1. 试图决定性地影响人类的物质、道德和社会生活;试图回答有关人类自身存在提出的问题;努力去理解和控制自然;尽力去探求和确立已经获得知识的最深刻的和最完美的内涵。——克莱因《西方文化中的数学》

1. Attempting to decisively influence human material, moral, and social life; trying to answer questions about the existence of humanity itself; striving to understand and control nature; and making every effort to explore and establish the deepest and most perfect connotations of the knowledge that has already been acquired. - Klein, "Mathematics in Western Culture"

2. 数学发明创造的动力不是推理，而是想象力的发挥。

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

3. 数学是科学的女王，而数论是数学的女王。

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

4. 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。

4. In the process of learning, we 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.

5. 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。

5. I have heard some people 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 have not.

6. 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。

6. Awakening the expression of originality and the joy of seeking knowledge is the most supreme secret formula for a teacher.

7. 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。

7. After modern high-energy physics entered the realm of quantum physics, there are many things that cannot be experimentally tested. People calculate them at home with paper and pen, which is not much different from what mathematicians do. Therefore, it can be said that mathematics has an incredible power in physics.

8. 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

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

9. 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。

9. To feel the beauty of mathematics, to sense the harmony between numbers and forms, and to perceive the elegance of geometry—this is the genuine, authentic sense of beauty that all true mathematicians are acutely aware of.

10. 学习解题的最好方法之一就是研究例题。

10. One of the best ways to learn how to solve problems is to study example problems.

11. 要主动提高综合分析问题的能力，借助文字阅读去分析理解。

11. It is necessary to actively enhance the ability to comprehensively analyze problems, using text reading to analyze and understand.

12. 历史使人聪明，诗歌使人机智，数学使人精细。

12. History makes men wise, poetry makes men clever, and mathematics makes men accurate.

13. 没有一些诗人气质的数学家绝不是一位完全的数学家。

13. A mathematician who lacks some poetic temperament is never a complete mathematician.

14. 数学是一种理性的精神，使人类的思维得以运用到最完善的程度。——克莱因

14. Mathematics is a rational spirit that enables human thought to reach its most perfect degree of application. — Klein

15. 纯粹数学可以是实际有用的，而应用数学也可以是优美高雅的。

15. Pure mathematics can be practically useful, and applied mathematics can also be elegant and refined.

16. 立志于物理学的人，不懂下列的事情是不行的：第一是数学，第二是数学，第三是数学。

16. For those who aspire to the field of physics, it is imperative to understand the following: first, mathematics; second, mathematics; third, mathematics.

17. 解决数学问题，关键是建立正确的数学理念，要从数学角度去思考，利用数学规律去解决。

17. The key to solving mathematical problems is to establish correct mathematical concepts. One should think from a mathematical perspective and utilize mathematical laws to solve them.

18. 数学之所以比一切其它科学受到尊重，一个理由是因为他的命题是绝对可靠和无可争辩的，而其它的科学经常处于被新发现的事实推翻的危险。——爱因斯坦

18. One reason why mathematics is more respected than all other sciences is that its propositions are absolutely reliable and uncontestable, whereas other sciences frequently risk being overturned by new discoveries of facts. – Einstein

19. 数学是知识的工具，亦是其它知识工具的泉源。所有研究顺序和度量的科学均和数学有关。——笛卡儿

19. Mathematics is a tool of knowledge, and also the source of other tools of knowledge. All sciences that study order and measurement are related to mathematics. — Descartes

20. 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。

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

21. 深刻理解知识点，仔细阅读课本，认真听讲，理解联系实际。

21. Deeply understand the key points of knowledge, carefully read the textbook, listen attentively, and understand the connection with reality.

22. 数学家实际上是一个著迷者，不迷就没有数学。

22. Mathematicians are actually enthusiasts; without fascination, there would be no mathematics.

23. 数学主要的目标是公众的利益和自然现象的解释。——傅立叶

23. The main aim of mathematics is the benefit of the public and the explanation of natural phenomena. —— Fourier

24. 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

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

25. 数支配着宇宙。——毕达哥拉斯，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。

25. Numbers rule the universe. — Pythagoras, 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.

26. 如果我继承可观的财产，我在数学上可能没有多少价值了。

26. If I inherit a considerable amount of property, I might not have much value in terms of mathematics.

27. 要将所学知识贯穿在一起形成系统，我们可以运用类比联系法。

27. To integrate the knowledge acquired into a systematic whole, we can apply the method of analogical association.

28. 数学科学呈现出一个最辉煌的例子，表明不用借助实验，纯粹的推理能成功地扩大人们的认知领域。

28. The mathematical sciences present the most splendid example of how pure reasoning, without the aid of experiments, can successfully expand the realm of human cognition.

29. 学习数学，要熟记并正确地叙述概念和规律性内容。

29. In studying mathematics, one should memorize and correctly narrate the concepts and regularity contents.

30. 请找一些习题，把在书上学到的解题方法用上去！

30. Please find some exercises and apply the problem-solving methods you've learned from the book!

31. 上帝创造了整数，所有其余的数都是人造的。

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

32. 不管数学的任一分支是多么抽象，总有一天会应用在这实际世界上。——罗巴切夫斯基

32. No matter how abstract any branch of mathematics may be, it will eventually be applied in this practical world. — Lobachevsky

33. 数学是上帝用来书写宇宙的文字。

33. Mathematics is the language with which God wrote the universe.

34. 数学是一种精神，一种理性的精神。正是这种精神，激发、促进、鼓舞并驱使人类的思维得以运用到最完善的程度，亦正是这种精神。

34. Mathematics is a spirit, a rational spirit. It is this spirit that激发, promotes, encourages, and drives the human mind to be applied to the most perfect degree, and it is also this spirit.

35. 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。——高斯

35. What brings me the greatest joy is not the knowledge I have already acquired, but the continuous learning; not what I already possess, but the constant acquisition; not the heights I have already reached, but the continuous climbing upwards. - Gauss

36. 认真听讲，一方面能更好地掌握知识的来龙去脉，加深理解，另一方面，还能学会老师分析问题，解决问题的思路方法。

36. Paying close attention to the lecture can not only help you better grasp the origin and development of knowledge, deepen your understanding, but also learn the teacher's way of analyzing and solving problems.

37. 数学知识是最纯粹的逻辑思维活动，以及最高级智能活力美学体现。

37. Mathematical knowledge is the purest form of logical thinking activity, and the highest expression of the aesthetic vitality of the most advanced intelligence.

38. 看得懂的例题，请仔细看；看不懂的例题，请硬着头皮看。?>

38. Please read the example problems that you understand carefully; for the ones you don't understand, please force yourself to read through them.

39. 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。

39. As long as a branch of science can pose a large number of questions, it is full of vitality; while a lack of questions portends the termination or decline of independent development.

40. 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。

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

41. 学习数学，不仅要关注题型，更要关注典型题型。

41. When studying mathematics, it is not only important to focus on the types of questions but also to pay attention to typical types of questions.

42. 问题是数学的心脏。

42. The question is the heart of mathematics.