/kloc-In the middle of the 0/7th century, a French nobleman, De Meyer, who was keen on dice games, discovered the fact that a dice was thrown four times in a row, and there was more chance of at least one six, while two dice were thrown 24 times at the same time, and there was little chance of at least one double six.
What is the reason? Later generations will call this the famous Demeyer problem. Someone put forward the "gambling problem":
Two people decided to bet a few games, and it was agreed in advance that whoever won six games first would be the winner. If one person wins three games and another person wins four games, and for some reason he stops gambling, how should he divide the gambling books?
Many gambling questions like this need to calculate the probability, but they can't give the answer themselves.
Mathematicians take part in gambling. Gamblers asked Pascal, a French mathematician at that time, about the above problems they encountered. Pascal accepted these questions, but he didn't answer them immediately, but gave them to Fermat, another French mathematician. They communicate with each other frequently, and start a thorough and detailed study around the mathematical problems in gambling. These problems were later understood by Huygens, a Dutch scientist who came to Paris. After returning to Holland, he conducted research independently.
Pascal and Fermat, while doing their own gambling experiments, made detailed analysis and calculation of various problems in gambling, and finally solved the "gambling problem" completely, and extended the solution of this problem to a more general situation, thus establishing a basic concept of probability theory-mathematical expectation, which is a quantity describing the average level of random variables. After years of hard research, Huygens solved some mathematical problems in dice rolling. 1657 wrote his own research results into a monograph "On Calculation in Dice Games". This book is regarded as the earliest monograph on probability theory so far. Therefore, it can be said that the real founders of early probability theory are Pascal, Fermat and Huygens. This period is called combined probability period, and various classical probabilities are calculated.
After them, several members of Bernoulli family, a Swiss mathematical family, made contributions to the subject of probability theory. On the basis of previous studies, Jacob Bernoulli continued to analyze other problems in gambling, gave a detailed solution to the problem of gamblers losing money, and proved a theorem called "law of large numbers", which is an extremely important result in the classical probability theory of equal possibility events. The discovery of the proof of the law of large numbers is extremely difficult. He did a lot of experimental calculations, first guessed this fact, and then it took Jacques the cloth flower 20 years to improve the proof of this conjecture. Jacob devoted all his energy to this mathematical research, from which he developed many new methods and achieved many new results, and finally proved this theorem.
17 13, Jacob's book conjecture was published. Unfortunately, Jacob had been dead for eight years when his masterpiece came out. Jacob's nephew Nikolai Benuri did participate in this "gambling". He put forward the famous "St. Petersburg problem": A and B gambled, A tossed a coin until it was a head game. If a throws a head, b pays a ruble; If a throws a reverse for the first time and a forward for the second time, b pays A 2 ruble; If A throws his head twice and gets it the third time, B pays A 22 rubles. Generally speaking, if A throws heads for the n- 1 th time and heads for the n-th time, B will pay A 2n- 1 ruble. How many rubles does Party A have to pay to Party B before the gambling starts to have the right to participate in the gambling without losing to Party B?
Many mathematicians of Nicholas's contemporaries have studied this problem and given some different solutions. But the result is very strange, and the amount paid is infinite. That is, no matter how much money A gives B in advance, as long as the gambling continues, B will definitely lose.
With the development of science in 18 and 19 centuries, people noticed that some biological, physical and social phenomena were similar to games of chance, so probability theory originated from games of chance was applied to these fields, which greatly promoted the development of probability theory itself.
French mathematician Laplace upgraded the classical probability theory to modern probability theory. He first gave a clear classical definition of probability, and introduced more powerful mathematical analysis tools into probability theory, which pushed probability theory to a new development stage. He also proved the "de Morville-Laplace Theorem", extended the conclusion of de Morville to general occasions, and established the observation error theory and the least square method. Laplace published his book Probability Theory of Analysis in 18 12, which is a future-oriented book. What people want to know most at this time is whether probability theory will have greater application value. Whether it can have greater development and become a rigorous discipline.
Due to the urgent need of the development of science and technology, probability theory developed rapidly in the 20th century. 1906, Russian mathematician Markov proposed a mathematical model called "Markov chain". 1934, Qin Xin, a mathematician of the former Soviet Union, put forward the theory of stationary process which is carried out uniformly in time.
How to base probability theory on strict logic is a problem that people have been concerned about since the birth of probability theory. Over the years, many mathematicians have tried, but because of the immature conditions, it has been delayed for 300 years.
Lebesgue's theory of measurement and integration, which was completed in the early 20th century, and the abstract theory of measurement and integration, which was developed later, laid the foundation for the establishment of axiomatic system of probability theory. Under this background, André Andrey Kolmogorov gave the definition of measure theory of probability and a set of strict axioms for the first time in his book "Fundamentals of Probability Theory" 1933. His axiomatic method became the basis of modern probability theory, making probability theory a rigorous branch of mathematics.
Now, probability theory, together with mathematical statistics based on it, plays an indispensable role in natural science, social science, engineering technology, military science, industrial and agricultural production and many other fields.
Intuitively speaking, satellites in the sky, missile cruises, aircraft manufacturing, spacecraft traveling in space, etc. Have the contribution of probability theory; Timely and accurate weather forecast, ocean exploration and archaeological research are inseparable from probability theory and mathematical statistics; The development of electronic technology, the progress of film and television culture, population census and educational equivalent probability theory are also inseparable from mathematical statistics.
Monte Carlo method is a calculation method based on probability theory and mathematical statistics. With the help of computer, this method plays an important role in the research of nuclear physics, surface physics, electronics, biology, polymer chemistry and other disciplines.
As a branch of mathematics with rigorous theory and wide application, probability theory has attracted more and more attention and will develop with the development of science and technology.