C.F.Gauss (1777- 1855), a great mathematician in Germany, is the greatest and most outstanding scientist in Germany. If only based on his mathematical achievements, he seldom uses some of his research results in a branch of mathematics. My grandfather was born in a poor family in Gauss and was a farmer. Besides gardening, my father also worked as a handyman, such as a berm worker and a builder. Because of poverty, his father has no education. My mother got married at the age of 34 and gave birth to Gauss at the age of 35. She is the daughter of a stonemason. She has a very clever brother. He is a famous local silk expert. This uncle Gauss takes good care of little Gauss. He educates him and teaches him some knowledge whenever he has the chance. This father can be said to be a "lout", thinking that only strength can make money, and learning is useless to the poor. In his later years, Gauss likes to tell his little grandson stories about his childhood. He said that he had learned to calculate before he could speak. When he was less than three years old, one day he watched his father calculating the weekly salary of the workers under his jurisdiction. Father was mumbling to count, finally sighed and finally worked out the money. When my father finished reading the money and was ready to write it down, a small voice came from around him: "Dad! Wrong calculation, the money should be like this. " Father was surprised to calculate it again, and sure enough, the number Gauss said was right. Strangely, no one taught Gauss how to calculate, but Gauss learned to calculate by himself through daily observation without the knowledge of adults. Another famous story can also show that Gauss had fast computing ability at an early age. When he was still in primary school, one day, the arithmetic teacher asked the whole class to work out the following formula:1+2+3+4+...+98+99+100 =? Soon after the teacher finished the problem, Gauss wrote the answer 5050 on his small stone board, while the other children were all confused and still couldn't figure it out. In the end, only Gauss's answer is correct. Originally:1+100 =101,2+99 =10/,3+98 =101. After dinner in winter night, his father will go to bed, which can save fuel and lamp oil. Gauss likes reading very much. He often takes a bundle of turnips to his attic. He hollowed out the radish, stuffed it into a wick made of coarse cloth, and made candle oil with some grease, so he concentrated on reading in this dim light. He didn't go to bed until fatigue and cold overwhelmed him. Gauss's arithmetic teacher used to have a bad attitude towards his students. He often thinks that he is incompetent to teach in the backcountry. Now he is happy to find a "child prodigy". But soon he felt ashamed that he didn't know much about mathematics and couldn't help Gauss. He went to town and bought a math book for Gauss. Gauss is very happy to study this book with a teaching assistant who is almost ten years older than him. Children and teenagers have formed a deep affection, and they spend a lot of time discussing what's inside. At the age of eleven, Gauss discovered the general case of binomial theorem (x+y)n, where n can be a positive and negative integer or a positive and negative fraction. When he was a pupil, he paid attention to infinite problems. One day, on his way home, Gauss was absorbed in reading and unconsciously walked into the garden of Brunswick Palace. At this time, the Duchess of Brunswick saw that the child liked reading so much and talked to him. She found that he fully understood the profound content of the book he read. The duchess went back and reported to the duke that the duke had heard the story of a clever boy in the territory under his jurisdiction, so he sent someone to call Gauss to the palace. Duke Ferdinand liked the shy boy very much and appreciated his talent, so he decided to give him financial aid to give him a chance to receive higher education. Duke Ferdinand's care for Gauss is beneficial, otherwise Gauss's father is against children reading too many books. He always thinks that it is more useful to work to earn money than to do some math research. How can Gauss become a useful person? With the kind help of Duke Ferdinand, 15-year-old Gauss entered a famous college (equivalent to high school and university). There, he studied ancient and modern languages and began to study advanced mathematics. He absorbed in reading the works of famous European mathematicians such as Newton, Euler and Lagrange. He especially praised Newton's work and soon mastered Newton's calculus theory. 1795 10 In June, he left his hometown college to go to university in G? ttingen. The University of G? ttingen is very famous in Germany, and its rich mathematical collection attracts Gauss. Many foreign students also go there to study language, theology, law or medicine. This is a city with a strong academic atmosphere. Gauss doesn't know which department to study at this time, the language department or the mathematics department. From a practical point of view, it is not easy to find a life after learning mathematics. But on the eve of his eighteenth birthday, a new discovery in mathematics made him decide to study mathematics all his life. This discovery is very important in the history of mathematics. We know that when n≥3, regular N polygons refer to those N polygons with equal sides and the same internal angles. Greek mathematicians have long known to draw regular triangles, quadrilaterals, pentagons and pentagons with compasses and scale-free rulers. However, for more than two thousand years, no one knows how to construct polygons with eleven sides, thirteen sides, fourteen sides and seventeen sides with rulers and compasses. Gauss, who was less than 18 years old, found that a regular N-polygon can be drawn with a ruler and compasses if and only if N is one of the following two forms: k = 0, 1, 2 ... 1 7th century. The French mathematician Fermat thought that this formula gave k = 0,1,2,3. Gauss solved geometric problems for more than 2000 years by algebraic method, and discovered the ruler method of regular heptagon. He was so excited that he decided to study mathematics all his life. It is said that he also expressed the hope that after his death, he could carve a regular heptagon on the tombstone to commemorate the most important mathematical discovery in his youth. Gauss put forward his doctoral thesis in 1799, and proved an important theorem of algebra: any unary algebraic equation has roots. This result is called "the basic theorem of algebra" in mathematics. In fact, many mathematicians in Gauss think that the proof of this result has been given, but none of them are rigorous. Gauss was the first mathematician to give an accurate proof. Gauss thought this theorem was very important and gave four different proofs in his life. Gauss has no money to publish his paper. Fortunately, Duke Ferdinand gave him money for printing. At the age of twenty, Gauss wrote in his diary that he had many mathematical ideas in his mind, but only a small part could be recorded because of the uncertain time. Fortunately, he wrote his research results into the book Arithmetic Research, which was published at the age of 24. This book is written in Latin. Originally there were eight chapters, but due to lack of money, seven chapters had to be printed. This book can be said to be the first systematic work on number theory. Gauss introduced the concept of "congruence" for the first time.