De moivre is a French mathematician. Born on May 26th, 1667, Vitry Le Francois1754165438+died in London, England on October 27th.
Chinese name: de moivre.
Abraham de Morville
Nationality: France
Place of birth: Vitry Lefrancois, France.
Date of birth:1May 26th, 667.
Date of death:1754165438+1October 27th.
Occupation: Mathematician
Faith: Calvinism
Representative Works: Essay Analysis (1730)
outline
Abraham de Moivre was born in Fran? ois, Vitri Province on May 26th, 1967. 1754 165438+ died in London, England on1October 27th.
De moivre was born in the home of a French country doctor. His father was thrifty all his life, and his medical income barely supported his family. De moivre was educated by his father since childhood. When he was a little older, he entered a local Catholic school. The religious atmosphere in this school is not strong, and students can study in a relaxed and free environment, which has a great influence on his character. Later, he left the countryside and went to a Puritan college in Sarah for further study. However, it is suffocating that the school requires students to swear allegiance to the church. De Moif refused to obey, so he was severely punished and was punished for reciting various religious teachings. At that time, the school did not attach importance to mathematics education, but De Moif often secretly studied mathematics. Among the mathematics works he learned in his early years, he was most interested in Huygens' works on gambling, especially the book Deratiociniisinludoaleae published by Huygens in 1657, which inspired him.
life experience
1684, de Moivre came to Paris, and he was lucky enough to meet J. Ozanam, an outstanding French mathematics educator and enthusiastic disseminator of mathematical knowledge. With the encouragement of Ozaram, De Moivre studied Creed's Elements and some important mathematical works by other mathematicians.
1685, together with many Protestants, De Moivre participated in the religious riots that shocked Europe. In this riot, he was imprisoned with many people. It was in this year that the Nanz Act, which protected Calvinists, was revoked. Subsequently, many talented scholars, including De Morville, emigrated from France to Britain. According to church records, De Moivre was imprisoned until 1688 and moved to London that year. However, according to a material discovered in the 1960s, De Moivre had already arrived in Britain as early as 1685. Since then, De Moivre has been living in England, and all his contributions to mathematics have been made in England.
After arriving in London, De Moivre immediately discovered many excellent scientific works, so he studied eagerly. By chance, he read the Mathematical Principles of Natural Philosophy just published by Newton, and was deeply attracted by this work. Later, he recalled how he studied Newton's masterpiece: he made a living as a tutor and had to teach children from many families, so time was tight, so he took it apart. When he finished teaching children in one family, he quickly read a few pages on his way to another family and finished the book quickly. In this way, de Moivre soon had a solid academic foundation and began to conduct academic research.
1692, de Morville visited E. Halley, secretary of the Royal Society. Harley read De Moivre's first mathematical paper "On Newton's Flow Principle" at the Royal Society, which attracted academic attention. 1697, due to Harley's efforts, de Morville was elected as a member of the Royal Society.
De moivre's genius and achievements have been widely concerned and respected by people. Harley presented De Morville's important book Opportunity in October to Newton, who appreciated De Morville very much. It is said that when a student asked Newton a question about probability, he said, "Such questions should be asked to De Morville, who has studied these questions much more profoundly than I have." . 17 10, de Moivre was appointed to participate in the investigation of Newton-Leibniz calculus priority Committee by the Royal Society, which shows that he was highly respected by the academic community. 1735, de Moivre was elected as an academician of the Berlin Academy of Sciences. 1754 was accepted as a member of the French Academy of Sciences in Paris.
De moivre never got married. Although he has made great achievements in academic research, he is poor. From his arrival in London, England to his later years, he served as a math tutor. He writes articles from time to time, and also participates in the study of practical problems in the determination of insurance annuity, but his income is extremely meager and he can barely maintain his life. He often complains that it is a waste of time to teach children from one house to another and run around from employer to employer monotonously. To this end, he has tried many times to change his situation, but to no avail.
De moivre suffered from narcolepsy at the age of 87 and slept for 20 hours every day. When he couldn't sleep for 24 hours, he died in poverty.
There is a magical legend with mathematical color about the death of De Moivre: A few days before his death, De Moivre found that he needed to sleep 1/4 hours more than the day before, so the sleep time every day would constitute a arithmetic progression. When this arithmetic series reaches 24 hours, De Moivre will never wake up.
Major achievements
De moivre's probability theory
Probability theory began in17th century. Cardano, Fei Erman, Pascal and others were early researchers in probability theory. They mainly study the probability-chance of independent random events, and discuss the "chance" in the process of gambling and lottery winning. People gradually demand to solve the probability or expectation problem related to a large number of event sets. For example, if the total number of lottery tickets is large and it is known that each lottery ticket has an equal chance of winning, what is the winning probability of drawing 1 000 and 1 000 lottery tickets? People want to know how many lottery tickets they should buy at least if the probability of winning is to reach 90%. Consider a series of random events (such as random coin toss). The probability of one event (such as head-on flip) is p, n represents the total number of all random events, and m is the number of one event. What is the law of the ratio of the number of occurrences (m) of this event to the number of all events (n)? This is a very important problem in17th century probability theory.
17 13 published Jacob Bernoulli's posthumous work "Arsconjectandi", which shows that after repeated experiments, the above probability is proved to be 0.9999; If you add 5708 tests, that is, 36966 tests, the above probability is 0.99999, and so on. Therefore, Jacob Bernoulli pointed out: "Through infinite experiments, we can finally correctly calculate the probability of anything and see the order of things from accidental phenomena." However, he did not express the order in this accidental phenomenon. The work was done by de Moif.
Before the publication of Jacob Bernoulli's Conjecture, De Moivre made extensive and in-depth research on probability theory. 17 1 1 published Demensuresortis in Philosophical Transactions of the Royal Society in, and was translated into The Doctrine of Opportunities when it was published in English in 17 18. He didn't discuss the problems discussed by Jacob Bernoulli in his book, but when The Theory of Opportunity was reprinted in 1738, De Moivre gave an important solution to these problems.
Chance theory
It is often said that there are three landmark works in the early history of probability, among which De Moivre's Theory of Opportunity is one, and the other two are Bo's Theory of Speculation and Laplace's Theory of Probability Analysis.
The statistical significance of De Morville's work;
1 In the special case of frequency estimation probability, the accuracy of the arithmetic average of observation values is directly proportional to the square root of the observation times n, which can be regarded as a great progress in human understanding of nature.
Of course, the greatest influence of De Moivre's work on mathematical statistics lies in the central limit theorem named after him today. About 40 years after de moivre made his discovery, Laplace established a more general central limit theorem, and the most general independent and central limit theorems were finally completed in the 1930 s. Later, statisticians found that a series of important statistical data, in the sample size n->; ; ∞, and its limit distribution has a normal form, which forms the basis of this method in mathematical statistics. At present, this method plays a very important role in statistical methods. De Moifer's work can be said to be the source of this important development.
theorem
Let two complex numbers (expressed in triangular form) z1= r1(cos θ1+isinθ1) and Z2=r2(cosθ2+isinθ2), then:
Z 1Z2=r 1r2。