1. 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。

1. Mathematical methods permeate and dominate all theoretical branches of the natural sciences. They are increasingly becoming the main criterion for measuring scientific achievements.

2. 读书时要深思多问。只读而不想，就可能人云亦云，沦为书本的奴隶；或者走马看花，所获甚微。——王梓坤

2. While reading, one should ponder deeply and ask many questions. To merely read without thinking might lead to parroting others and becoming a slave to the books; or to merely glance at things superficially, yielding very little. - Wang Zikuang

3. 书籍是全世界的营养品，生活里没有书籍就好像没有阳光；智慧里没有书籍就好像鸟儿没有翅膀。——莎士比亚

3. Books are the nourishment of the world; without books in life is like without sunlight; without books in wisdom is like birds without wings. — Shakespeare

4. 历史使人贤明，诗造成气质高雅的人，数学使人高尚，自然哲学使人深沉，道德使人稳重，而伦理学和修辞学则使人善于争论。

4. History makes people wise, poetry creates elegant individuals, mathematics elevates character, natural philosophy deepens thought, morality makes one steady, and ethics and rhetoric make one skilled in debate.

5. 无限！再也没有其他问题如此深刻地打动过人类的心灵。

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

6. 三更灯火五更鸡，正是男儿读书时。黑发不知勤学早，白首方悔读书时！——颜真卿

6. At the sixth watch, the lanterns are lit, and the fifth watch the chickens crow; it is the time for a man to study. Black hair does not know the value of studying early, and only when the hair turns white does one regret the time for studying! —— Yan Zhenqing

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。

7. In mathematics, it is very important to distinguish what is important and what is not, and to know what to choose.

8. 我总是尽我的精力和才能来摆脱那种繁重而单调的计算。

8. I always exert my energy and talent to escape from that heavy and monotonous calculation.

9. 一本新书像一艘船，带领我们从狭隘的地方，驶向生活的无限广阔的海洋。——海伦·凯勒

9. A new book is like a ship that leads us from narrow places to the infinite vastness of the ocean of life. — Helen Keller

10. 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。

10. Mathematics makes an important contribution to observing nature, as it explains the simple primitive elements in the structure of regularities, which celestial bodies are constructed from.

11. 以我一生最好的时光追寻那个目标……书已经写成了。现代人读或后代读都无关紧要，也许要等一百年才有一个读者。

11. Having pursued that goal with the best years of my life... the book has been written. Whether it is read by modern people or by future generations is of no consequence; perhaps it will take a hundred years before there is a reader.

12. 尽心下山径之蹊闲，介然用之而成路。为闲不用，则茅塞之矣。

12. To diligently tread the path down the mountain, firmly using it will form a road. If it is not used for leisure, it will become overgrown and blocked.

13. 时间应分配得精密，使每年、每月、每天和每小时都有它的特殊任务。——笛卡尔

13. Time should be meticulously allocated so that each year, each month, each day, and each hour has its special task. — Descartes

14. 勤劳一日，可得一夜安眠；勤劳一生，可得幸福长眠。——达·芬奇

14. "A day of toil brings a night of rest; a lifetime of toil brings eternal rest." — Leonardo da Vinci

15. 处处是创造之地，天天是创造之时，人人是创造之人。——陶行之

15. Every place is a land of creation, every day is a time for creation, and every person is a creator. — Tao Xingzhi

16. 时间，就像海绵里的水，只要愿挤，总是有的。——鲁迅

16. Time, like water in a sponge, is always there if you are willing to squeeze it out. — Lu Xun

17. 国家之前进在于人人勤奋奋发向上，正如国家之衰落由于人人懒惰自私堕落。——斯马尔兹

17. The progress of a nation lies in the diligence and upward striving of each individual, just as the decline of a nation is due to the laziness, selfishness, and decline of each individual. — Smoltsch.

18. 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。

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

19. 新的数学方法和概念，常常比解决数学问题本身更重要。

19. New mathematical methods and concepts are often more important than solving mathematical problems themselves.

20. 非数学归纳法在数学的研究中，起着不可缺少的作用。

20. Non-mathematical induction plays an indispensable role in the research of mathematics.

21. 业精于勤而荒于嬉，行成于思而毁于随。——韩愈

21. "Diligence makes skillful, while leisure makes dilatory; actions are formed through thought, but destroyed through carelessness." — Han Yu

22. 数学发明创造的动力不是推理，而是想象力的发挥。

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

23. 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。

23. We find that every new group is mathematically structured, as we cannot have any other guidance.

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。

24. This is a reliable rule: when the author of a mathematical or philosophical work writes in vague, obscure language, he is talking nonsense.

25. 我的发奋求学没有得到别的好处，只但是是愈来愈发觉自我的无知。——笛卡儿

25. My diligent pursuit of learning has brought no other benefit than the increasing realization of my own ignorance. — Descartes

26. 二虎相斗，必有一伤。

26. When two tigers fight, one must be injured.

27. 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。

27. From the vastness of the universe to the minuteness of particles, the speed of rockets, the ingenuity of chemical engineering, the changes of the Earth, the mysteries of biology, the complexity of daily use, mathematics is applied everywhere.

28. 君之视臣如手足，则臣视君如腹心；君之视臣如犬马，则臣视君如国人；君之视臣如土芥，则臣视君如寇仇。

28. If a ruler treats his ministers as his own hands and feet, then his ministers will regard him as their bosom friend; if a ruler treats his ministers as dogs and horses, then his ministers will regard him as a common citizen; if a ruler treats his ministers as the earth and the weeds, then his ministers will regard him as an enemy.

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 problems is more important than the art of solving them.

30. 不愤不启，不悱不发，举一隅，不以三隅反，则不复也。

30. If one is not indignant and does not inspire, not sorrowful and does not express, and when pointing to one corner, does not respond with the other three corners, then one will not return.

31. 伟大的成绩和辛勤劳动是成正比例的，有一分劳动就有一分收获，积累，从少到多，奇迹就可以创造出来。——鲁迅

31. Great achievements and hard work are proportional; there is a harvest for every bit of labor, accumulation, from little to much, and miracles can be created. — Lu Xun

32. 只要一门科学分支能提出大量的问题，它就充满着生命力，而问题缺乏则预示着独立发展的终止或衰亡。

32. As long as a branch of science can raise a large number of questions, it is full of vitality, and the lack of questions indicates the termination or decline of independent development.

33. 不参加变革社会的斗争，理想永远是一种幻影。——吴运铎

33. Not participating in the struggle for a changed society, ideals will always remain a phantom. — Wu Yunduo

34. 富与贵，是人之所欲也；不以其道，得之不处也。贫与贱，是人之所恶也。

34. Riches and honor are what people desire; but if not obtained through the right means, they are not worth having. Poverty and low status are what people detest.

35. 我扑在书籍上，像饥饿的人扑在面包上一样。——高尔基

35. I threw myself into books, just like a hungry person throws themselves onto bread. — Gorky

36. 与其进也，不与其退也。唯何甚。人洁己以进，与其洁也，不保其往也。

36. It is not about advancing, but avoiding retreat. What is so severe about it? People cleanse themselves to advance, but they do not preserve their past.

37. 愚者千虑，必有一得。?>

37. Even a fool, when he thinks a thousand times, must come up with something useful.

38. 天才是百分之一的灵感加百分之九十九的勤奋。——爱迪生

38. Genius is one percent inspiration and ninety-nine percent perspiration. — Edison

39. 空谈之类，是谈不久，也谈不出什麽来的，它始终被事实的镜子照出原形，拖出尾巴而去。——鲁迅

39. Empty talk, after all, does not last long and does not yield much; it is always exposed to the mirror of facts, which reveals its true form and then it drags its tail away. — Lu Xun

40. 那些你打算焚毁却又舍不得松手的书才是有用的。——塞·翰逊

40. The books you intend to burn but can't bear to let go of are the useful ones. - Samuel Johnson

41. 得道者多助，失道者寡助。寡助之至，亲戚畔之；多助之至，天下顺之。

41. The one who follows the right path has many helpers, while the one who deviates from it has few. When help is at its lowest, even relatives desert them; when help is abundant, the whole world supports them.

42. 坚强的意志，是不会被假设所谓的命运击败的。——富兰克林

42. A strong will is not defeated by the supposed fate. — Franklin

43. 二一添作五。

43. Divide 21 into five equal parts.

44. 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。

44. 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.

45. 游手好闲的学习并不比学习游手好闲好。——约·贝勒斯

45. Idle learning is not better than learning to be idle. — John Bellers

46. 勤奋者废寝忘食，懒惰人总没有时间。——日本

46. The diligent forget to eat and sleep, while the lazy always find no time. - Japan

47. 贤哉，回也！一箪食，一瓢饮，在陋巷，人不堪其忧。回也不改其乐。

47. Oh, what virtue in Hui! With only a bamboo basket of food and a瓢 of drink, living in a narrow alley, others cannot bear their distress. But Hui remains unchanged in his joy.

48. 在数学中，我们发现真理的主要工具是归纳和模拟。

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

49. 读书务在循序渐进；一书已熟，方读一书，勿得卤莽躐等，虽多无益。——胡居仁［明］

49. The pursuit of reading should be done step by step; one book should be thoroughly mastered before moving on to the next. Do not be hasty or skip levels, for even with many books, it will be of no benefit. — Hu Ju Ren [Ming Dynasty]

50. 臣闻郊关之内，有囿方四十里，杀其麋鹿者如杀人之罪。

50. I have heard that within the suburbs of the capital, there is a park covering forty square miles, and those who kill the deer and elk there are punished as if they had killed a person.

51. 君子之事亲孝，故忠可移于君。事兄悌，故顺可移于长。居家理，故治可移于官。是以行成于内，而名立于后世矣。

51. A gentleman is filial to his parents, thus his loyalty can be transferred to the ruler. He treats his elder brother with respect, thus his obedience can be transferred to superiors. When managing a household, he is orderly, thus his governance skills can be transferred to official positions. Therefore, through actions within, his reputation is established for future generations.

52. 观察可能导致发现，观察将揭示某种规则、模式或定律。

52. Observation may lead to discovery, and observation will reveal some rules, patterns, or laws.

53. 旦旦而学之，久而不怠焉，迄乎成。——（清）彭瑞淑

53. Devote oneself diligently to learning, and after a long period, not to weary, until it is achieved. —— (Qing Dynasty) Peng Ruishu

54. 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。

54. Only when a country experiences a vigorous development in mathematics can it demonstrate the strength of its national power. The development and perfection of mathematics are closely related to the prosperity and prosperity of the nation.

55. 科学是为了那些勤奋好学的人，诗歌是为了那些知识渊博的人。——约瑟夫·鲁

55. Science is for those who are diligent and studious, poetry is for those who are knowledgeable and learned. - Joseph Ruff

56. 学到很多东西的诀窍，就是一下子不要学很多。——洛克

56. The knack of learning a lot of things is not to learn too many at once. — Locke

57. 信仰，是人们所必须的。什麽也不信的人不会有幸福。——雨果

57. Faith is something that people must have. A person who believes in nothing will not have happiness. — Victor Hugo

58. 艺术的大道上荆棘丛生，这也是好事，常人望而却步，只有意志坚强的人例外。——雨果

58. The path of art is full of thorns, which is also a good thing. Most people shrink back from it, except for those with strong willpower. — Hugo

59. 十拿九稳。

59. Sure thing.

60. 人的知识愈广，人的本身也愈臻完善。——高尔基

60. The broader a person's knowledge, the more perfect the person themselves becomes. – Maxim Gorky

61. 一失足成千古恨。

61. A single misstep can lead to eternal regret.

62. 父在观其志，父没观其行；三年无改于父之道，可谓孝矣。

62. When the father is alive, he observes his son's aspirations; after the father's death, he observes his son's actions. If a son does not change his father's ways for three years, he can be considered filial.

63. 石可破也，而不可夺坚；丹可磨也，而不可夺赤。

63. Stones can be broken, but their hardness cannot be taken away; cinnabar can be worn down, but its redness cannot be taken away.