1. 上帝创造了整数，所有其余的数都是人造的。——克隆内克

1. God created integers, all the rest are man-made. — Konrád Lorenzec

2. 数学是人类的思考中最高的成就。

2. Mathematics is the highest achievement in human thought.

3. 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

3. Perhaps I may not be inappropriately claiming the title of 'Adam' in mathematics, because I believe that the mathematical rational creations named by me (already popular and widely used) exceed those of other contemporary mathematicians combined.—Sylvester

4. 思维的经济原则在数学中得到了高度的发挥。数学是各门科学在高度发展中所达到的最高形式的一门科学，各门自然学科都频繁的求助于它。

4. The economic principles of thought are highly manifested in mathematics. Mathematics is a science that has reached the highest form achieved by all sciences in their highly developed state, and all natural sciences frequently turn to it for assistance.

5. 没有那门学科能比数学更为清晰的阐明自然界的和谐性。

5. No subject can elucidate the harmony of nature more clearly than mathematics.

6. 历史使人明智，诗歌使人聪慧，数学使人精密，哲理使人深刻，伦理学使人有修养，逻辑与修辞使人善辩。

6. History makes men wise, poetry makes men wise, mathematics makes men precise, philosophy makes men profound, ethics makes men cultivated, and logic and rhetoric make men eloquent.

7. 一个数学家越超脱越好。

7. The more detached a mathematician is, the better.

8. 在数学中，我们发现真理的主要工具是归纳和模拟。

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

9. 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

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

10. 数学是研究现实生活中数量关系和空间形式的数学。

10. Mathematics is the study of quantity relationships and spatial forms in real-life situations.

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 determined to abandon that geometry which is merely abstract. This means no longer considering those problems that are merely used to exercise the mind. I am doing this in order to study another geometry, which aims to explain natural phenomena. — Descartes

12. 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

12. I always exert my energy and talent to free myself from that heavy and monotonous calculation. — Napier

13. 数学是科学之王。

13. Mathematics is the king of sciences.

14. 数学，科学的女皇；数论，数学的女皇。——高斯

14. Mathematics, the queen of sciences; number theory, the queen of mathematics. - Gauss

15. 数学发明创造的动力不是推理，而是想象力的发挥。

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

16. 给我最大快乐的，不是已懂得知识，而是不断的学习；不是已有的东西，而是不断的获取；不是已达到的高度，而是继续不断的攀登。

16. What brings me the greatest joy is not the knowledge I already possess, but the continuous learning; not the things I already have, but the ongoing acquisition; not the heights I have already reached, but the continuous striving to climb higher.

17. 世界上那些最容易的事情中，拖延时间最不费力。

17. Among the easiest things in the world, procrastinating takes the least effort.

18. 数学主要的目标是公众的利益和自然现象的解释。

18. The main goal of mathematics is the public interest and the interpretation of natural phenomena.

19. 第一是数学，第二是数学，第三是数学。——伦琴

19. First is mathematics, second is mathematics, third is mathematics. - Röntgen

20. 请重视解题中的细节错误，并在考试前提醒自己。

20. Please pay attention to the detail errors in problem-solving and remind yourself of them before the exam.

21. 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

21. A person with scientific and innovative capabilities not only needs to possess scientific knowledge but also needs to have a cultural and artistic upbringing. ——Qian Xuesen

22. 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

22. If someone thinks about the truths of mathematics as deeply and perseveringly as I do, he too will find my discoveries. — Gauss

23. 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。

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

24. 每当我的头脑没有问题思考时，我就喜欢将已经知道的定理重新验证一番。这样做并没有什么目的，只是让自己有个机会充分享受一下专心思考的愉快。

24. Whenever my mind is free from any specific problem to ponder, I enjoy re-verifying the known theorems. There is no particular purpose in doing so; it is just an opportunity to fully savor the joy of focused thinking.

25. 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

25. The simple composition of integers has been a source of new vitality for mathematics for several centuries. — GD Birkhoff

26. 每一个目标，我都要它停留在我的眼前，从第一到曙光初现开始，一直保留，慢慢展开，直到整个大地光明为止。

26. Every goal, I want it to stay before my eyes, from the very first to the break of dawn, preserved and gradually unfolded, until the entire earth is illuminated.

27. 数统治着宇宙。 ——毕达哥拉斯

27. Numbers rule the universe. — Pythagoras

28. 学习数学的秘诀是：解题，解题，再解题。

28. The secret to learning mathematics is: solve problems, solve problems, and solve more problems.

29. 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

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

30. 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。

30. Do not neglect certain problem-solving conventions that you are not proficient in just because the topic is small. Good habits are cultivated, not memorized all at once.

31. 解题是一种实践性的技能，就像游泳、滑雪或弹钢琴一样，只能通过模仿、练习和钻研来学到它。

31. Problem-solving is a practical skill, like swimming, skiing, or playing the piano, which can only be learned through imitation, practice, and research.

32. 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。

32. 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 people's hearts, arousing their appreciation for it, which is very similar to the beauty of art.

33. 哪里有数，哪里就有美。

33. Where there is number, there is beauty.

34. 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。

34. In the field of mathematics, the art of posing problems is more important than the art of solving problems.

35. 数学，如果正确地看，不但拥有真理，而且也具有至高的美。

35. Mathematics, if properly viewed, not only possesses truth but also has the highest form of beauty.

36. 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

36. Infinity! There is no other problem that has so profoundly touched the human heart. — D. Hilbert

37. 新的数学方法和概念，常常比解决数学问题本身更重要。

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

38. 学数学，绝不会有过份的努力。

38. Studying mathematics will never require excessive effort.

39. 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。

39. Because the structure of the universe is the most perfect and the most wise creation of the almighty God, therefore, if there were no certain great or small laws in the universe, nothing would happen at all. - Euler.

40. 唤起独创性的表现与求知之乐，是为人师者至高无比的秘方。

40. Awakening the expression of originality and the joy of seeking knowledge is the highest and most extraordinary secret formula for a teacher.

41. 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

41. Climbing to the peak of science is like a mountaineer ascending Mount Everest, requiring the overcoming of countless difficulties and dangers. Cowards and indolent individuals are unable to enjoy the joy and happiness of victory. -- Chen Jingrun

42. 在数学里，分辨何是重要，何事不重要，知所选择是很重要的。

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

43. 初等数学是近代思想最具有代表性的创造之一，它的特点是通过直接的途径把理论和实践联系起来了。

43. Primary mathematics is one of the most representative creations of modern thought, characterized by its direct approach to linking theory with practice.

44. 下棋要找高手。只有不怕在能者面前暴露自己的弱点，才能不断进步，自学，不怕起点低，就怕不到底。

44. To play chess, one should seek out experts. Only by not fearing to expose one's weaknesses in the presence of the skilled can one continuously improve, learn by oneself, and not fear a low starting point; what one should fear is not reaching the bottom.

45. 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

45. When there is a lack of numbers, the shape is less intuitive, and when there is a lack of shape, it is difficult to be precise in detail. He also said that to lay a solid foundation in mathematics, there are two essential processes: first, to learn and accept the 'from thin to thick'; and then to digest and refine 'from thick to thin.' ——Hua Luogeng

46. 数学是规律和理论的裁判和主宰者。

46. Mathematics is the judge and master of rules and theories.

47. 孩子有个性才能成才，文艺家、政治家、科学家都靠个性的发展才获得成功。

47. A child must have a unique personality to excel, as artists, politicians, and scientists all rely on the development of their personalities to achieve success.

48. 不要因为数学中的一些词语与自然语言中的词语看上去相同，就认为它们的意义完全一样。

48. Do not assume that the meanings of some words in mathematics are completely the same as those in natural language just because they look similar.

49. 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

49. There is no Nobel Prize in mathematics, which might be a good thing. The Nobel Prize is too attention-grabbing, which might prevent mathematicians from focusing on their own research. — Chen Jingrun

50. 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。

50. 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.

51. 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。

51. 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.

52. 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。

52. To learn mathematics, one should do a lot of exercises and think while doing them. First, understand what it is, and then understand why it is so.

53. 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

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

54. 在任何时刻都不要认为自己解过的题已经足够多了。

54. At no time should you believe that you have solved enough problems.

55. 学习专看文学书，也是不好的。先前的文学青年，往往厌恶数学、理化、史地、生物学，以为这些都无足轻重，后来变成连常识也没有。——鲁迅

55. It is also not good to only study literature. The literary youth of the past often disliked mathematics, physics and chemistry, history and geography, and biology, thinking that all these were unimportant. Later on, they even lost common sense. — Lu Xun