(1) Mathematics is an infinite science. -Weil

(2) The problem is the heart of mathematics. -P.R. halmos

(3) As long as a branch of science can raise a large number of questions, it is full of vitality, while the lack of questions indicates the termination or decline of independent development. -Hilbert

(4) Some beautiful theorems in mathematics have the following characteristics: they are easy to be induced from facts, but their proofs are extremely hidden. -Gauss

(5) Mathematics is the queen of science, while number theory is the queen of mathematics-Gauss.

(6) Mathematical metaphor: Zhi Nuo, an ancient Greek philosopher, is called the father of paradox. He has four mathematical paradoxes that have been passed down to this day. He once said a famous saying: the knowledge of the big circle is a little more than that of the small circle, but because the circumference of the big circle is longer than that of the small circle, the contact surface with the outside world is larger than that of the small circle, so I feel more lack of knowledge and need to study hard.

(7) Learn mathematics as a language, learn the usage of every term, and be familiar with the meaning of every symbol.

(8) Don't let go of any seemingly simple examples-they are often not that simple or can lead to many knowledge points.

(9) Just because you can use mathematical formulas doesn't mean you know mathematics.

2. Tales of famous mathematicians

(1) Galois was born in a small town not far from Paris. His father is the headmaster of the school and has served as mayor for many years. The influence of family makes Galois always brave and fearless. 1823, 12-year-old galois left his parents to study in Paris. Not content with boring classroom indoctrination, he went to find the most difficult mathematics original research by himself. Some teachers also helped him a lot. Teachers' evaluation of him is "only suitable for working in the frontier field of mathematics".

(2) The famous German scientist Gauss (1777 ~ 1855) was born in a poor family. Gauss learned to calculate by himself before he could speak. When he was three years old, he watched his father calculate his salary one night and corrected his father's calculation mistakes. When he grew up, he became the most outstanding astronomer and mathematician of our time. He made some contributions to physics electromagnetism, and now a unit of electromagnetism is named after him. Mathematicians call him "the prince of mathematics".

(3)/kloc-Rudolph, a German mathematician in the 6th century, spent his whole life calculating pi to 35 decimal places, which became Rudolph's number. After his death, someone else carved this number on his tombstone. ?

(4) Jacques Bernoulli, a Swiss mathematician, studied the spiral (known as the thread of life) before his death. After his death, a logarithmic spiral was carved on the tombstone, and the inscription also said, "Although I have changed, I am the same as before." This is a pun, which not only describes the essence of spiral, but also symbolizes his love for mathematics.