1. There is a famous story about Irish mathematician William Longwan Hamilton, who suddenly invented the four-element method when he walked across a stone bridge. His wonderful idea at that time was that he suddenly realized that not the whole algebraic system had to follow the exchange law. He was so excited that he immediately carved these basic formulas on the stone bridge. It is said that this stone engraved with formula has been preserved to this day.

2.

French mathematician Poincare also benefited from the flash of inspiration and intuition in his scientific creation. According to his own memory, one night, he broke the routine and accidentally drank coffee, so he couldn't sleep. Various ideas flooded into his mind and collided with each other. There are two related ideas. By the early morning of the next day, he finally found that there was a Fox function, which could be derived from hypergeometric series. Later, he took part in a geological survey trip. Traveling all the way made him forget all about mathematics. After he arrived in Costa Rica, he shared a bus with others. Just as his foot stepped on the pedal of the car, a new idea suddenly flooded into his mind: the definition transformation of fox function is the same as some transformations of non-Euclidean geometry.

3. After solving a problem (Gauss and symbols) that has plagued him for many years, Gauss wrote to a friend and said, "Just a few days ago, it succeeded (I want to say, not because of my hard exploration, but because of God's grace), just like the moment of lightning bombardment, the mystery was solved; My previous knowledge, the method I tried last time and the reason for my success, how these three are related, I have not been able to sort out the clue myself. "