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

1. The unparalleled permanence and universality of mathematics, as well as its independence from the moment and cultural context, are direct consequences of its essence. A· Ebbinghaus

2. 生命只为两件事，发展数学与教授数学。 ——普尔森

2. Life is for only two things: developing mathematics and teaching mathematics. —— Poulson

3. 数学主要的目标是公众的利益和自然现象的解释。

3. The primary goal of mathematics is the public interest and the explanation of natural phenomena.

4. 数学家通常是先透过直觉来发现一个定理；这个结果对于他首先是似然的，然后他再着手去制造一个证明。哈代

4. Mathematicians usually discover a theorem first through intuition; this result is initially plausible to them, and then they set about creating a proof. Hardy

5. 攀登科学**，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

5. Climbing the science, just like mountaineers climbing Mount Everest, one must overcome countless hardships and dangers. Cowards and idlers cannot enjoy the joy and happiness of victory. - Chen Jingrun

6. 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

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

7. 数学发明创造的动力不是推理，而是想象力的发挥。德摩根

7. The driving force behind mathematical inventions is not reasoning, but the exercise of imagination. - Demorgan

8. 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

8. A scholar, besides acquiring knowledge, must also have "tast," which is a word that is not easy to translate. Some translations include "taste" and "liking." For a person to achieve great success, they must have a rather clear "tast." -- Yang Zhenning

9. 思维的运动形式通常是这样的：有意识的研究潜意识的活动有意识的研究。庞加莱

9. The form of movement of thought is usually as follows: conscious research into the activities of the subconscious is carried out consciously. Poincaré

10. 我之所以比笛卡儿看得远些，是因为我站在巨人的肩上。牛顿

10. The reason why I see further than Descartes is that I stand on the shoulders of giants. Newton

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 abstract geometry. This means no longer considering those problems that are merely for the exercise of thought. I am doing this in order to study another type of geometry, which aims to explain natural phenomena. Descartes?

12. 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

12. There is no Nobel Prize in mathematics, which may be a good thing. The Nobel Prize is too prominent, which may distract mathematicians from focusing on their own research. — Chen Shengshen

13. 数学的本质在於它的自由。康扥尔

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

14. 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

14. The incommensurable permanence and versatility of mathematics, as well as its independence from the time and cultural context, are direct consequences of its essence. - Ebo

15. 给我五个系数，我将画出一头大象；给我六个系数，大象将会摇动尾巴。——柯西

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

16. 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

16. When numbers are not tangible, intuition is less; when forms are few, it is hard to penetrate to the minute details. Numbers and forms, inherently dependent on each other, cannot be separated and soar apart. — Hua Loo-Keng

17. 一个国家的科学水平能够用它消耗的数学来度量拉奥

17. A country's scientific level can be measured by the mathematics it consumes, according to Lao.

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。柯西

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

19. 数统治着宇宙。毕达哥拉斯

19. Number rules the universe. Pythagoras

20. 上帝创造了整数，所有其余的数都是人造的。 ——克隆内克

20. God created the integers, all the rest are the work of man. — Kronecker

21. 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

21. The aim of a mathematician is to understand mathematics. Historically, the progress of mathematics has been achieved in two ways: by increasing understanding of the known material, and by expanding the scope. Chen Xing-Shan

22. 上帝创造了整数，所有其余的数都是人造的。克隆内克

22. God created the integers, all the rest are the work of man. Kronecker

23. 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

23. A mathematician who does not possess a bit of poetic talent will never become a complete mathematician. — Weierstrass

24. 虚数是奇妙的人类棈神寄托，它好像是存在与不存在之间的一种两栖动物。莱布尼茨

24. Imaginary numbers are a wonderful human intellectual寄托, as if they were amphibians existing between existence and non-existence. Leibniz

25. 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

25. Time is a constant, but to the diligent, it is a 'variable.' Those who calculate time in 'minutes' have 59 times more time than those who calculate time in 'hours.' — Rybakov

26. 一个人的贡献和他的自负严格地成反比，这似乎是品行上的一个公理。——拉格朗日

26. A person's contribution is inversely proportional to their ego, which seems to be an axiom of character. — Lagrange

27. 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

27. The unshakable foundation of mathematical sciences, a rich source promoting the progress of human endeavors. Barrow

28. 不发生作用的东西是不会存在的。莱布尼茨

28. That which does not exert an effect does not exist. — Leibniz

29. 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。

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

30. 我之所以比笛卡儿看得远些， 是因为我站在巨人的肩上。 ——牛顿

30. The reason why I see further than Descartes is that I stand on the shoulders of giants. — Newton

31. 有时候，你一开始未能得到一个最简单，最美妙的证明，但正是这样的证明才能深入到高等算术真理的奇妙联系中去。这是我们继续研究的动力，并且最能使我们有所发现。高斯

31. Sometimes, at first, you may not obtain the simplest and most delightful proof, but it is precisely such proofs that can delve deeply into the wonderful connections of higher arithmetic truths. This is the driving force that continues our research, and is most likely to lead us to new discoveries. Gauss

32. 在数学的天地里，重要的不是咱们知道什么，而是咱们怎样知道什么。毕达哥拉斯

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

33. 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

33. 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

34. 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

34. Things are interconnected and each has its own place. Therefore, although the branches are divided, they all know the same trunk. It is enough to explore one aspect of it. Furthermore, the analysis of principles is done through words, and the structure is explained with diagrams, which may also be concise yet comprehensive, and clear without being muddy. Those who view it will have thought through more than half of it. Liu Hui.

35. 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

35. We find that every new group is formally mathematical, because it is impossible for us to have any other guidance. — Darwin

36. 我曾听到有人说我是数学的反对者，是数学的敌人，但没有人比我更尊重数学，因为它完成了我不曾得到其成就的业绩。

36. I have heard some say that I am an opponent of mathematics, its enemy, but no one respects mathematics more than I do, for it has achieved what I never could.

37. 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

37. Number theory is one of the oldest branches of human knowledge, yet some of its deepest secrets are closely connected with its most ordinary truths. - Smith

38. 9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

38. Infinity! No other question has ever so deeply touched the human heart. — Hilbert

39. 迟序之数，非出神怪，有形可检，有数可推。祖冲之

39. The numbers of delayed sequence are not from the supernatural, they have tangible forms that can be inspected and numerical patterns that can be inferred. Zu Chongzhi

40. 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

40. I regard mathematics as an interesting occupation, not as a means to build a monument to myself. It can be safely said that I prefer others' work to my own. I am always dissatisfied with my own work. — Lagrange

41. 异常抽象的问题，必须讨论得异常清楚。笛卡儿

41. Exceptionally abstract issues must be discussed with exceptional clarity. Descartes

42. 在奥林匹斯山上统治著的上帝，乃是永恒的数学。雅可比

42. The God reigning on Mount Olympus is eternal mathematics. - Jacobi

43. 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我的研究。陈省身

43. There is no Nobel Prize in mathematics, which might be a good thing. The Nobel Prize is too prominent, which could make mathematicians unable to focus on their own research. Chen Xing-shen

44. 数学是科学的女王，而数论是数学的女王。高斯

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

45. 一个有科学创新能力的人不但要有科学知识，还要有文化艺术修养。钱学森

45. A person with scientific innovation capabilities not only needs to have scientific knowledge, but also needs to be well-versed in arts and culture. -- Qian Xuesen

46. 如果我们想要预见数学的将来，适当的途径是研究这门学科的历史和现状。庞加莱

46. If we wish to foresee the future of mathematics, the proper approach is to study the history and current state of this discipline. Poincaré

47. 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

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

48. 数学是无穷的科学。赫尔曼外尔

48. Mathematics is the science of infinity. Hermann Weyl

49. 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

49. Discover that every new group is formally mathematical, because we cannot have any other guidance. Darwin

50. 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

50. A mathematician without a bit of poet in him can never become a complete mathematician. - Weierstrass

51. 新的数学方法和概念，常常比解决数学问题本身更重要。

51. New mathematical methods and concepts are often more important than the mathematical problems themselves.

52. 如果没有数所制造的关於宇宙的永恒的仿造品，则人类将不能继续生存。尼采

52. Without the number created by the eternal counterfeit of the universe, humanity would not be able to continue to exist. - Nietzsche

53. 用心智的全部力量，来选择我们应遵循的道路。笛卡儿

53. Use all the power of your mind to choose the path we should follow. Descartes

54. 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。——怀德海

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

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

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

56. 如果咱们想要预见数学的将来，适当的途径是研究这门学科的历史和现状。庞加莱

56. If we want to foresee the future of mathematics, an appropriate approach is to study the history and current state of this discipline. Poincaré.

57. 前进吧，前进将使你产生信念。达朗贝尔

57. March forward, for forward movement will instill faith in you. D'Alembert

58. 直接向大师们而不是他们得的学生学习。阿贝尔

58. Learn directly from the masters rather than their students. Abel

59. 生命只为两件事，发展数学与教授数学。普尔森

59. Life is for only two things: the development of mathematics and the teaching of mathematics. Poulson

60. 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

60. If anyone does not know that the diagonal of a square is incommensurable with its side, he is not worthy of the title of a human being. - Plato

61. 一个国家的科学水平可以用它消耗的数学来度量。拉奥

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

62. 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

62. Infinity! No other question has so profoundly touched the human heart. D. Hilbert

63. 没有大胆的猜测，就做不出伟大的发现。牛顿

63. "Without bold conjectures, no great discoveries can be made." - Newton

64. 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

64. The great architecture of the universe is now beginning to appear in the face of a pure mathematician. Jings.

65. 数学，科学的女皇；数论，数学的女皇。——高斯

65. Mathematics, the queen of sciences; number theory, the queen of mathematics. — Gauss

66. 数学家实际上是一个著迷者，不迷就没有数学。诺瓦利斯

66. A mathematician is actually an enthusiast; without enthusiasm, there is no mathematics. Novalis

67. 我把数学看成是一件有意思的工作，而不是想为自我建立什么纪念碑。能够肯定地说，我对别人的工作比自我的更钟爱。我对自我的工作总是不满意。拉格朗日

67. I consider mathematics to be an interesting occupation, rather than something to build a monument to myself. I can confidently say that I have a greater fondness for others' work than my own. I am always dissatisfied with my own work. — Lagrange

68. 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。

68. The simple composition of integers has been a source of new vitality for mathematics for several centuries.

69. 思维的户外形式通常是这样的：有意识的研究潜意识的活动有意识的研究。庞加莱

69. The outdoor form of thought is usually such: conscious study of the activities of the subconscious, conscious study. Poincaré

70. 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

70. Some beautiful theorems in mathematics have the characteristic that they are very easy to generalize from facts, but their proofs are deeply hidden. Gauss

71. 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

71. The simple structure of integers has been a source of renewal for mathematics for several centuries. Berkhof

72. 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

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

73. 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

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

74. 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

74. Perhaps I could not inappropriately claim the title of 'Mathematical Adam,' as I believe that the mathematical creations of reason that I have named (already popular and widely used) exceed those of all other contemporary mathematicians combined. Sylvester.

75. 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。康扥尔

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

76. 数学是科学之王。高斯

76. Mathematics is the king of sciences. Gauss

77. 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

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

78. 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性是其本质的直接后果。

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

79. 我们必须知道，我们必将知道。希尔伯特

79. We must know, we shall know. Hilbert.

80. 1数学家实际上是一个著迷者，不迷就没有数学。 ——诺瓦利斯

80. 1 A mathematician is actually an enthusiast; without enthusiasm, there is no mathematics. – Novalis

81. 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

81. For God's sake, don't ever give up your work! It's your best medicine. D'Alembert

82. 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。GD伯克霍夫

82. The simple construction of integers has been a source of new vitality for mathematics for several centuries. G.D. Birkhoff

83. 一个人的贡献和他的自负严格地成反比，这似乎是品行上的一个公理。拉格朗日

83. A person's contribution is strictly inversely proportional to their arrogance, which seems to be an axiom of character. Lagrange

84. 自然这一巨举是用数学符号写成的。伽里略

84. Nature's grandeur is written in the mathematical symbols. Galileo

85. 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

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

86. 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

86. Because the structure of the universe is the most perfect and the most wise creation of the most sagacious God, therefore, if there is not some extreme law, great or small, in the universe, nothing at all would happen. Euler

87. 聪明出于勤奋，天才在于积累。华罗庚

87. Wisdom comes from diligence, genius lies in accumulation. Hua Loo-keng

88. 挑选好一个确定得研究对象，锲而不舍。你可能永远达不到终点，但是一路上准可以发现一些有趣的东西。克莱因

88. Choose a specific research subject and persevere. You may never reach the end, but along the way you are sure to discover some interesting things. - Klein