universe."
Misra said: "Mathematics is the highest achievement of human thinking."
Bacon (English philosopher) said, "Mathematics is the key to science."
Bourbaki School (a French mathematical research group) holds that "mathematics is a theory to study abstract structures".
Hegel said: "Mathematics is the symbol that God describes nature."
Oscar Wilde (president of the American Mathematical Society) said: "Mathematics is a culture that will continue to evolve."
Plato said, "Mathematics is the highest form of all knowledge."
Court said: "Mathematics is the brightest pearl in the crown of human wisdom."
Descartes said: "Mathematics is the tool of knowledge and the source of other knowledge tools. All the sciences that study order and measurement are related to mathematics. "
Engels (philosopher of dialectics of nature) said: "Mathematics is mathematics that studies the quantitative relationship and spatial form in real life.
Klein (American mathematician) said: "Mathematics is a rational spirit, which enables human thinking to be applied to the most perfect degree."
Galileo said, "Give me space, time and logarithm, and I can create a universe." Newton said, "Without bold guesses, great discoveries are impossible." Halmos said, "The creation of mathematics can never be realized by inference alone. First, it's usually some vague guesses, trying to figure out the possible promotion, and then drawing an uncertain conclusion. Then sort out the train of thought until you see the clues of the facts, and it often takes a lot of effort to put everything into logical proof. This process cannot be accomplished overnight. It is common to experience many failures and setbacks, guess and imitate again and again, and spend a few months in temptation. "
Laplace said: "In mathematics, the main tools for us to find truth are induction and simulation."
Wittgenstein said: "Mathematics is all kinds of proof skills."
Hua said: "New mathematical methods and concepts are often more important than solving mathematical problems themselves."
Napier said: "I always try my best to get rid of that heavy and monotonous calculation."
Kepler said, "Pursuing 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 have readers. "
Napoleon said: "Only by vigorously developing mathematics can a country show its national strength. The development and perfection of mathematics is closely related to the prosperity of the country. "