Story: 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.

One day, Gauss's math teacher was very depressed. Say to the students, "You calculated the sum of 1 plus 2 plus 3 to 100 for me today. Whoever can't figure it out will be punished for not going home for lunch. "

As a result, in less than half an hour, Xiao Gao Si picked up the slate and stepped forward. "Teacher, is this the answer?"

Without looking up, the teacher waved his thick hand and said, "Go, go back!"! Wrong. "

Gauss stood still and put the slate in front of the teacher: "Teacher! I think this answer is correct. "

The math teacher wanted to shout, but he was surprised when he saw the number written on the slate: 5050. How did this 8-year-old get the answer so quickly?

Gauss explained a method he discovered, which was used by the ancient Greeks and China people to calculate the sequence1+2+3+…+n. Gauss's discovery made the teacher feel ashamed, and felt that his previous view of being arrogant and belittling poor children was wrong. He also taught seriously in the future, and often bought some math books from the city for his own study and lent them to Gauss. With his encouragement, Gauss later did some important research in mathematics.

Major achievements:

Gauss, 17 years old, discovered the prime number distribution theorem and the least square method. After processing enough measurement data, new probability measurement results can be obtained. On this basis, Gaussian then focuses on the calculation of surfaces and curves, and successfully obtains Gaussian bell curve (normal distribution curve). Its function is named standard normal distribution (or Gaussian distribution), which is widely used in probability calculation.

The next year, it was proved that the 17 polygon can only be constructed with a ruler. It also provides the first important supplement to Euclidean geometry which has been circulated for 2000 years since ancient Greece.

Gauss summed up the application of complex numbers and strictly proved that every algebraic equation of order n must have n real numbers or complex numbers. In his first masterpiece, Arithmetic Research, he proved the law of quadratic reciprocity, which became an important basis for the continued development of number theory. The first chapter of this book deduces the concept of triangle congruence theorem.