1. 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

1. A science is only truly perfected when it successfully applies mathematics, as Marx said.

2. 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

2. To feel the beauty of mathematics, to feel the harmony between numbers and forms, to feel the elegance of geometry, this is a true and real sense of beauty that all true mathematicians are well aware of. Poincaré

3. 数学是一种别具匠心的艺术。哈尔莫斯

3. Mathematics is an art of great ingenuity. Harlow.

4. 学习数学要多做习题，边做边思索。先知其然，然后知其所以然。苏步青

4. To learn mathematics, one must do a lot of exercises and think while doing them. First, know what it is, and then know why it is so. Su Buqing

5. 数学，如果正确地看，不但拥有真理，而且也具有至高的美。罗素

5. Mathematics, if properly viewed, not only possesses truth but also has the highest beauty. — Russell

6. 数学是打开科学大门的钥匙。培根

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

7. 在数学里，分辨何是重要，何事不重要，知所选择是很重要的。广中平佑

7. In mathematics, it is very important to know what is important and what is not important, and to make the right choices. Guang Zhongpingyou.

8. 数学是一项工具，特别适合于处理任何一类抽象概念，而且，它在这方面的作用是无止境的。因此，一本论述新物理学的书，如果不是单纯地描述实验工作的，其本质上，必定是一本数学书。狄拉克

8. Mathematics is a tool particularly suited for dealing with any category of abstract concepts, and its role in this respect is limitless. Therefore, a book that discusses new physics must essentially be a mathematical book if it is not solely descriptive of experimental work. Dirac

9. 埋头苦干是第一，发白才知智叟。呆勤能补拙是良训，一分辛苦一分才。华罗庚

9. Hard work with heads down is the first principle, only when one's hair turns white will one know the wise. Diligence can compensate for one's deficiencies, a good saying: one's efforts lead to one's talents. Hua Luogeng

10. 上帝是一位算术家雅克比

10. God is an arithmetic Jacob

11. 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。高斯

11. Some beautiful theorems in mathematics have the characteristic that they can be easily归纳 from facts, but their proofs are hidden deeply. Gauss

12. 数学是科学之王。高斯

12. Mathematics is the king of sciences. Gauss

13. 数缺形时少直观，形缺数时难入微又说要打好数学基础有两个必经过程：先学习、接受由薄到厚；再消化、提炼由厚到薄。华罗庚

13. When there is a lack of numbers, the form lacks directness; when there is a lack of form, it is difficult to delve into the details. It is also said that to lay a solid foundation in mathematics, there are two essential processes: first, to learn and accept from thin to thick; and then, to digest and refine from thick to thin. Hua Luogeng

14. 数学是科学的女王，而数论是数学的女王。高斯

14. Mathematics is the queen of sciences, and number theory is the queen of mathematics. Gauss

15. 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

15. Another reason why mathematics is highly revered is that it is precisely mathematics that provides an unassailable guarantee of reliability to the precise natural sciences. Without mathematics, they cannot achieve such a level of reliability. - Einstein

16. 数学是研究现实生活中数量关系和空间形式的数学。恩格斯

16. Mathematics is the study of quantitative relationships and spatial forms in real life. — Engels

17. 数学是人类智慧皇冠上最灿烂的明珠。考特

17. Mathematics is the most brilliant pearl on the crown of human wisdom. - Cao Te

18. 自然这一巨举是用数学符号写成的。伽里略?>

18. This great leap of nature is written in mathematical symbols. Galileo?>

19. 数学能促进人们对美的特性数值比例秩序等的认识。亚里士多德

19. Mathematics can promote people's understanding of the quantitative proportionality and order of the characteristics of beauty. Aristotle

20. 数学对观察自然做出重要的贡献，它解释了规律结构中简单的原始元素，而天体就是用这些原始元素建立起来的。开普勒数学主要的目标是公众的利益和自然现象的解释。傅立叶

20. Mathematics has made significant contributions to observing nature, explaining the simple original elements in the structure of regularities, which celestial bodies are constructed from. The main goal of Kepler's mathematics is the public interest and the explanation of natural phenomena. Fourier

21. 宇宙的伟大建筑是现在开始以纯数学家的面目出现了。京斯

21. The grand architecture of the universe is now beginning to appear in the face of a pure mathematician. Jingshi.

22. 宇宙之大，粒子之微，火箭之速，化工之巧，地球之变，生物之谜，日用之繁，无处不用数学。华罗庚

22. In the vastness of the universe, the minuteness of particles, the speed of rockets, the ingenuity of chemical engineering, the changes on Earth, the mysteries of life, the complexity of everyday use, mathematics is used everywhere. Hua Loo-keng

23. 数学如同音乐或诗一样显然地确实具有美学价值。雅可比

23. Mathematics, like music or poetry, clearly indeed possesses aesthetic value. Jacobi

24. 这是一个可靠的规律，当数学或哲学著作的作者以模糊深奥的话写作时，他是在胡说八道。怀德海

24. This is a reliable rule: when an author of mathematical or philosophical works writes in vague, profound language, he is talking nonsense. — Whitehead

25. 一个没有几分诗人气的数学家永远成不了一个完全的数学家。维尔斯特拉斯

25. A mathematician without a bit of poet's spirit can never be a complete mathematician. — Weierstrass

26. 纯数学是魔术家真正的魔杖。诺瓦列斯

26. Pure mathematics is the true wand of the magician. Novales.

27. 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

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

28. 二分之一个证明等于高斯

28. Half a proof equals Gauss

29. 数学之所以有高声誉，另一个理由就是数学使得自然科学实现定理化，给予自然科学某种程度的可靠性。爱因斯坦

29. Another reason for the high reputation of mathematics is that mathematics has enabled the natural sciences to be formalized through theorems, providing a certain degree of reliability to the natural sciences. - Einstein

30. 如果谁不知道正方形的对角线同边是不可通约的量，那他就不值得人的称号。柏拉图

30. If anyone does not know that the diagonal of a square is incommensurable with its side, he is not worthy of the name of a human being. — Plato

31. 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

31. Just as mathematicians derive equations and formulas, they derive great joy, like when they see the beautiful landscape of statues, hear beautiful melodies, and so on. — Kopnin

32. 数学的本质在于它的自由。――康托尔

32. The essence of mathematics lies in its freedom. – Cantor

33. 数学方法渗透并支配着一切自然科学的理论分支。它愈来愈成为衡量科学成就的主要标志了。冯纽曼

33. The mathematical method permeates and dominates all branches of theoretical natural sciences. It is increasingly becoming the main indicator of scientific achievements. Von Neumann

34. 数学主要的目标是公众的利益和自然现象的解释。傅立叶

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

35. 数学是人类的思考中最高的成就。米斯拉

35. Mathematics is the highest achievement of human thought. Mysore.

36. 问题是数学的心脏。Halmos

36. The problem is the heart of mathematics. - Halmos

37. 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

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

38. 在现实中，不存在像数学那样有如此多的东西，持续了几千年依然是确实的如此美好。苏利文确。

38. In reality, there is nothing as abundant as mathematics, which has remained true and wonderful for thousands of years. Sullivan is right.

39. 一个国家只有数学蓬勃的发展，才能展现它国立的强大。数学的发展和至善和国家繁荣昌盛密切相关。拿破仑

39. A country can only demonstrate the strength of its national power through the vigorous development of mathematics. The development and perfection of mathematics are closely related to the prosperity and prosperity of the nation. - Napoleon

40. 数学是无穷的科学。赫尔曼外尔

40. Mathematics is the science of infinity. Hermann Weyl.

41. 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

41. After modern high-energy physics reached quantum physics, there are many things that cannot be done through experiments, and people have to calculate them at home with paper and pens. This is not much different from what mathematicians do, so it is said that mathematics has an incredible power in physics. Qiu Chengtong.

42. 数学发明创造的动力不是推理，而是想象力的发挥。德摩根

42. The driving force of mathematical invention is not reasoning but the exercise of imagination. Demorgan

43. 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

43. Mathematicians derive equations and formulas with the same full enjoyment as they experience when they see statues, beautiful landscapes, listen to melodious tunes, and so on. — Kopnin

44. 数学家本质上是个着迷者，不迷就没有数学。努瓦列斯

44. A mathematician is essentially an enthusiast; without fascination, there is no mathematics. - Nuñez de Arce

45. 宁可少些，但要好些。高斯

45. Better fewer, but better. Gauss

46. 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

46. The unparalleled permanence and universality of mathematics, as well as its independence from time and cultural context, are direct consequences of its essence. Ebo

47. 新的数学方法和概念，常常比解决数学问题本身更重要。华罗庚

47. New mathematical methods and concepts are often more important than solving mathematical problems themselves. - Hua Loo-Keng

48. 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

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

49. 数学是各式各样的证明技巧。维特根斯坦

49. Mathematics is a variety of proof techniques. Wittgenstein

50. 数学是研究抽象结构的理论。布尔巴基学派

50. Mathematics is the theory that studies abstract structures. The Bourbaki school

51. 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

51. A peculiar beauty reigns over the realm of mathematics, a beauty that is not as similar to the beauty of art and nature, but it deeply touches the hearts of people, arousing their appreciation for it, which is very similar to the beauty of art. Kummer

52. 数学，科学的皇后；算术，数学的皇后。――高斯

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

53. 整数的简单构成，若干世纪以来一直是使数学获得新生的源泉。伯克霍夫

53. The simple composition of integers has been a source of renewal for mathematics for several centuries. Birkhoff.

54. 数学支配着宇宙。毕达哥拉斯

54. Mathematics governs the universe. Pythagoras

55. 观察可能导致发现，观察将揭示某种规则、模式或定律。波利亚

55. Observation may lead to discovery; observation will reveal some rule, pattern, or law. Polya

56. 上帝是一位算术家。雅克比

56. God is a mathematician. Jacobi

57. 硬说数学科学无美可言的人是错误的。美的主要形式是秩序匀称与明确。亚里斯多德

57. Those who claim that there is no beauty in mathematical science are wrong. The main forms of beauty are order, symmetry, and clarity. Aristotle

58. 数学是一种会不断进化的文化。魏尔德

58. Mathematics is a culture that will continue to evolve. Weilde.

59. 天才？请你看看我的臂肘吧。拉码努扬

59. Genius? Please take a look at my elbow. Lameunuang.

60. 哲学家也要学数学，因为他必须跳出浩如烟海的万变现象而抓住真正的实质。……又因为这是使灵魂过渡到真理和永存的捷径。柏拉图

60. Philosophers too must study mathematics, as they must rise above the overwhelming multitude of changing phenomena and grasp the true essence. ... Moreover, this is the shortcut for the soul to transition to truth and eternity. — Plato