Eight-year-old Gauss discovered the mathematical theorem
The famous German scientist Gauss (1777~1855) was born in a poor family. Gauss learned calculations on his own before he could speak. When he was three years old, one night he watched his father calculating wages and corrected his father's calculation errors.
When he grew up, he became the most outstanding astronomer and mathematician of our time. He made some contributions to electromagnetism in physics, and now a unit of electromagnetism is named after him. Mathematicians call him the "Prince of Mathematics".
When he was eight years old, he entered a rural primary school. The math teacher was a man from the city. He felt that teaching a few little hozens to read in a remote rural area was really overkill. And he has some prejudices: poor children are born stupid, and there is no need to teach these stupid children to study seriously. If there is an opportunity, they should be punished to add some fun to this boring life.
This is a dark day for math teachers. When the students saw the teacher's depressed face, they shrank inwardly, knowing that the teacher would catch and punish these students again today.
"You will calculate the sum from 1 plus 2 plus 3 to 100 for me today. Whoever cannot calculate will be punished and cannot go home for lunch." After the teacher said this, he remained silent. Fa picked up a novel and sat on a chair to read it.
The children in the classroom picked up the slate and began to count: "1 plus 2 equals 3, 3 plus 3 equals 6, 6 plus 4 equals 10..." Some children erased the slate after adding a number. If you add the above results, the number will become larger and larger, which is very difficult to calculate. Some children's faces turned red, and some had sweat on their palms and foreheads.
Less than half an hour later, little Gauss picked up his slate and stepped forward. "Teacher, is this the answer?"
The teacher didn't even raise his head, waved his fat hand and said, "Go, calculate again when you get back! Wrong." He thought it would not be possible so soon. There is an answer.
But Gauss stood still and stretched out the slate in front of the teacher: "Teacher! I think this answer is right."
The math teacher wanted to roar, but after a while Seeing the number written neatly on the slate: 5050, he was surprised, because he had calculated it himself and the number he got was also 5050. How did this 8-year-old kid get this value so quickly?
Gauss explained a method he discovered, which was the method used by the ancient Greeks and Chinese to calculate the series 1+2+3+…+n. Gauss's discovery made the teacher feel ashamed and felt that his previous views of being arrogant and contemptuous of children from poor families were wrong. He also started teaching seriously in the future, and often bought some mathematics books from the city to study by himself and lent them to Gauss. With his encouragement, Gauss later conducted some important research in mathematics.
Little Euler cleverly changed the sheepfold
Euler is a famous mathematician in the history of mathematics. He was active in several branches of mathematics such as number theory, geometry, astronomical mathematics, and calculus. Both have achieved outstanding results. However, this great mathematician was not liked by his teachers at all when he was a child. He was a primary school student who was expelled from the school.
Things are caused by stars. At that time, little Euler was studying in a mission school. Once, he asked the teacher how many stars there were in the sky. The teacher is a believer in theology. He does not know how many stars there are in the sky, and the Bible does not answer this question. In fact, the stars in the sky are countless and infinite. There are thousands of stars visible to our naked eyes. The teacher didn't understand and pretended to understand, so he replied to Euler: "It doesn't matter how many stars there are in the sky. It's enough to know that the stars in the sky are inlaid by God."
Euler felt very Strange: "The sky is so big, so high, and there are no escalators on the ground. How did God put the stars on the canopy one by one? God himself put them on the canopy one by one. Why did he forget the stars? What about the number? Could God be too careless?
He asked the teacher the question in his mind. The teacher was stunned again and blushed, not knowing how to answer. Anger suddenly arose in my heart, not only because a child who had just started school asked the teacher such a question, which made the teacher unable to step down, but more importantly, the teacher actually valued God above all else. Blaming God for not remembering the number of stars implies doubting the omnipotence of God. In the mind of the teacher, this was a serious problem.
In Euler's time, it was absolutely true. There is no doubt that people can only be slaves to their thoughts and are absolutely not allowed to think freely. When little Euler failed to "be consistent" with the church and God, the teacher asked him to leave school and go home. However, in little Euler's heart, God. The divine halo disappeared. He thought, God is a loser. Why can't he remember the stars in the sky? He also thought, God is a dictator, and even asking questions has become a sin. He also thought, God may be someone who made it up. The guy who came out didn't exist at all.
After he returned home and had nothing to do, he helped his father herd the sheep and became a shepherd boy. He read a lot of mathematics while tending the sheep. Book.
Dad’s flock gradually increased, reaching 100. The original sheepfold was a bit small, so Dad decided to build a new sheepfold.
He measured a rectangular piece of land with a ruler, 40 meters long and 15 meters wide. He calculated that the area was exactly 600 square meters, and each sheep occupied an average of 6 square meters. When he was about to start construction, he found that he only had enough materials to surround a 100-meter fence, which was not enough. If you want to enclose a sheepfold that is 40 meters long and 15 meters wide, its circumference will be 110 meters (15+15+440=110). My father felt very embarrassed. If he wanted to build it according to the original plan, he would have to add another 10 meters. long material; if the area is reduced, the area of ??each sheep will be less than 6 square meters.
Little Euler told his father that there was no need to shrink the sheepfold, and there was no need to worry that each sheep’s territory would be smaller than originally planned. He has a solution. His father didn't believe that little Euler could do anything, so he ignored him. Little Euler became anxious and said loudly that all he had to do was move the stakes of the sheepfold slightly.
After hearing this, his father shook his head and thought: "How can there be such a cheap thing in the world?" However, little Euler insisted that he would get the best of both worlds. The father finally agreed to let his son give it a try.
When little Euler saw that his father agreed, he stood up and ran to the sheepfold where construction was about to begin. He used a wooden stake as the center and shortened the original 40-meter side length to 25 meters. The father was anxious and said, "How can it be done? How can it be done? This sheepfold is too small, too small." Little Euler did not answer, but ran to the other side and stretched the original 15-meter side. It was extended and added another 10 meters to 25 meters. After such changes, the originally planned sheepfold became a square with a side length of 25 meters. Then, little Euler confidently said to his father: "Now, the fence is enough, and the area is enough."
Father put up a fence according to the sheepfold designed by little Euler, 100 meters The long fence is really enough, no more, no less, all used up. The area is sufficient and slightly larger. My father felt very happy. If your child is smarter than you and can really use your brain, he will definitely be very successful in the future.
The father felt that it was a pity to let such a smart child herd sheep. Later, he tried to get little Euler to meet Bernoulli, a great mathematician. Through the recommendation of this mathematician, little Euler became a college student at the University of Basel in 1720. This year, little Euler was 13 years old and the youngest college student in this university.
Serving the Motherland’s Ambition------The Story of Hua Luogeng
Students all know that Hua Luogeng is a world-class mathematician who is self-taught. He only had a junior high school diploma. After publishing a paper in the magazine "Science", he was appreciated by the mathematician Xiong Qinglai. From then on, Hua Luogeng went north to Tsinghua University and began his career in mathematics.
In 1936, upon the recommendation of Professor Xiong Qinglai, Hua Luogeng went to England to study in Cambridge. Hardy, a famous mathematician in the 20th century, had long heard that Hua Luogeng was very talented. He said: "You can get a doctorate in two years." But Hua Luogeng said: "I don't want to get a doctorate. I only ask for a visit." "I came to Cambridge to learn, not to get a degree." In two years, he concentrated on the theory of stacked prime numbers and published 18 papers on the Waring problem, the Talley problem, and the odd Goldbach problem. The famous "Fahrenheit's Theorem" was derived, showing the outstanding wisdom and ability of Chinese mathematicians to the world.
In 1946, Hua Luogeng was invited to give lectures in the United States and was hired as a tenured professor at the University of Illinois with a high salary. His family also came to the United States to settle down, with a house and a car, and they lived a very comfortable life. At that time, many people thought that Hua Luogeng would not come back.
The birth of New China touched the heart of Hua Luogeng, who loved the motherland. In 1950, he resolutely gave up his wealthy life in the United States and returned to his motherland. He also wrote an open letter to Chinese students studying in the United States, mobilizing them to return to China and participate in socialist construction. In his letter, he revealed his pure love for China: "Friends! Although Liangyuan is good, it is not the hometown where I have lived for a long time. I am coming back... For the sake of the country and the nation, we should go back..." Although mathematics has no national boundaries , but mathematicians have their own motherland.
Hua Luogeng returned from overseas and was warmly welcomed by the party and the people. He returned to Tsinghua University and was appointed director of the Department of Mathematics, and was soon appointed director of the Institute of Mathematics, Chinese Academy of Sciences. From then on, the real golden period of his mathematical research began. Not only did he continuously make outstanding achievements that attracted world attention, he also enthusiastically cared for and trained a large number of mathematical talents. In order to win the crown jewel of mathematics, he devoted a lot of effort to the research, experiment and promotion of applied mathematics.
According to incomplete statistics, Hua Luogeng *** published 152 important mathematics papers, 9 mathematics books, and 11 mathematics popular science books in the past few decades. He was also elected as a foreign member of the Academy of Sciences and an academician of Third World Scientists.
From graduating from junior high school to becoming the People’s Mathematician, Hua Luogeng has gone through a tortuous and glorious life path and won great honors for his motherland.
Archimedes (about 287~212 BC)
——Greek physicist and mathematician.
Archimedes’ father was an astronomer and mathematician. He received a good education since he was a child and especially loved mathematics. Once, the king asked him to determine whether the crown the goldsmith had just made for him was pure gold or a mixture mixed with silver, and warned him not to damage the crown. At first, Archimedes was at a loss.
Until one day, when he soaked in a full basin of bath water, the volume of the overflowing water was equal to the volume of the part of his body immersed in the water. Then, if the crown is immersed in water and the volume of the crown is equal to the volume of gold of equal weight based on the rise of the water surface, it means that the crown is pure gold; if it is mixed with silver, the volume of the crown will be larger. He excitedly jumped out of the bathtub and ran to the palace naked, shouting: "I found it! I found it!" He invented the principle of buoyancy for this purpose. In addition, he also discovered the famous lever principle. Along with this invention, there was also a well-known saying: "As long as you give me a fulcrum, I can move the earth."
In Archimedes' old age, his motherland and There was a war in Rome. When the city where he lived was plundered, Archimedes was still studying the geometric figures he drew on the sand. The ferocious Roman soldiers stabbed the 75-year-old man to death, and the great scientist fell to the ground. On the geometric figures stained red by blood...
After Archimedes' death, people compiled and published "The Complete Works of Archimedes" to forever commemorate the great achievements of this scientific giant.
Newton (1642～1727)
Newton was a British physicist and mathematician. Served as President of the Royal Society.
Newton is universally recognized as one of the greatest scientists of all time. His childhood was full of bitterness. His father died 3 months before he was born, and his mother remarried. He was raised by his maternal grandmother. 23 After graduating from the famous Cambridge University, he stayed at school to work. Later, he came to his mother's farm to escape the plague in London. Here, he was attracted by a phenomenon that ordinary people turned a blind eye to. Once, he saw a ripe apple falling to the ground, and he began to wonder why the apple fell vertically to the ground instead of flying into the sky. There must be a force pulling it, so could this force pulling the apple down control the moon? It was through this seemingly simple phenomenon that he discovered the famous law of universal gravitation. The huge role of this law was quickly revealed. It explained all the movements of celestial bodies known at that time. At the same time, Newton completed an important optical experiment, which proved that white light is composed of synthetic light arranged in the order of red, orange, yellow, green, cyan, blue and violet. In 1687, Newton published the greatest scientific work of all time, Principia Mathematica. Here, he studied Galileo's theories and summarized the famous three laws of motion. In addition, the binomial theorem he discovered also has a place in the world of mathematics. In 1704, he published the book "Optics", which summarized the results of his optical research.
When Newton was 61 years old, he was elected president of the Royal Society and was re-elected every year until his death. As the most outstanding scientific giant recognized by the world, he still said humbly: "If I can see further than others, it is because I stand on the shoulders of giants." March 20, 1727, 84 years old Newton passed away. As a great man who contributed to the country, he was buried in the British National Cemetery and was respected by the world.
Euler (1707～1783)
Euler was a Swiss mathematician and a member of the Royal Society.
Euler was obsessed with mathematics since he was a child and was an out-and-out mathematical genius. He became a student at the famous University of Basel at the age of 13, received a master's degree at the age of 16, and was promoted to professor at the age of 23. In 1727, he was invited to work at the Academy of Sciences in St. Petersburg, Russia. Excessive exertion caused him to go blind. However, this did not affect his work. Euler had an amazing memory. Hydrogen said that a fire in St. Petersburg in 1771 reduced his large collection of books and manuscripts to ashes. With his amazing memory, he dictated and published more than 400 papers and many books. Euler, a mathematical superstar in the 18th century, made great contributions in the fields of calculus, differential equations, geometry, number theory, variations, etc., thus confirming his status as the founder of the calculus of variations and the pioneer of complex functions. . At the same time, he was also an excellent popular science writer, and his popular science books were continuously reprinted for 90 years. Euler was the most prolific mathematician of all time. It is said that the precious cultural legacy he left behind was enough to keep all the printing presses in St. Petersburg busy for several years at the same time.
As one of the four mathematicians who have made the greatest contributions to mathematics in history (the other three are Archimedes, Newton, and Gauss), Euler is known as the "Shakespeare of mathematics".
Gauss (1777～1855)
Gauss was a German mathematician, physicist and astronomer, and a member of the Royal Society.
Gauss was the son of a farmer. When he was young, he showed extraordinary talent in mathematics. At the age of 3, he could correct his father's calculation errors; at the age of 10, he independently discovered the summation formula of arithmetic series; at the age of 11, he discovered the binomial theorem. The young Gauss's intelligence and precociousness won the favor and support of the prestigious Duke of Brick, which enabled him to continue his studies. Not long after entering university, the 19-year-old Gauss invented a method of making a regular 17-sided polygon using only a compass and a ruler, solving a geometric problem that had remained unresolved for two thousand years. In 1801, he published "Researches in Arithmetic", which elaborated on certain issues in number theory and advanced algebra. He made significant contributions to hypergeometric series, complex functions, statistical mathematics, and elliptic function theory.
As a physicist, he collaborated with William Weber to study electromagnetism and invented the electrode. In order to conduct experiments, Gauss also invented the double-wire magnetometer, which was a very practical result of his research on electromagnetic problems. At the age of 30, Gauss served as the director of the Observatory of a famous German university and worked at the observatory until his death. He also enjoyed literature and linguistics throughout his life and knew more than a dozen foreign languages. During his lifetime, he published 323 works (kinds), proposed 404 scientific innovations, and completed 4 important inventions.
After Gauss's death, people erected a statue of him in the city where he was born. To commemorate his discovery of the method of making a 17-sided figure, the base of the statue was shaped into a 17-sided shape. The world recognizes him as a mathematician as famous as Newton, Archimedes and Euler.
Zu Chongzhi (429～500)
A mathematician, astronomer and physicist in the Southern and Northern Dynasties of China. Fan Yangqiu (now Laishui, Hebei Province)
The grandfather of Zu Chongzhi (429-500) was named Zuchang, and he was an official in charge of court buildings in the Song Dynasty. Zu Chongzhi grew up in such a family and read many books since he was a child. People praised him as a learned young man. He was particularly fond of studying mathematics and astronomy and calendars. He often observed the movements of the sun and planets and made detailed records.
Emperor Xiaowu of the Song Dynasty heard about his reputation and sent him to work in the "Hualin Academic Province", an official agency specializing in academic research. He was not interested in being an official, but there he could concentrate more on studying mathematics and astronomy.
There have been officials who studied astronomy in all dynasties in our country, and calendars were formulated based on the results of astronomical research. By the time of the Song Dynasty, the calendar had made great progress, but Zu Chongzhi thought it was not accurate enough. Based on the results of his long-term observations, he created a new calendar called the "Daming Calendar" ("Daming" is the reign name of Emperor Xiaowu of the Song Dynasty). The number of days in each tropical year (that is, the time between two winter solstice points) measured by this calendar is only fifty seconds different from that measured by modern science; the number of days it takes for the moon to circle around is no different from that measured by modern science. For a second, you can see how accurate it is.
In 462 AD, Zu Chongzhi asked Emperor Xiaowu of the Song Dynasty to promulgate a new calendar, and Emperor Xiaowu convened ministers for discussion. At that time, Dai Faxing, a favored minister of the emperor, came out to object, believing that Zu Chongzhi's unauthorized change of the ancient calendar was an act of deviance. Zu Chongzhi used the data he studied to refute Dai Faxing on the spot. Dai Faxing relied on the emperor's favor and said arrogantly: "The calendar was established by the ancients and should not be changed by future generations." Zu Chongzhi was not afraid at all. He said solemnly: "If you have factual basis, just use it to argue. Don't scare people with empty words." Emperor Xiaowu of Song Dynasty wanted to help Dai Faxing, so he found some people who knew the calendar to argue with Zu Chongzhi, but they were all refuted by Zu Chongzhi. . However, Emperor Xiaowu of Song Dynasty still refused to promulgate the new calendar. It was not until ten years after Zu Chongzhi's death that the Daming Calendar created by him was implemented.
Although the society was very turbulent at that time, Zu Chongzhi still studied science tirelessly. His greater achievement was in mathematics. He once commented on the ancient mathematical work "Nine Chapters on Arithmetic" and compiled a book "Zhu Shu". His most outstanding contribution was the fairly accurate calculation of pi. After long-term and painstaking research, he calculated that pi was between 3.1415926 and 3.1415927, becoming the first scientist in the world to calculate pi to more than seven digits.
Zu Chongzhi was a versatile man in scientific inventions. He built a compass. No matter how the car turned, the bronze figure on the car always pointed to the south; he also built the "Thousand-mile Ship", which is located in Xinting After trial navigation on the Yangtze River (southwest of today's Nanjing City), it could sail more than a hundred miles a day. He also used water power to turn stone mills and pound rice to grind millet, which was called "water mill".
In Zu Chongzhi's later years, Xiao Daocheng, who controlled the imperial guards of the Song Dynasty, destroyed the Song Dynasty.
Hua Luogeng (1910～1985)
Chinese mathematician, mathematics educator, academician of the Chinese Academy of Sciences, native of Jintan, Jiangsu.
Hua Luogeng's father was a small business owner who ran a grocery store. Due to the bleak business and the deterioration of his family's financial situation, Hua Luogeng dropped out of middle school and became a bookkeeper in a grocery store. In the tedious and monotonous work, he did not give up his biggest hobby-mathematical research. While he was studying hard on his own, disaster struck from the sky - he contracted the terrible typhoid fever and was sentenced to "death" by the doctor. However, he miraculously survived, but his left leg became permanently disabled. What he often talks about is this sentence: "The so-called genius is based on persistent efforts." This mathematician without a college diploma relied on unremitting efforts and hard self-study. In 1930, with "Su Jiaju" The paper "The Reasons Why the Algebraic Quintic Equation Cannot Be Established" made the Chinese mathematics community look with admiration. Later, he was recommended by Professor Xiong Qinglai to serve as a teaching assistant in the Department of Mathematics, Tsinghua University. Here, thanks to the guidance of Xiong Qinglai and Yang Wuzhi, he made great academic progress and gradually established his position in the world of mathematics. In 1948, he was invited by a university in the United States to teach. After the founding of New China, he resolutely gave up the superior working and living conditions, returned to China with his wife and children, and served as a professor in the Department of Mathematics at Tsinghua University and later as the director of the Institute of Mathematics of the Chinese Academy of Sciences.
He attached great importance to and advocated the application of mathematical theory to production practice, and personally organized and promoted the "optimization method" and "coordination method", so that they showed great power in the socialist modernization drive. He worked diligently throughout his life and published more than 200 academic papers and 10 monographs. As a mathematics educator, he trained a number of outstanding mathematicians such as Chen Jingrun, Wang Yuan, and Lu Qikeng, and formed the Chinese School of Mathematics, some of whom have become world-class mathematicians.
On June 12, 1985, Hua Luogeng died of a sudden myocardial infarction while giving a lecture in Japan. He was 75 years old. Hua Luogeng, who encouraged himself throughout his life by saying that "the greatest hope is to work until the last moment of his life", will always live in the hearts of the people.
Chen Jingrun (1933～1966)
Chinese mathematician and academician of the Chinese Academy of Sciences. A native of Minhou, Fujian.
Chen Jingrun was born in a family of clerks, with an older brother and younger siblings, ranking third. Because there are many children in the family and the father's income is meager, family life is very tight. Therefore, Chen Jingrun seemed to be a burden to his parents as soon as he was born, a person who considered himself unwelcoming. After going to school, he was often bullied because he was thin and weak. This special living situation shaped him into an extremely introverted person who was not good at talking. Coupled with his obsession with mathematics, he developed the habit of being alone and thinking behind closed doors. Therefore, he was actually Others think of him as a "weird". Chen Jingrun chose to study mathematics, an extremely difficult life path, because of Professor Shen Yuan. It was there that Chen Jingrun learned about Goldbach's conjecture for the first time, and it was from there that Chen Jingrun determined to pick the crown jewel of mathematics from the first moment. In 1953, he graduated from Xiamen University and stayed at the school to work in the library. However, he never forgot Goldbach's conjecture. He sent his mathematics paper to Professor Hua Luogeng. After reading it, Hua Luogeng appreciated his talent very much and transferred him to the Department of Mathematics of the Chinese Academy of Sciences. He worked as an intern researcher at the institute, and from then on he was fortunate enough to work towards Goldbach's conjecture under the guidance of Hua Luogeng. In May 1966, a dazzling new star shone over the world of mathematics - Chen Jingrun announced that he had proved the "1+2" ??in Goldbach's conjecture; in February 1972, he completed the verification of "1 +2"Proof of modification. What is unbelievable is that foreign mathematicians used large high-speed computers to prove "1+3", while Chen Jingrun relied entirely on paper, pen and head. If this is puzzling, the six sacks of manuscript paper he used just to simplify the "1+2" ??proof are enough to explain the problem. In 1973, he published the famous "Chen's Theorem", which is hailed as the glorious pinnacle of the sieve method.
For Chen Jingrun’s achievements, a famous foreign mathematician once admired and praised Chen Jingrun with emotion: He moved mountains!
Neumann
Neumann (1903~1957), a Hungarian-American mathematician and an academician of the American Academy of Sciences.
Neumann was born in a family of Jewish bankers and was a rare child prodigy. He mastered calculus at the age of 8 and read "Theory of Functions" at the age of 12. There was such an interesting story on the way he grew up: In the summer of 1913, the banker Mr. Max published a revelation that he was willing to hire a teacher for his 11-year-old eldest son Neumann at 10 times the salary of an ordinary teacher. Tutor. Although this alluring revelation has made many people's hearts flutter, no one dared to teach such a well-known prodigy... After receiving his Ph.D. in Physics-Mathematics at the age of 21, he began multidisciplinary research, first in mathematics. , mechanics, physics, then moved to economics, meteorology, then to atomic bomb engineering, and finally, devoted to the research of electronic computers. All this made him an out-and-out scientific all-rounder. His main achievement was mathematical research. He has made important contributions in many branches of advanced mathematics. His most outstanding work is to open up a new branch of mathematics--game theory. In 1944, he published his outstanding book "Game Theory and Economic Behavior". During World War II, he made important contributions to the development of the first atomic bomb. After the war, he used his mathematical skills to guide the construction of large-scale electronic computers and was hailed as the father of electronic computers.