1. Goldbach conjecture 1742 Goldbach in Germany wrote a letter to Euler, a great mathematician living in Petersburg, Russia at that time. In the letter, he raised two questions: First, can every even number greater than 4 be expressed as the sum of two odd prime numbers? Such as 6=3+3, 14=3+ 1 1 and so on. Second, can every odd number greater than 7 represent the sum of three odd prime numbers? Such as 9 = 3+3+3, 15 = 3+5+7, etc. This is the famous Goldbach conjecture. This is a famous problem in number theory, which is often called the jewel in the crown of mathematics.

2. A long time ago, there was a man named Caesar in India. He carefully designed a game for the king, which is now 64-square chess. The king was very satisfied with the game and decided to give it to Cesar. The king asked Cesar what he needed. Cesar pointed to the small squares on the chessboard and said, "Just give me the first square 1 grain of wheat, the second square with 2 grains of wheat and the third square with 4 grains of wheat. At this rate, the wheat in each square is twice as much as that in the previous one. Your Majesty, give me all the 64 tablets that fill the chessboard like this. " The king readily agreed to Cesar's request without thinking. However, after calculation, ministers found that it was not enough to give Cesar all the wheat harvested in one year. Cesar is right. His demands can't really be met. According to the calculation, the total number of wheat in 64 squares on the chessboard will be a 19 digit, which is about 200 billion tons by weight. The king has supreme power, but he interprets the profoundness of knowledge with his ignorance.

3. How did the wise men in ancient Greece measure the height of the pyramids? First, a bamboo pole is erected on the ground, and the length of the shadow of the bamboo pole and the shadow of the pyramid are measured at the same time when the sun is shining, and then the ratio of the length of the bamboo pole to the shadow of the bamboo pole is calculated, that is, the ratio of the height of the pyramid to the length of the shadow of the pyramid. Using this ratio and the shadow length of the pyramid, the height of the pyramid can be calculated.