1. 天才是不足恃的，聪明是不可靠的，要想顺手拣来的伟大科学发明是不可想象的。——华罗庚

1. Talent is not to be relied upon, intelligence is not reliable, and it is unimaginable to easily pick up great scientific inventions as if they were at one's disposal. - Hua Luogeng

2. 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

2. Infinity! There is no other question that has so deeply touched the hearts of humanity. - Hilbert

3. 没有大胆的猜测，就做不出伟大的发现……——牛顿

3. "Without daring to guess, one cannot make great discoveries..." - Newton

4. 多数的数学创造是直觉的结果，对事实多少有点儿直接的知觉或快速是理解，而与任何冗长的或形式的推理过程无关。——卢斯卡

4. The majority of mathematical creations are the result of intuition, with a somewhat direct perception or quick understanding of facts, and have nothing to do with any lengthy or formal reasoning process. — Luska

5. 我把数学看成是一件有意思的工作，而不是想为自己建立什么纪念碑。可以肯定地说，我对别人的工作比自己的更喜欢。我对自己的工作总是不满意。拉格朗日

5. I view mathematics as an interesting endeavor, not as a means to build a monument for myself. It can be safely said that I prefer others' work over my own. I am always dissatisfied with my own work. Lagrange

6. 一个人就好像一个分数，他的实际才能好比分子，而他对自己的估价好比分母。分母越大，则分数的值就越小。托尔斯泰

6. A person is like a fraction, with his actual abilities being the numerator and his self-evaluation being the denominator. The larger the denominator, the smaller the value of the fraction. - Tolstoy

7. 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

7. Mathematics makes an important contribution to observing nature, explaining the simple original elements in the structure of regularities, which celestial bodies are built upon. Kepler

8. 攀登科学高峰，就像登山运动员攀登珠穆朗玛峰一样，要克服无数艰难险阻，懦夫和懒汉是不可能享受到胜利的喜悦和幸福的。——陈景润

8. Climbing the peak of science is like mountaineers scaling Mount Everest, where one must overcome countless difficulties and dangers. Cowards and lazy people can never enjoy the joy and happiness of victory. -- Chen Jingrun

9. 在数学的天地里，重要的不是我们知道什么，而是我们怎么知道什么。——毕达哥拉斯

9. In the realm of mathematics, what is important is not what we know, but how we know it. – Pythagoras

10. 观察可能导致发现。观察将揭示某种规律模式或定律。——波利亚

10. Observation may lead to discovery. Observation will reveal some regular pattern or law. — Polya

11. 我决心放弃那个仅仅是抽象的几何。这就是说，不再去考虑那些仅仅是用来练思想的问题。我这样做，是为了研究另一种几何，即目的在于解释自然现象的几何……——笛卡儿

11. I am resolved to abandon that geometry which is merely abstract. This means that I will no longer consider those problems which are merely used to train the mind. I do this in order to study another geometry, which aims to explain natural phenomena... - Descartes

12. 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

12. New mathematical methods and concepts are often more important than solving the mathematical problems themselves. - Hua Loo-keng

13. 纯数学是魔术家真正的魔杖。诺瓦列斯

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

14. 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

14. A mathematician who lacks a bit of poetism can never become a complete mathematician. - Weierstrass

15. 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

15. We find that each new group is, in form, mathematical because it is impossible to have any other guide. - CG Darwin

16. 在学习中要敢于做减法，就是减去前人已经解决的部分，看看还有那些问题没有解决，需要我们去探索解决。——华罗庚

16. In the process of learning, one should dare to do subtraction, that is, to subtract the parts that have already been solved by predecessors, and see which problems have not been solved and need us to explore and solve them. — Hua Luogeng

17. 数无形时少直觉，形少数时难入微，数与形，本是相倚依，焉能分作两边飞。华罗庚

17. When there are fewer numbers and less intuition, it is difficult to perceive the minute details; when there are fewer shapes, it is challenging to delve into the subtle. Numbers and shapes, inherently interdependent, cannot be separated and soar apart. — Hua Loo-keng

18. 数无形时少直觉，形少数时难入微，数与形，本是相倚依，焉能分作两边飞。——华罗庚

18. When there are few numbers and no shapes, intuition is lacking; when there are few shapes and few numbers, it is difficult to perceive the minute. Numbers and shapes, by nature, depend on each other, how can they be separated and fly apart? — Hua Loo-keng

19. 如果我继承可观的财产，我在数学上可能没有多少价值了。——拉格朗日

19. If I inherit considerable wealth, I may have little value in mathematics, mathematically speaking. — Lagrange

20. 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

20. A mathematician who lacks a bit of poetic talent will never become a complete mathematician. — Weierstrass

21. 考虑了很少的那几样东西之后，整个的事情就归结为纯几何，这是物理和力学的一个目标……——莱布尼茨

21. After considering only a few things, the entire matter boils down to pure geometry, which is a goal of physics and mechanics... — Leibniz

22. 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。——康扥尔

22. In the field of mathematics, the art of posing questions is more important than the art of solving them. — Condorcet

23. 数学中没有诺贝尔奖，这也许是件好事。诺贝尔奖太引人注目，会使数学家无法专注于自己的研究。陈省身

23. There is no Nobel Prize in mathematics, and that may be a good thing. The Nobel Prize is too prominent, which might distract mathematicians from focusing on their own research. - Chen Xing-Shen

24. 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

24. From the vastness of the universe to the minuteness of particles, the speed of rockets, the ingenuity of chemical engineering, the changes on Earth, the mysteries of life, and the complexity of everyday items, mathematics is applied everywhere. — Hua Luogeng

25. "数学是人类知识活动留下来最具威力的知识工具，是一些现象的根源。数学是不变的，是客观存在的，上帝必以数学法则建造宇宙……——笛卡儿

25. "Mathematics is the most powerful knowledge tool left behind by human intellectual activities, the source of some phenomena. Mathematics is unchanging and objectively existing; God must have constructed the universe according to mathematical laws... — Descartes"

26. 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

26. Give me five coefficients, and I'll draw an elephant; give me six coefficients, and the elephant will wag its tail. — AL Cauchy

27. 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

27. When mathematicians derive equations and formulas, they experience a full measure of joy, much like when they see statues, beautiful landscapes, listen to melodious tunes, and so on, as Kopnin said.

28. 数学科学不可动摇的基石，促进人类事业进步的丰富源泉。巴罗

28. The unshakable cornerstone of mathematical sciences, a rich source promoting the progress of human undertakings. Barrow

29. 数学是科学之王。高斯

29. Mathematics is the king of sciences. Gauss

30. 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?>

30. Philosophers also need to learn mathematics, as they must rise above the vast sea of ever-changing phenomena to grasp the true essence. Moreover, this is the shortcut for the soul to transition to truth and eternity. — Plato?

31. 学数学，绝不会有过份的努力。卡拉吉奥多里

31. There is never too much effort in studying mathematics. —卡拉吉奥多里

32. 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

32. If anyone does not know that the diagonal of a square is an incommensurable quantity with its side, he does not deserve to be called a human being. - Plato

33. 数学是符号加逻辑。罗素

33. Mathematics is symbols plus logic. Russell

34. 也许我可以并非不适当地要求获得数学上亚当这一称号，因为我相信数学理性创造物由我命名(已经流行通用)比起同时代其它数学家加在一起还要多……——西尔维斯特

34. Perhaps I may not inappropriately claim the title of Mathematical Adam, because I believe that the mathematical rational creations named by me (already popularly so) are more than those of all the other contemporary mathematicians combined... — Sylvester

35. 时间是个常数，但对勤奋者来说，是个‘变数’。用‘分’来计算时间的人比用‘小时’来计算时间的人时间多59倍。雷巴柯夫

35. Time is a constant, but to the diligent, it is a 'variable'. The person who calculates time in 'minutes' has 59 times more time than the person who calculates time in 'hours'. - Rybakov

36. 第一是数学，第二是数学，第三是数学。伦琴

36. The first is mathematics, the second is mathematics, the third is mathematics. Röntgen.

37. 读读欧拉，读读欧拉，他是我们大家的老师。——拉普拉斯

37. Read Euler, read Euler, he is the teacher of us all. — Laplace

38. 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。A·埃博

38. The unparalleled permanence and universality of mathematics and its independence from the time and cultural context are direct consequences of its essence. A· Ebel

39. 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

39. After modern high-energy physics reached quantum physics, there are many things that cannot be tested experimentally; calculations are done at home with paper and pens, which isn't too different from what mathematicians do. Therefore, it is said that mathematics has an incredible power in physics. Qiu Chengtong.

40. 数学是人类智慧皇冠上最灿烂的明珠。考特

40. Mathematics is the most brilliant gem on the crown of human wisdom. Court.

41. 一个国家的科学水平可以用它消耗的数学来度量。——拉奥

41. The scientific level of a country can be measured by the mathematics it consumes.—Rao

42. 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。C·G·达尔文

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

43. 一个数学家的目的，是要了解数学。历史上数学的进展不外两途:增加对于已知材料的了解，和推广范围。——陈省身

43. The purpose of a mathematician is to understand mathematics. Historically, the progress of mathematics has been through two paths: increasing understanding of known materials, and expanding the scope. — Chen Jingrun

44. 我决不把我的作品看做是个人的私事，也不追求名誉和赞美。我只是为真理的进展竭尽所能。是我还是别的什么人，对我来说无关紧要，重要的是它更接近于真理。——维尔斯特拉斯

44. I never consider my works as a matter of personal interest, nor do I seek fame or praise. I merely strive to the best of my ability for the progress of truth. Whether it is me or someone else, it is of no importance to me; what matters is that it is closer to the truth. — Weierstrass

45. 一个数学家的目的，是要了解数学。历史上数学的进展不外两途：增加对于已知材料的了解，和推广范围。陈省身

45. The purpose of a mathematician is to understand mathematics. Historically, the progress of mathematics has taken two paths: increasing understanding of known materials, and extending the scope. Chen Shengshen

46. 在学习中要敢于做减法，就是减去前人已经解决的部分，看看还有那些问题没有解决，需要我们去探索解决。华罗庚

46. In the process of learning, one should dare to do subtraction, that is, to subtract the parts that have already been solved by predecessors, and see what other problems have not been solved and require us to explore and solve them. — Hua Loo-keng

47. 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

47. Mathematics is the study of quantity relationships and spatial forms in real life, as stated by Engels.

48. 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

48. In the field of mathematics, the art of posing questions is more important than the art of solving them. – Cantor

49. 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

49. We can expect that with the development of education and entertainment, more people will appreciate music and painting. However, the number of people who can truly appreciate mathematics is very few. - Bales

50. 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。A·L·柯西

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

51. 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

51. Some beautiful theorems in mathematics have the characteristic that they are极易 from facts to be归纳出来, but their proofs are hidden very deeply. Mathematics is the king of sciences. —— Gauss

52. 看在上帝的份上，千万别放下工作!这是你最好的药物。——达朗贝尔

52. For the sake of God, please don't give up your work! It's your best medicine.—Diderot

53. 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

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

54. 数学是一门演绎的学问，从一组公设，经过逻辑的推理，获得结论。陈省身

54. Mathematics is a deductive discipline, obtaining conclusions through logical reasoning from a set of axioms. Chen Xiangshen

55. 因为宇宙的结构是最完善的而且是最明智的上帝的创造，因此，如果在宇宙里没有某种极大的或极小的法则，那就根本不会发生任何事情。——欧拉

55. Because the structure of the universe is the most perfect and the most wise creation of the Most High God, therefore, if there were not some laws of extreme great or extreme small in the universe, nothing at all would happen. - Euler

56. 如果别人思考数学的真理像我一样深入持久，他也会找到我的发现。高斯

56. If someone thinks about the truths of mathematics as deeply and persistently as I do, he will also find my discoveries. Gauss

57. 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

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

58. 数学家实际上是一个著迷者，不迷就没有数学。诺瓦利斯

58. A mathematician is actually an enthusiast; without fascination, there is no mathematics. Novalis

59. 时间是个常数，但对勤奋者来说，是个‘变数’。用‘分’来计算时间的人比用‘小时’来计算时间的人时间多59倍……——雷巴柯夫

59. Time is a constant, but for the diligent, it is a 'variable.' The person who calculates time in 'minutes' has 59 times more time than the person who calculates time in 'hours'... —— Rybakov

60. 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

60. There is no question that can so deeply stir the emotions as the infinite does, and few other ideas can inspire the intellect to fruitful thoughts as the infinite does. However, there is no other concept that requires such elucidation as the infinite does. — Hilbert

61. 生命只为两件事，发展数学与教授数学。普尔森

61. Life is for just two things: the development of mathematics and the teaching of mathematics. Polzen

62. 事类相推，各有攸归，故枝条虽分而同本干知，发其一端而已。又所析理以辞，解体用图，庶亦约而能周，通而不黩，览之者思过半矣……——刘徽

62. Things are interconnected and each has its own place. Therefore, although the branches are divided, they all share the same root. It is enough to understand one aspect of it. Moreover, the analysis of principles is done through words, and the structure and function are explained with diagrams, which may be concise yet comprehensive, and clear without being muddy. Those who read it will have understood more than half of it... —— Liu Hui

63. 数学是各式各样的证明技巧。维特根斯坦

63. Mathematics is a variety of proof techniques. Wittgenstein

64. 数论是人类知识最古老的一个分支，然而他的一些最深奥的秘密与其最平凡的真理是密切相连的。——史密斯

64. Number theory is one of the oldest branches of human knowledge, yet some of its most profound secrets are closely linked to its most ordinary truths. — Smith

65. 数论是人类知识最古老的一个分支，然而他的一些最深奥的秘密与其最平凡的真理是密切相连的。史密斯

65. Number theory is one of the oldest branches of human knowledge, yet some of its most profound secrets are closely connected to its most ordinary truths. Smith

66. 生命只为两件事，发展数学与教授数学。——普尔森

66. Life is for two things only: the development of mathematics and the teaching of mathematics. — Polzen

67. 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。——A·N·怀德海

67. This is a reliable rule: when the author of a mathematical or philosophical treatise writes in vague and obscure language, he is talking nonsense. — A.N. Whitehead

68. 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

68. In mathematics, it is very important to distinguish what is important and what is not, and to know what to choose. Guang Zhong Pingyou.

69. 在数学的天地里，重要的不是我们知道什么，而是我们怎么知道什么。毕达哥拉斯

69. In the realm of mathematics, what is important is not what we know, but how we know it. Pythagoras

70. 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

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

71. 时间是个常数，但对勤奋者来说，是个‘变数’。用‘分’来计算时间的人比用‘小时’来计算时间的人时间多59倍。——雷巴柯夫

71. Time is a constant, but to the diligent, it is a 'variable.' A person who calculates time in 'minutes' has 59 times more time than a person who calculates time in 'hours.' — Rybakov

72. 虽然不允许我们看透自然界本质的秘密，从而认识现象的真实原因，但仍可能发生这样的情形:一定的虚构假设足以解释许多现象。——欧拉

72. Although it is not allowed for us to penetrate the secrets of the essence of nature, thereby understanding the true causes of phenomena, it is still possible that such a situation may occur: certain fictional assumptions are sufficient to explain many phenomena. – Euler

73. 数学是研究抽象结构的理论。布尔巴基学派

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

74. 在数学中最令我欣喜的，是那些能够被证明的东西。罗素

74. What delights me most in mathematics is that which can be proven. Russell

75. 一个做学问的人，除了学习知识外，还要有tast,这个词不太好翻译，有的译成品味，喜爱。一个人要有大的成就，就要有相当清楚的tast。——杨振宁

75. A scholar, besides acquiring knowledge, must also possess 'tast,' which is not an easy word to translate. Some translations include 'taste' or 'liking.' For a person to achieve great things, they must have a rather clear 'tast.' — Yang Zhenning

76. 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。——AN怀德海

76. This is a reliable rule: when the author of a mathematical or philosophical work writes in vague and obscure language, he is talking nonsense. — A.N. Whitehead