Complex numbers can be used to represent plane vectors and are widely used in physics. People will naturally think: can we find a "three-dimensional complex number" to represent the space by imitating the complex number set? From 65438 to 0828, Hamilton began to study quaternions carefully. Quaternion is a part of linear algebra and a kind of hypercomplex number. But before Hamilton, no one put forward quaternion, and Hamilton was also studied to solve the problem of expressing space quantity. After studying for more than ten years, Hamilton made no progress. He is a genius in mathematics and has few problems. He's really in trouble this time. By 1843, Hamilton had studied 15 years.
One afternoon, the sunset is infinite, the autumn colors are bright and beautiful, and the scenery is pleasant. Hamilton's wife saw her husband immersed in research, hardly knowing whether it was cold or hot, and wanted him to go out to relax and adjust his body. She said, "honey, the nature outside is not as interesting as your math, but it is not inferior." Go out and have a look. What a beautiful autumn! " Hamilton, persuaded by his wife, put down the problem at hand and walked out of the study. The husband and wife walked and unconsciously came to the moat. The autumn wind is soft and cool and the river is sparkling. The fresh air with the aroma of ripe fruits and natural soil makes people feel refreshed and clear-headed. They are intoxicated with nature, and when the twilight is boundless, the evening scenery is pleasant. They came to Bolohan Bridge, facing the fresh water vapor and looking at the lights. Hamilton's mind is thinking without something, which seems far and near, and what seems clear and vague lingers in his mind for a long time. I can't take it out. I can't take it out. All of a sudden, these impression-like feelings turned into bright spots, all the fog of the past disappeared, and the lightning of thinking flashed across the sky of the soul. Hamilton's eyes lit up, and those clear dots appeared one by one. Hamilton quickly took out his notebook and recorded the ecstatic results. In the past 15 years, a whole 15 years, I finally found a solution here! Taking this opportunity, Hamilton strode home and plunged into the study, forgetting to eat and sleep. For several days, I was almost motionless, concentrating on writing and calculating from time to time. In a few inches of manuscript paper, Hamilton sorted out an epoch-making paper. 1843, 1 1 In June, 2006, the field of mathematics was a sensation, and Hamilton and the Irish Academy of Sciences announced "quaternions" to the world.