1960 1777 On April 30th, Gauss was born in a peasant family in Germany. When I was a child, Gauss liked math very much. When learning English, Gauss often lies in the yard and counts chickens. When he was a little older, he followed his neighbor's children to do math problems, which were fast and accurate every time. After school, Gauss is particularly interested in mathematics. But math teachers look down on rural children and often make things difficult for students. Once, the teacher asked them to sum from 1 to 100, stipulating that they were not allowed to go home for dinner unless they could do it. The children began to calculate at once. But there are too many figures. If you do the math, you will be wrong if you are not careful. Just as everyone was in a hurry, Gauss stood up and reported, "Teacher, I did it." When reading a novel, the teacher said without looking up, "You must be wrong. Recalculate. " But Gauss was so confident that he took the answer sheet to the teacher to show him. Suddenly, the teacher's eyes widened. 5050! The answer is correct! The teacher asked him in surprise what method he used. Gauss said with confidence: "1+100 =10/,2+99= 10 1, 3+98 =1kloc. Teacher, do you think I did the right thing? " The teacher was ashamed. Since then, he has devoted himself to teaching and even tutored Gauss more carefully. Gauss studies very hard. Later, he made great achievements in mathematics. At the same time, he also made outstanding contributions in astronomy, electromagnetism, geodesy and other scientific fields.
Countermeasures to win
During the Warring States Period, Qi Weiwang and Tian Ji raced, and Qi Weiwang and Tian Ji each had three good horses: getting on, winning and dismounting. The race is divided into three times, and thousands of dollars are bet on each horse race. Because the horsepower of the two horses is almost the same, and Qi Weiwang's horse is better than Tian Ji's, most people think that Tian Ji will lose. However, Tian Ji took the advice of his disciple Sun Bin (a famous strategist) and dismounted Qi Weiwang, Ma Zhong of Qi Weiwang and Qi Weiwang. As a result, Tian Ji beat Qi Weiwang 2-/kloc-0-and got a daughter. This is an example of China's ancient substitution game theory to solve problems.
Here is a game played by two people: take turns to report numbers, and the number reported cannot exceed 8 (nor can it be 0). Add up the figures reported by two people, and whoever reports more figures will win if the total is 88. If you were allowed to count first, how many times should you count first to win?
Analysis: Because everyone reports at least 1 and at most 8 at a time, someone reports and another person will find a number, so the sum of this number and a reported number is 9. According to the rules, whoever counts and makes the sum 88 wins, so it can be inferred that whoever counts and makes the sum 79 (= 88-9) wins. 88 = 9× 9+7, and so on. Whoever counts 16 wins. Furthermore, whoever reports 7 first will win. Therefore, the winning strategy of the first whistleblower is: report 7 first, and then if the other party reports K( 1≤K≤8), you report (9-K). In this way, you will win if you quote 10.
The lineage of a revolutionary.
After a hundred years of war, Lorraine left behind a group of hardworking and philosophical French who were able to face the hardships of the environment. Charles Hermite (1822 12) was born in Diyug, a small village in Lorraine. His parents and grandparents both participated in the French Revolution. His grandfather was arrested by extremist political groups after the Revolution and later died in prison. Some relatives died on the guillotine; His father was an outstanding metallurgical engineer. Because he was wanted by the commune, he fled to the small village of Lorraine on the French border and worked incognito as a miner in an iron mine.
The owner of the iron mine is Lallemand, a standard and tenacious Lorraine. He has a stronger daughter, Madeleine. In that conservative era, Madeleine was famous for "daring to wear pants without skirts outdoors" and her management of miners was fierce. But as soon as she met this engineer from Paris, she softened up, knew whether the other person was killed or married to him, and gave birth to seven children for him. Hermite ranks fifth among seven children. He was born with a disability in his right foot and needed to walk with crutches. Half of him has the blood of his father's excellent intelligence and ideal struggle, and the other half has the strong blood of Lorraine, whose mother dares to do things and loves and hates each other. This is the first sign of his extraordinary career.
Understanding the beauty of mathematics from the master
Hermite was a problem student since he was a child. He always likes to argue with the teacher in class, especially some basic questions. He especially hates exams; Later, I wrote: "Learning is like the sea, and exams are like hooks. The teacher always hangs the fish on the hook, so how can the fish learn to swim freely and balance in the sea? " Seeing that he didn't do well in the exam, the teacher hit him on the foot with a wooden stick. He hates it. Later? Quot The purpose of education is to use the brain, not the feet. What's the use of kicking? Can kicking make people smart? "He did badly in the math exam, mainly because he was particularly good at math; What he said even made the math teacher mad. He said: "Math class is a pool of smelly water and a pile of rubbish. Those who do well in math are second-rate people, because they only know how to move garbage. "He pretended to be a first-class scientific madman. However, what he said is true. Most of the greatest mathematicians in history came from literature, diplomacy, engineering, military and other fields. They have nothing to do with mathematics. Hermite spent a lot of time reading the original works of mathematicians, such as Newton and Gauss. He believes that only there can we discover the beauty of mathematics, and only there can we return to the basic point of argument and get the source of mathematics excitement. " In his later years, he recalled the frivolity of his youth and wrote: "Traditional mathematics education requires students to learn step by step and cultivate them to apply mathematics to engineering or business, so it has not stimulated students' creativity. But mathematics has its own beauty of abstract logic. For example, in the program of solving multiple squares, the existence of roots is itself a kind of beauty. The value of mathematics is not only for the application in life, but also should not be reduced to a tool for engineering and commercial applications. The breakthrough of mathematics still needs to constantly break through the existing pattern. "
Filial piety genius
Hermite's performance worried his parents. They sent him to "Louis-le-Grande" in Paris, but begged him to study hard and was willing to pay more money. Because of his outstanding talent in mathematics, he can't put himself into the mold of mathematics education, but in order to comply with his parents' wishes, he has to face those subtle and complicated calculations every day, which makes him extremely painful. This filial genius seems destined to torture himself all his life. The entrance examination of Paris Institute of Technology is held twice a year. He/kloc-began to take the exam at the age of 0/8, and only passed the fifth exam with the score of Hewei. In the meantime, when he almost gave up, he met a math teacher, Richard. Teacher Richard said to Hermite, "I believe you are the second mathematical genius after Lagrange." Lagrange is known as Beethoven in mathematics, and his approximate root solution is known as "the poem of mathematics". But Hermite's talent is not enough. Teacher Richard said, "You need God's grace and persistence to complete your studies, so that you won't be sacrificed by the traditional education that you think is rubbish." So, he failed again and again, but continued to take the exam.
A man riding on the back of a snail.
One year after Hermite entered the technical college, the French education authorities suddenly gave an order: people with physical disabilities were not allowed to enter the engineering department, so Hermite had to transfer to the literature department. Mathematics in the literature department has been much easier, and as a result, he still failed in mathematics. Interestingly, at the same time, he published "Reflections on the Solution of Quintic Equation" in the French Journal of Mathematical Research "Journal of Pure and Applied Mathematics", which shocked the mathematical community.
In human history, Greek mathematicians in the third century discovered the solutions of first-order equations and second-order equations. After that, many first-class mathematicians have been puzzling over the solution of the fourth-order equation to the nth power, and they have never found a solution. Unexpectedly, 300 years later, a student in the literature department, who often failed the math exam, actually put forward the correct solution. Hermite knew that he had been "deeply poisoned by the pioneering research of mathematics and deeply loved it". Fortunately, his good friend Bertrand quickly helped him make up the math he was going to learn at school. For this pioneering genius, rigid mathematics education brings endless pain; Only the understanding and encouragement of friendship can support him to go on and let him graduate from college with marginal results at the age of 24. Unable to cope with the exam and continue his studies, he had to find a school to help him correct his students' homework. I have been a teaching assistant for almost twenty-five years. Although he published algebra continued fraction theory, function theory and equation theory in these twenty-five years, he was famous all over the world, and his mathematics level far exceeded that of all university professors at that time, but he could not take the exam. Without an advanced degree, Hermite can only continue to correct students' homework. Social reality is so cruel and ignorant to him.
Teachers who don't take exams
What prompted Hermite to advance cynically? There are three important factors, one is the wife's understanding and concentricity. Hermite's wife, that is, the sister of Bertrand, his good friend in college, followed this talented husband year after year without any regrets. Second, some people really appreciate him and will not despise him because he is physically disabled and lacks a dazzling degree. People who admired him later became famous in the field of mathematics-including Cauchy, who is famous for studying the convergence and divergence of infinite series and differential equations, Jacoby, who is famous for publishing elliptic functions and determinant theory, and joseph liouville, editor-in-chief of Journal of Pure and Applied Mathematics. These are careerists who admire each other and come from real experts. They can support a loser to go a long way more than a little vanity in getting high marks. The third is Hermite's belief. Hermite was seriously ill at the age of 43. Cauchy came to see him and spread the gospel to him. Faith gave him another kind of value and satisfaction. When Hermite was 49 years old, Paris University asked him to be a professor. In the next twenty-five years, almost all the great French mathematicians came from his door. We don't know how he attends classes, but one thing is certain-there is no exam.
Understanding another world in trigonometric geometry
Failure to pass the exam brought him a lot of troubles: his work was not smooth, he retaken the exam many times, others looked down on him and he felt inferior. But it brought him many blessings: knowing his wife, friends, beliefs and the maturity of his whole life. Later, Bell, a professor of mathematics at California Institute of Technology, described Hermite in a passage in "Review of Great Mathematicians in History": The more talented mathematicians in history, the more cynical they are, and the more ironic they speak. There is only one exception, that is, Hermite, who has a truly perfect personality. Hermite died on190165438+1October 4th. In his later years, he wrote: "Trigonometric geometry is immortal. Nothing in nature is an absolute triangle, but there is a perfect absolute triangle in human mind to measure the external shape. Nobody knows why the sum of triangles is 180, and nobody knows why the longest hypotenuse of a triangle corresponds to the largest angle. These basic features of trigonometric geometry were not invented or imagined by people, but existed when people were ignorant, and will not change no matter how time and space change. I'm just a person who stumbled across these features. The existence of triangular geometry proves that there is a world that will never change. "
1858, the Scottish antique collector Rand bought a roll of ancient Egyptian papyrus on the Nile River in Africa. He was surprised to find that there was some obvious evidence in this papyrus scroll left around 1600 BC, indicating that the ancient Egyptians had been dealing with some algebraic problems as early as 1700 BC. Since the reign of Pharaoh in ancient Egypt, people have been seeking the same mathematical goal: to solve a mathematical problem with unknowns. There are some unknown mathematical problems on this papyrus scroll, which are of course represented by hieroglyphics. For example, there is a question translated into mathematical language:
"Aha, all, all, its sum is equal to 19."
The "aha" here was unknown to the ancient Egyptians at that time. If this unknown number is represented by X, the problem is transformed into an equation. To solve this equation, you must.
What is even more surprising is that the ancient Egyptians got this answer even though they didn't have the expression of the equation we use today.