In the process of growing up, young Gauss mainly paid attention to his mother and uncle. Gauss's grandfather was a stonemason who died of tuberculosis at the age of 30, leaving two children: Gauss's mother Luo Jieya and his uncle Flier. Flier Ritchie is smart, enthusiastic, intelligent and capable, and has made great achievements in textile trade. He found his sister's son clever, so he spent part of his energy on this little genius and developed Gauss's intelligence in a lively way. A few years later, Gauss, who was an adult and achieved great success, recalled what his uncle had done for him and felt that it was crucial to his success. He remembered his prolific thoughts and said sadly, "We lost a genius because of the death of our uncle". It is precisely because Flier Ritchie has an eye for talents and often persuades her brother-in-law to let her children develop into scholars that Gauss didn't become a gardener or a mason.
In the history of mathematics, few people are as lucky as Gauss to have a mother who strongly supports his success. Luo Jieya got married at the age of 34 and was 35 when she gave birth to Gauss. He has a strong personality, wisdom and sense of humor. Since his birth, Gauss has been very curious about all phenomena and things, and he is determined to get to the bottom of it, which is beyond the scope allowed by a child. When the husband reprimands the child for this, he always supports Gauss and resolutely opposes the stubborn husband who wants his son to be as ignorant as he is.
Luo Jieya sincerely hopes that his son can do something great and cherish Gauss's talent. However, he was afraid to put his son into mathematics research that could not support his family at that time. /kloc-when she was 0/9 years old, although Gauss had made many great achievements in mathematics, she still asked her friend W. Bolyai (the father of J. Bolyai, one of the founders of non-Euclidean geometry): Will Gauss have a future? W Bolyai said that her son would become "the greatest mathematician in Europe", and her eyes were filled with tears.
At the age of seven, Gauss went to school for the first time. Nothing special happened in the first two years. 1787 years old, Gauss 10. He entered the first math class. Children have never heard of such a course as arithmetic before. The math teacher is Buttner, who also played a certain role in the growth of Gauss.
According to a story widely circulated all over the world, Gauss's most famous story is that when he was ten years old, the primary school teacher gave an arithmetic problem: "Calculate 1+2+3 …+ 100 =?" . This is difficult for beginners of arithmetic, but Gauss solved the answer in a few seconds. He used the symmetry of arithmetic progression (arithmetic progression) and then put the numbers together like a general arithmetic progression sum: 1+ 100, 2+99, 3+98, ... 49+52. However, this is probably an untrue legend. According to the research of E·T· Bell, a famous mathematical historian who has studied Gauss, Butner gave the children a more difficult addition problem: 81297+81495+81693+…+100899.
Of course, this is also a summation problem of arithmetic progression (the tolerance is 198 and the number of items is 100). As soon as Butner finished writing, Gauss finished the calculation and handed in the small tablet with the answers written on it. E. T. Bell wrote that in his later years, Gauss often liked to talk about this matter with people, saying that only his answer was correct at that time, and all the other children were wrong. Gauss didn't specify how he solved the problem so quickly. Mathematical historians tend to think that Gauss had mastered arithmetic progression's summation method at that time. For a child as young as 10, it is unusual to discover this mathematical method independently. The historical facts described by Bell according to Gauss's own account in his later years should be more credible. Moreover, it can better reflect the characteristics that Gauss paid attention to mastering more essential mathematical methods since he was a child.
Gauss's computing ability, mainly his unique mathematical methods and extraordinary creativity, made Butner sit up and take notice of him. He specially bought Gauss the best arithmetic book from Hamburg and said, "You have surpassed me, and I have nothing to teach you." Then Gauss and Bater's assistant Bater established a sincere friendship until Bater died. They studied together and helped each other, and Gauss began real mathematics research.
1788, 1 1 year-old gauss entered a liberal arts school. In his new school, all his classes are excellent, especially classical literature and mathematics. On the recommendation of Bater and others, the Duke of zwick summoned Gauss, who was 14 years old. This simple, clever but poor child won the sympathy of the Duke, who generously offered to be Gauss' patron and let him continue his studies.
Duke Brunswick played an important role in Gauss's success. Moreover, this function actually reflects a model of scientific development in modern Europe, indicating that private funding was one of the important driving factors for scientific development before the socialization of scientific research. Gauss is in the transition period of privately funded scientific research and socialization of scientific research.
1792, Gauss entered Caroline College in Brunswick for further study. 1795, the duke paid various expenses for him and sent him to the famous University of G? ttingen in Germany, which made Gauss study hard and started creative research according to his own ideals. 1799, Gauss finished his doctoral thesis and returned to his hometown of Brunswick-Zwick. Just when he fell ill because he was worried about his future and livelihood-although his doctoral thesis was successfully passed, he was awarded a doctorate and obtained a lecturer position, but he failed to attract students, so he had to go back to his hometown and the duke gave him a helping hand. The Duke paid for the printing of Gauss's long doctoral thesis, gave him an apartment, and printed Arithmetic Research for him, so that the book could be published in 180 1. Also bear all the living expenses of Gauss. All this moved Gauss very much. In his doctoral thesis and arithmetic research, he wrote a sincere dedication: "To Dagong" and "Your kindness relieved me of all troubles and enabled me to engage in this unique research".
1806, the duke was killed while resisting the French army commanded by Napoleon, which dealt a heavy blow to Gauss. He is heartbroken and has long been deeply hostile to the French. The death of Dagong brought economic difficulties to Gauss, the misfortune that Germany was enslaved by the French army, and the death of his first wife, all of which made Gauss somewhat disheartened, but he was a strong man and never revealed his predicament to others, nor did he let his friends comfort his misfortune. It was not until19th century that people knew his state of mind at that time when sorting out his unpublished mathematical manuscripts. In a discussion of elliptic functions, a subtle pencil word was suddenly inserted: "For me, it is better to die than to live like this."
The generous and kind benefactor died, and Gauss had to find a suitable job to support his family. Because of Gauss's outstanding work in astronomy and mathematics, his fame spread all over Europe from 1802. The Academy of Sciences in Petersburg has continuously hinted that since Euler's death in 1783, Euler's position in the Academy of Sciences in Petersburg has been waiting for a genius like Gauss. When the Duke was alive, he strongly discouraged Gauss from going to Russia. He is even willing to raise his salary and set up an observatory for him. Now, Gauss is facing a new choice in life.
In order not to lose Germany's greatest genius, B.A. von von humboldt, a famous German scholar, joined other scholars and politicians to win Gauss the privileged positions of professor of mathematics and astronomy at the University of G? ttingen and director of the G? ttingen Observatory. 1807, Gauss went to Kottingen to take office, and his family moved here. Since then, he has lived in G? ttingen except for attending a scientific conference in Berlin. The efforts of Humboldt and others not only made the Gauss family have a comfortable living environment, but also enabled Gauss himself to give full play to his genius, and created conditions for the establishment of Gottingen Mathematics School and Germany to become a world science center and mathematics center. At the same time, it also marks a good beginning of scientific research socialization.
Gauss's academic position has always been highly respected by people. He has the reputation of "prince of mathematics" and "king of mathematicians" and is considered as "one of the three (or four) greatest mathematicians in human history" (Archimedes, Newton, Gauss or Euler). People also praised Gauss as "the pride of mankind". Genius, precocity, high yield, persistent creativity, ..., almost all the praises in the field of human intelligence are not too much for Gauss.
Gauss's research field covers all fields of pure mathematics and applied mathematics, and has opened up many new fields of mathematics, from the most abstract algebraic number theory to intrinsic geometry, leaving his footprints. Judging from the research style, methods and even concrete achievements, he is the backbone of 18- 19 century. If we imagine mathematicians in the18th century as a series of high mountains, the last awe-inspiring peak is Gauss; If mathematicians in the19th century are imagined as rivers, then their source is Gauss.
Although mathematical research and scientific work did not become an enviable career at the end of 18, Gauss was born at the right time, because the development of European capitalism made governments around the world pay attention to scientific research when he was almost 30 years old. With Napoleon's emphasis on French scientists and scientific research, Russian czars and many European monarchs began to look at scientists and scientific research with new eyes. The socialization process of scientific research is accelerating and the status of science is improving. As the greatest scientist at that time, Gauss won many honors, and many world-famous scientists regarded Gauss as their teacher.
1802, Gauss was elected as an academician of communication and a professor of Kazan University by the Academy of Sciences in Petersburg, Russia. 1877, the Danish government appointed him as a scientific adviser, and this year, the government of Hanover, Germany also hired him as a government scientific adviser.
Gauss's life is a typical scholar's life. He has always maintained the frugality of a farmer, making it hard to imagine that he is a great professor and the greatest mathematician in the world. He was married twice, and several children annoyed him. However, these have little influence on his scientific creation. After gaining a high reputation and German mathematics began to dominate the world, a generation of Tianjiao completed the journey of life.
In the photo processing software photoshop, there is a menu called Gaussian blur, which is very useful for blurring some unnecessary places. Gauss 1777~ 1855 was born in Brunswick, north-central Germany. His grandfather is a farmer, his father is a mason, his mother is a mason's daughter, and he has a very clever brother, Uncle Gauss. He takes good care of Gauss and occasionally gives him some guidance, while his father can be said to be a "lout" who thinks that only strength can make money, and learning this kind of work is useless to the poor.
Gauss showed great talent very early, and at the age of three, he could point out the mistakes in his father's book. At the age of seven, I entered a primary school and took classes in a dilapidated classroom. Teachers are not good to students and often think that teaching in the backcountry is a talent. When Gauss was ten years old, his teacher took the famous "from one to one hundred" exam and finally discovered Gauss's talent. Knowing that his ability was not enough to teach Gauss, he bought a deep math book from Hamburg and showed it to Gauss. At the same time, Gauss is familiar with bartels, a teaching assistant who is almost ten years older than him. bartels's ability is much higher than that of the teacher. Later, he became a university professor, giving Professor Gauss more and deeper mathematics.
Teachers and teaching assistants went to visit Gauss's father and asked him to let Gauss receive higher education. But Gauss's father thought that his son should be a plasterer like him, and there was no money for Gauss to continue his studies. The final conclusion is-find a rich and powerful person to be his backer, although I don't know where to find it. After this visit, Gauss got rid of weaving every night and discussed mathematics with Bater every day, but soon there was nothing to teach Gauss in Bater.
1788, Gauss entered higher education institutions despite his father's opposition. After reading Gauss's homework, the math teacher told him not to take any more math classes, and his Latin soon surpassed the whole class.
179 1 year, Gauss finally found a patron-the Duke of Brunswick, and promised to help him as much as possible. Gauss's father had no reason to object. The following year, Gauss entered Brunswick College. This year, Gauss was fifteen years old. There, Gauss began to study advanced mathematics. Independent discovery of the general form of binomial theorem, quadratic reciprocity law in number theory, prime number theorem and arithmetic geometric average.
1795 gauss enters gottingen (g? Ttingen) university, because he is very talented in language and mathematics, so there was a time when he was worried about whether to specialize in classical Chinese or mathematics in the future. At the age of 1796 and 17, Gauss got an extremely important result in the history of mathematics. It was the theory and method of drawing regular heptagon ruler that made him embark on the road of mathematics.
Mathematicians in the Greek era already knew how to make a positive polygon of 2m×3n×5p with a ruler, where m is a positive integer and n and p can only be 0 or 1. However, for two thousand years, no one knew the regular drawing of regular heptagon, nonagon and decagon. Gauss proved that:
If and only if n is one of the following two forms, you can draw a regular n polygon with a ruler:
1、n = 2k，k = 2，3，…
2, n = 2k × (product of several different Fermat prime numbers), k = 0, 1, 2, …
Fermat prime number is a prime number in the form of Fk = 22k. For example, F0 = 3, F 1 = 5, F2 = 17, F3 = 257 and F4 = 65537 are all prime numbers. Gauss has used algebra to solve geometric problems for more than 2000 years. He also regarded it as a masterpiece of his life and told him to carve the regular heptagon on his tombstone. But later, his tombstone was not engraved with a heptagon, but with a 17 star, because the sculptor in charge of carving thought that a heptagon was too similar to a circle, so people would be confused.
1799, Gauss submitted his doctoral thesis and proved an important theorem of algebra:
Any polynomial has (complex) roots. This result is called "Basic Theorem of Algebra".
In fact, many mathematicians think that the proof of this result was given before Gauss, but none of them is rigorous. Gauss pointed out the shortcomings of previous proofs one by one, and then put forward his own opinions. In his life, he gave four different proofs.
180 1 year. At the age of 24, Gauss published "Problem Arithmetic AE" written in Latin. There were eight chapters originally, but he had to print seven chapters because of lack of money. This book is all about number theory except the basic theorem of algebra in Chapter 7. It can be said that it is the first systematic work on number theory, and Gauss introduced the concept of "congruence" for the first time. "Quadratic reciprocity theorem" is also among them.
At the age of 24, Gauss gave up the study of pure mathematics and studied astronomy for several years.
At that time, the astronomical community was worried about the huge gap between Mars and Jupiter, and thought that there should be planets between Mars and Jupiter that had not been discovered. 180 1 year, Italian astronomer Piazi discovered a new star between Mars and Jupiter. It was named Cere. Now we know that it is one of the asteroid belts of Mars and Jupiter, but at that time, there was endless debate in the astronomical circles. Some people say it's a planet, others say it's a comet. We must continue to observe to judge, but Piazi can only observe its 9-degree orbit, and then it will disappear behind the sun. So it is impossible to know its orbit, and it is impossible to determine whether it is a planet or a comet.
Gauss became interested in this problem at this moment, and he decided to solve this elusive star trajectory problem. Gauss himself created a method to calculate the orbits of planets with only three observations. He can predict the position of the planets very accurately. Sure enough, Ceres appeared in the place predicted by Gauss. This method-although it was not announced at that time-was the "least square method".
1802, he accurately predicted the position of the asteroid II Pallas Athena. At this time, his reputation spread far and wide, and honor rolled in. Russian Academy of Sciences in St. Petersburg elected him as an academician. Olbers, the astronomer who discovered pallas, asked him to be the director of the G? ttingen Observatory. He didn't agree immediately and didn't go to Gottingen until 1807.
1809, he wrote two volumes on the motion of celestial bodies. The first volume contains differential equations, circular spine parts and elliptical orbits. The second volume shows how to estimate the orbits of planets. Most of Gauss's contributions to astronomy were before 18 17, but he kept observing until he was seventy years old. Although doing the work of the observatory, he took time out to do other research. In order to solve the differential force path of celestial motion by integral, he considered infinite series and studied its convergence. 18 12 years, he studied hypergeometric series, and wrote his research results into a monograph and presented them to the Royal Academy of Sciences in G? ttingen.
From 1820 to 1830, Gauss began to do geodesy in order to draw a map of Hanover Principality (where Gauss lived). He wrote a book about geodesy, and because of the need of geodesy, he invented the heliograph. In order to study the earth's surface, he began to study the geometric properties of some surfaces.
1827, he published "Solving General Circa Superficies Curva", which covered some "differential geometry" he studied in university now.
During the period from 1830 to 1840, Gauss and Withelm Weber, a young physicist 27 years younger than him, were engaged in magnetic research. Their cooperation is ideal: Weber did experiments and Gauss studied theories. Weber aroused Gauss's interest in physical problems, while Gauss used mathematical tools to deal with physical problems, which influenced Weber's thinking and working methods.
1833, Gauss pulled an 8,000-foot-long wire from his observatory, passed through the roofs of many people, and arrived at Weber's laboratory. Using Volt battery as power supply, he built the world's first telegraph.
1835, Gauss set up a geomagnetic observatory at the Observatory and organized the "Magnetism Association" to publish the research results, which promoted the research and measurement of geomagnetism in many parts of the world.
Gauss got an accurate geomagnetic theory. In order to obtain the proof of experimental data, his book General Theory of Geomagnetism was not published until 1839.
1840, he and Weber drew the world's first map of the earth's magnetic field, and determined the positions of the earth's magnetic south pole and magnetic north pole. 184 1 year, American scientists confirmed Gauss's theory and found the exact positions of the magnetic south pole and the magnetic north pole.
Gauss's attitude towards his work is to strive for perfection, and he is very strict with his own research results. He himself once said: I would rather publish less, but I publish mature results. Many contemporary mathematicians asked him not to be too serious, and to write and publish the results, which is very helpful for the development of mathematics. One of the famous examples is about the development of non-Euclidean geometry. There are three founders of non-Euclidean geometry, namely Gauss, Lobachevski (1793 ~ 1856) and Bolyai (Boei, 1802 ~ 1860). Among them, Bolyai's father is a classmate of Gauss University. He tried to prove the parallel axiom. Although his father opposed him to continue this seemingly hopeless research, Bolyai Jr. was addicted to parallel axioms. Finally, non-Euclidean geometry is developed, and the research results are published in 1832 ~ 1833. Old Bolyai sent his son's grades to his old classmate Gauss, but he didn't expect Gauss to write back:
Dressing means dressing myself. I can't praise him, because praising him means praising myself. As early as several decades ago, Gauss had obtained the same result, but he was afraid that this result would not be accepted by the world and was not published. The famous American mathematician Bell (E.T.Bell) once criticized Gauss in his book Mathematicians:
Only after Gauss's death did people know that he had foreseen some mathematics in the19th century, and had predicted that they would appear before 1800. If he can reveal what he knows, it is likely that mathematics will be half a century or even earlier than it is now. Abel and jacoby can start from where Gauss stayed, instead of spending their best efforts on discovering what Gauss knew at birth. Those creators of non-Euclidean geometry can apply their genius to other aspects.
1On the morning of February 23rd, 855, Gauss died peacefully in his sleep.
[2] Physical unit
Gauss (g), non-international unit of magnetic induction intensity. Named in memory of German physicist and mathematician Gauss.
If a wire is placed in a magnetic field with uniform magnetic induction intensity, a constant current of 1 emu (equal to 10 amp) flows in a long straight wire perpendicular to the direction of magnetic induction intensity, and the electromagnetic force is 1 dyne per centimeter of wire, the magnetic induction intensity is defined as 1 gauss.
Gauss is a very small unit, and 10000 gauss is equal to 1 Tesla.
supplement
Gauss is a German mathematician and scientist. He, Newton and Archimedes are considered as the three greatest mathematicians in history. Gauss is one of the founders of modern mathematics, and he has a great influence in history. He can be juxtaposed with Archimedes, Newton and Euler, and is known as the "prince of mathematics".
He showed superhuman mathematical genius when he was young. 1795 entered the University of G? ttingen. The next year, he discovered the regular drawing of regular heptagon. The condition that a ruler can be used as a regular polygon is given, and the unsolved problem since Euclid is solved.
Gauss's mathematical research covers almost all fields and has made pioneering contributions in number theory, algebra, non-Euclidean geometry, complex variable function, differential geometry and so on. He also applied mathematics to the study of astronomy, geodesy and magnetism, and invented the principle of least square method. Korea's research on number theory was summarized in Arithmetic Research (180 1), which laid the foundation of modern number theory. It is not only an epoch-making work in number theory, but also one of the rare classic works in the history of mathematics. Gauss's important contribution to algebra is to prove the basic theorem of algebra, and his existence proof opens up a new way of mathematical research. Gauss got the principle of non-Euclidean geometry around 18 16. He also deeply studied the complex variable function, established some basic concepts and discovered the famous Cauchy integral theorem. He also discovered the double periodicity of elliptic functions, but these works were not published before his death. 1828, Gauss published "General Theory of Surfaces", which comprehensively and systematically expounded the differential geometry of spatial surfaces and put forward the theory of intrinsic surfaces. Gaussian surface theory was later developed by Riemann. Gauss published 155 papers in his life. He is very strict with his studies and only publishes what he thinks is mature. His works include the concept of geomagnetism and the law of universal gravitation. Repulsion is inversely proportional to the square of distance.
Gauss's most famous story is that when he was ten years old, the primary school teacher gave an arithmetic problem: "Calculate 1+2+3 …+ 100 =?" . This is difficult for beginners of arithmetic, but Gauss solved the answer in a few seconds. He used the symmetry of arithmetic progression (arithmetic progression) and then put the numbers together like a general arithmetic progression sum: 1+ 100, 2+99, 3+98, ... 49+52.
In 180 1 year, Gauss had the opportunity to dramatically demonstrate his superb computing skills. On New Year's Day that year, a celestial body named Ceres was discovered, which was later proved to be an asteroid. At that time, it seemed to be approaching the sun. Although astronomers have 40 days to observe it, they can't calculate its orbit. After only three observations, Gauss proposed a method to calculate the orbital parameters, and the accuracy achieved enabled astronomers to reposition Ceres at the end of 180 1 and the beginning of 1802 without any difficulty. In this calculation method, Gauss used the least square method he created in about 1794 (a method that can get the best estimate from the minimum sum of variance in a specific calculation), and this method was recognized in astronomy. The method described in his celestial motion theory is still used today, and it can meet the requirements of modern computers with a little modification. Gauss achieved similar success on the asteroid "Pallas Athena".
Because of his outstanding research achievements in mathematics, astronomy, geodesy and physics, Gauss was elected as a member of many academies and academic groups. The title of "King of Mathematics" is an appropriate tribute to his life.