There is a bridge called Bolohan in Dublin, Ireland. There is still a stone tablet standing at the bridge. The inscription reads: "1843 10 October 16. When William Hamilton crossed the bridge, he discovered the basic formula of quaternion multiplication. " When people pass by here, they should stop to watch the inscription and remember Hamilton's great contribution to science.

Hamilton was born in Dublin, Ireland, on 1805. His father is a lawyer and businessman, his mother is a famous woman, and his parents are very talented. However, by the time he 14 years old, his parents had died one after another. From then on, his uncle James Hamilton became his guardian. James is an expert in many languages. Hamilton was influenced by him since he was a child, and his language developed at an early stage. It was the early language development that improved his logical thinking ability and laid the foundation for his achievements in mathematics.

/kloc-When he was 0/2 years old, Hamilton finished the Elements of Geometry, and then he finished the Algebraic Basis by French mathematician Claire Locke. 13 years old, a math prodigy came to America. As a result, the two prodigies learn from each other and learn from each other's strong points, which greatly increases his interest in mathematics. At the age of 17, Hamilton mastered calculus and studied mathematical astronomy to calculate solar and lunar eclipses. /kloc-took the entrance examination of Trinity College in Dublin at the age of 0/8, and was admitted with the first place among more than 0/00 candidates.

1827 Hamilton university, 22 years old, wrote a paper on optical system theory before graduation. This paper lays a material foundation for the establishment of geometric optics, and introduces the so-called optical eigenfunction. Later, Hamilton made three supplements to this paper, and deduced from mathematical theory that light propagating in a special direction in biaxial crystals will produce a cone of refracted light. This argument was later confirmed by optical experiments.

At that time, there was an influential astronomy professor named Brickley in the college, and he appreciated Hamilton's talent very much. 1827, Brickley announced his resignation as professor of astronomy at Trinity College Dublin. He strongly recommended and persuaded the school. At the age of 22, Hamilton became the heir of Brackley and became an astronomy professor. At the same time, Hamilton was awarded the title of Royal Irish Astronomer.

However, Hamilton's ambition is not astronomy. He devoted himself to mathematics. Starting from 1828, he began to study quaternions. Quaternion is the development of number system of real number and complex number, and it is a kind of hypercomplex number, that is, it belongs to four-dimensional vector. In modern terms, it is a part of linear algebra.

However, after more than ten years of painstaking research, Hamilton still failed. 1843 It has been 15 years since he studied quaternions. One night in June 65438+1October 65438+June this year, Hamilton's wife saw her husband buried himself in reading all day, exhausted, and had a great effort to persuade him to take him out for a walk.

The autumn is crisp and the scenery is pleasant. Hamilton, accompanied by his wife, strolled along the boulevard next to the royal moat. A gust of autumn wind blew, with the aroma of ripe fruit. Hamilton greedily breathed the fresh air by the river and couldn't help feeling relaxed and happy. He temporarily forgot his favorite math problem and reveled in nature.

The couple walked onto the Bolohan Bridge, stopped on it and looked at the shadow of the Street View Bridge in the twilight. Hamilton's brain suddenly became active again, flashing, jumping, searching and associating ... Suddenly, the door of his thinking opened, and the shock wave of wisdom broke through the obstacles ahead, and he suddenly realized the mystery of quaternion operation. He immediately took out his notebook with him and quickly recorded the points that flashed in his mind. After pursuing the research goal of quaternion 15 years, we finally found its solution on Bolohan Bridge. Hamilton was afraid that his thoughts would be interrupted, so he quickly picked up his wife and ran home. At this time, other men, women and children who came looked at this pair of weirdos with strange eyes.

At home, Hamilton shut himself in his study, refused to come out for several days, and even had to have his food brought in. Finally, he finally copied a valuable paper from hundreds of pages of calculus papers.

1843, 1 1 In June, Hamilton announced the discovery of quaternion in the Irish Academy of Sciences, which caused a sensation in the mathematics field at that time. The discovery of quaternion strongly promoted the development of vector algebra. In the past, complex number theory can only be used for plane vectors, but the space vector problem should be solved by quaternion vector part. Hamilton also introduced quaternion into calculus and defined a series of concepts to describe the change of the number or direction of functions. For example, "gradient" and "spinor" have become important computing tools for studying physics and engineering.

10 years later, Hamilton wrote a lecture on quaternion, which was published in 1857. Maxwell, a famous physicist at that time, was studying electricity and magnetism. He can't describe electromagnetic motion and its changing law. Electricity and magnetism are both directional quantities. To understand the law of electromagnetic motion, we must first find a solution from mathematical methods. Maxwell used complex vector processing for a long time, but he never got the correct result. When Hamiltonian quaternion came out, Maxwell finally got out of the predicament, and his electromagnetic research succeeded, and Maxwell equations were obtained, which predicted the existence of electromagnetic waves.

Hamilton knew the great significance of quaternion in science. Therefore, in the last 20 years of his life, he has been devoted to research. He foresaw that the application of quaternion would cause great changes in physics. Unfortunately,1September 2, 865, when this change did not come, he died of chronic alcoholism at the age of 60.