1. 在任何时刻都不要认为自己解过的题已经足够多了。

1. Never think that you have solved enough problems at any moment.

2. 数学是无穷的科学。赫尔曼外尔

2. Mathematics is the science of infinity. Herman Weyl

3. 感觉到数学的美，感觉到数与形的协调，感觉到几何的优雅，这是所有真正的数学家都清楚的真实的美的感觉。庞加莱

3. To feel the beauty of mathematics, to sense the harmony between numbers and shapes, to perceive the elegance of geometry, this is a genuine, authentic sense of beauty that all true mathematicians are aware of. Poincaré

4. 没有任何问题可以向无穷那样深深的触动人的情感，很少有别的观念能像无穷那样激励理智产生富有成果的思想，然而也没有任何其他的概念能向无穷那样需要加以阐明。希尔伯特

4. There is no question that can touch the human heart as deeply as infinity, and few ideas can stimulate the intellect to produce fruitful thoughts as much as infinity. However, no other concept requires clarification as much as infinity. Hilbert.

5. 现代高能物理到了量子物理以后，有很多根本无法做实验，在家用纸笔来算，这跟数学家想样的差不了多远，所以说数学在物理上有着不可思议的力量。邱成桐

5. After modern high-energy physics entered the realm of quantum physics, there are many things that cannot be experimentally tested; calculations are done at home with paper and pens, which is not very different from what mathematicians do. Therefore, it is said that mathematics has an incredible power in physics. Qiu Chengtong.

6. 浮躁的人容易问：上课到底把老师的板书记下来好还是跟着老师的思维不记笔记好告诉你吧，都好只要你学就行。

6. People who are easily agitated often ask: Is it better to take down the teacher's notes during class or to just follow the teacher's thought process without taking notes? Let me tell you, both are good as long as you are learning.

7. 学习任何新知的最佳途径是由学生自己去发现，因为这种发现理解最深，也最容易掌握内在的规律和联系。

7. The best way to learn any new knowledge is for students to discover it themselves, as this method of discovery leads to the deepest understanding and is also the most effective in grasping the inherent rules and connections.

8. 迟疾之率，非出神怪，有形可检，有数可推、——祖冲之

8. The rate of illness and delay is not due to supernatural causes; it can be examined in tangible form and can be inferred from numbers —— Zu Chongzhi

9. 不管数学的任一分支是多么抽象，总有一天会应用在这实际世界上。罗巴切夫斯基

9. No matter how abstract any branch of mathematics may be, it will eventually be applied in this real world. Lobachevsky

10. 数学是研究抽象结构的理论。布尔巴基学派

10. Mathematics is the theory of the study of abstract structures. The Bourbaki school.

11. 一个没有几分诗人才能的数学家决不会成为一个完全的数学家。魏尔斯特拉斯纯粹数学，就其本质而言，是逻辑思想的诗篇。爱因斯坦

11. A mathematician without a bit of poetic talent would never become a complete mathematician. Weierstrass's pure mathematics, in its essence, is a poem of logical thought. - Einstein

12. 小学数学教师最大的失败和悲哀，莫过于因为你而使得某些学生害怕数学。

12. The greatest failure and tragedy for a primary school math teacher is to make certain students afraid of mathematics because of you.

13. 无限!再也没有其他问题如此深刻地打动过人类的心灵。D希尔伯特

13. Infinity! No other question has ever touched the human heart so deeply. David Hilbert

14. 立志于物理学的人，不懂下列的事情是不行的：第一是数学，第二是数学，第三是数学。伦琴

14. For those who aspire to physics, it is imperative to understand the following: first is mathematics, second is mathematics, and third is mathematics. Röntgen.

15. 浮躁的人容易问：我到底该怎么学;别问，学就对了。

15. People who are impulsive tend to ask: "How should I learn?" Just learn, don't ask.

16. 可以数是属统治着整个量的世界，而算数的四则运算则可以看作是数学家的全部装备。麦克斯韦

16. The numbers that govern the entire world of quantity can be said to be the ruler, while the four basic arithmetic operations can be regarded as the entire arsenal of the mathematician. Maxwell

17. 数学是最宝贵的研究精神之一。华罗庚

17. Mathematics is one of the most precious research spirits. Hua Loo-keng

18. 给我五个系数，我讲画出一头大象;给我六个系数，大象将会摇动尾巴。AL柯西

18. Give me five coefficients, and I can draw an elephant; give me six coefficients, and the elephant will wag its tail. A. L. Cauchy

19. 在数学的领域中，提出问题的艺术比解答问题的艺术更为重要。――康托尔

19. In the field of mathematics, the art of posing problems is more important than the art of solving them. -- Cantor

20. 数学是知识的工具，亦是其它知识工具的泉源。所有研究顺序和度量的科学均和数学有关。笛卡儿

20. Mathematics is a tool of knowledge, as well as the source of other tools of knowledge. All sciences that study order and measurement are related to mathematics. Descartes

21. 当数学家导出方程式和公式，如同看到雕像、美丽的风景，听到优美的曲调等等一样而得到充分的快乐。柯普宁

21. When mathematicians derive equations and formulas, they experience a profound joy, just as they do when they see statues, beautiful landscapes, listen to melodious tunes, and so on, as Kropotkin said.

22. 数学是一种会不断进化的文化。魏尔德

22. Mathematics is a culture that will continue to evolve. Weiye.

23. 我总是尽我的精力和才能来摆脱那种繁重而单调的计算。纳皮尔

23. I always do my best with all my energy and talent to free myself from that heavy and monotonous calculation. Napier.

24. 数支配着宇宙。毕达哥拉斯

24. Numbers govern the universe. Pythagoras

25. 发现每一个新的群体在形式上都是数学的，因为我们不可能有其他的指导。达尔文

25. We find that every new group is formally mathematical, as we cannot have any other guidance. - Darwin

26. 决不要因为题目很小就不遵循某些你不熟练的解题规范好习惯是培养出来的，而不是一次记住的。

26. Never neglect to follow certain well-habituated problem-solving norms just because the topic is small; good habits are cultivated, not memorized all at once.

27. 数学家本质上是个着迷者，不迷就没有数学。努瓦列斯

27. A mathematician is essentially an enthusiast; without enthusiasm, there is no mathematics. - Nuelles

28. 现代数学最主要的成就是真正揭示了数学的整个面貌及其实质存在。Russell

28. The greatest achievement of modern mathematics is that it truly reveals the entire face and the essential existence of mathematics. - Russell

29. 数学受到高度尊崇的另一个原因在于：恰恰是数学，给精密的自然科学提供了无可置疑的可靠保证，没有数学，它们无法达到这样的可靠程度。爱因斯坦

29. Another reason for the high regard in which mathematics is held is that it alone provides an unimpeachable guarantee of reliability to the精密 natural sciences, without which they could not reach such a reliable level. - Albert Einstein

30. 数学是一种理性的精神，使人类的思维得以运用到最完善的程度。克莱因

30. Mathematics is a rational spirit that enables human thought to be applied to the highest degree of perfection. Klein

31. 数学家们都试图在这一天发现素数序列的一些秩序，我们有理由相信这是一个谜，人类的心灵永远无法渗入。——欧拉

31. Mathematicians have all tried to find some order in the sequence of prime numbers on this day, and we have reason to believe that this is a mystery that the human mind can never penetrate. - Euler

32. 上帝创造了整数，所有其余的数都是人造的。克隆内克

32. God created integers, and all the rest are man-made. Kloniker.

33. 数学中的一些美丽定理具有这样的特性：它们极易从事实中归纳出来，但证明却隐藏的极深、数学是科学之王、——高斯

33. Some beautiful theorems in mathematics have the characteristic that they are very easy to generalize from facts, but their proofs are hidden very deeply. Mathematics is the king of sciences —— Gauss.

34. 数学，科学的皇后；算术，数学的皇后。――高斯

34. Mathematics, the queen of sciences; arithmetic, the queen of mathematics. -- Gauss

35. 数学是打开科学大门的钥匙。培根

35. Mathematics is the key to opening the gates of science. Bacon.

36. 数统治着宇宙。毕达哥拉斯

36. Numbers rule the universe. Pythagoras

37. 在数学中，我们发现真理的主要工具是归纳和模拟。拉普拉斯

37. In mathematics, we find that the main tools for discovering truth are induction and simulation. Laplace

38. 数学之所以比一切其它科学受到尊重，一个理由是因为他的命题是绝对可靠和无可争辩的，而其它的科学经常处于被新发现的事实**的危险。爱因斯坦

38. One reason why mathematics is more respected than all other sciences is because its propositions are absolutely reliable and uncontestable, while other sciences are frequently in danger from new discoveries of facts. - Einstein

39. 发现每一个新的群体在形式上都是数学的，因为我们不可能有其他的指导。CG达尔文

39. We find that every new group is formally mathematical because we cannot have any other guidance. C.G. Darwin

40. 我们能够期待，随着教育与娱乐的发展，将有更多的人欣赏音乐与绘画。但是，能够真正欣赏数学的人数是很少的。贝尔斯

40. We can expect that with the development of education and entertainment, more people will appreciate music and painting. However, the number of people who truly appreciate mathematics is very small. By Bells.

41. 纯数学这门科学在其现代发展阶段，可以说是人类精神之最具独创性的创造。怀特海

41. Pure mathematics, as a science in its modern development, can be said to be the most original creation of the human spirit. Whitehead

42. 数学的本质在於它的自由。康扥尔

42. The essence of mathematics lies in its freedom. Kantor

43. 一门科学，只有当它成功地运用数学时，才能达到真正完善的地步。马克思

43. A science is only truly perfected when it successfully applies mathematics. - Marx

44. 无限!再也没有其他问题如此深刻地打动过人类的心灵。希尔伯特

44. Infinity! No other question has so profoundly touched the hearts of humanity. Hilbert

45. 数学科学呈现出一个最辉煌的例子，表明不用借助实验，纯粹的推理能成功地扩大人们的认知领域。康德

45. The mathematical sciences provide the most brilliant example of how, without the aid of experiment, pure reasoning can successfully expand the realm of human cognition. - Kant

46. 把新奇的解题方法挂在嘴边，还不如把常规的解题方法记在心里。

46. It is better to keep the conventional methods of solving problems in mind rather than to keep novel methods on the tongue.

47. 在数学定理的评价中，审美标准既重于逻辑的标准，也重于实用的标准：在对数学思想的评价时，美与优雅比是否严密正确，比是否有用都重要得多。斯蒂恩

47. In the evaluation of mathematical theorems, aesthetic criteria are more important than logical criteria and also more important than practical criteria: in the evaluation of mathematical ideas, beauty and elegance are much more important than whether they are strictly correct or useful. Stein

48. 数学不可比拟的永久性和万能性及他对时间和文化背景的独立行是其本质的直接后果。埃博

48. The unparalleled permanence and universality of mathematics, as well as its independence from the temporal and cultural context, are direct consequences of its essence. Abo

49. 数学是创造性的艺术，因为数学家创造了美好的新概念；数学是创造性的艺术，因为数学家的生活言行如同艺术家一样；数学是创造性的艺术，因为数学家就是这样认为的。哈尔莫斯

49. Mathematics is a creative art because mathematicians create beautiful new concepts; mathematics is a creative art because the lives and actions of mathematicians are like those of artists; mathematics is a creative art because that is what mathematicians believe. - Polya

50. 数学主要的目标是公众的利益和自然现象的解释。傅立叶

50. The main goal of mathematics is the public interest and the explanation of natural phenomena. Fourier

51. 给我五个系数，我讲画出一头大象;给我六个系数，大象将会摇动尾巴。柯西

51. Give me five coefficients, and I can draw an elephant; give me six coefficients, and the elephant will wag its tail. Cauchy

52. 学生是数学学习的主人，教师是数学学习的组织者、引导者与合作者。

52. Students are the masters of mathematics learning, teachers are the organizers, guides, and collaborators of mathematics learning.

53. 纯数学这门科学再其现代发展阶段，可以说是人类精神之最具独创性的创造。怀德海

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

54. 数学是符号加逻辑。罗素

54. Mathematics is symbols plus logic. - Russell

55. 数学知识是最纯粹的逻辑思维活动，以及最高级智能活力美学体现。普林舍姆

55. Mathematical knowledge is the purest form of logical thinking activity, as well as the highest manifestation of intellectual vitality and aestheticism. Pringsheim.

56. 一种奇特的美统治着数学王国，这种美不像艺术之美与自然之美那么相类似，但她深深地感染着人们的心灵，激起人们对她的欣赏，与艺术之美是十分相象的。库默

56. A peculiar beauty reigns over the kingdom of mathematics, a beauty that is not as similar to the beauty of art and nature, but it deeply touches people's hearts, stirring up their admiration for it, and is extremely similar to the beauty of art. Kummer