Gauss (C.F. Gauss,1777.4.30-1855.2.23) is a German mathematician, physicist and astronomer, who was born in a poor family in Zwick, Germany. His father Gerchard de Derrych worked as a berm, bricklayer and gardener. His first wife lived with him for more than 65,438+00 years and died of illness, leaving him no children. Diderich later married Luo Jieya, and the next year their child Gauss was born, which was their only child. My father is extremely strict with Gauss, even a little too strict. He often likes to plan his life for the young Gauss according to his own experience. Gauss respected his father and inherited his honest and cautious character. De Derrick died in 1806, when Gauss had made many epoch-making achievements.

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.

A story that is widely circulated all over the world says that when Gauss was at 10, by adding all the integers from 1 to 100, he worked out the arithmetic problem that Butner gave to the students. As soon as Butner described the question, Gauss got the correct answer. 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 German family in G? ttingen, 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 Bren-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 and had to return to his hometown-the duke extended 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 make Germany lose its greatest genius, the famous German scholar Humboldt (B.A.Von

Humboldt), together with other scholars and politicians, won 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.

2. Swiss mathematician Leonard Euler

Swiss mathematician Leonard Euler (1707- 1783) has made outstanding contributions to mankind all his life, leaving 886 papers and works, leaving his footprints in almost every department of mathematics.

"Wisdom comes from labor, genius comes from diligence", and the golden flower of wisdom will not bloom for lazy people. 1735, when Euler was only 28 years old, one eye was blind. 1766, the other eye was blind, but he still engaged in mathematical research with great perseverance. His research work is rich and outstanding. In his later years, he dictated his findings and asked others to write them down, which wrote many glorious chapters for the history of human civilization.

Among Euler's 886 works, 530 are books and papers published before his death, many of which are textbooks.

Because the writing is simple, easy to understand and fascinating, it is not difficult to read even today. What is particularly worth mentioning is that the plane triangle textbook he wrote adopted modern symbols such as sin and cos. In fact, his teaching method has become the final form, and trigonometry is fully mature in his hands.

Euler made countless contributions to mathematics. Several examples are often praised and quoted. One is the so-called "Seven Bridges in Konigsberg", which is known as "the originator of topology" because Euler solved this interesting problem that has been circulating for a long time in history. Another example is the Euler formula of polyhedron V-E+F = 2(V is the number of vertices of polyhedron, E is the number of edges, and F is the number of faces). The third example, which is inevitably mentioned in almost any textbook on complex numbers, is EIX = COSX+ISINX. Any science has its relevance. Especially in middle school, learning Chinese well is very important for understanding and mastering mathematics knowledge. As an educator, Euler also attached great importance to this point. How to list algebraic equations to solve practical problems is a very old topic, but it has played an important role in the history of mathematical development and promoted the development of algebra. Like Newton's point of view, Euler didn't think that solving this kind of elementary mathematics problems was detrimental to his dignity. In his masterpiece Fundamentals of Algebra, he deliberately collected many topics.

The following is one of his topics: "When a father dies, his children are required to divide the property in the following ways: the first son gets 100 kronor, one tenth of the remaining property; The second son was given two hundred crowns and one tenth of the remaining property; The third son got three hundred crowns and one tenth of the remaining property; The fourth son got 400 crowns and a tenth of the remaining property ... and so on. Ask father * * * how much property? How many children does he have? How much does each child get? " In the end, I found that this division is simply too good, because all the children get exactly the same number. There is an old saying in China: "A bowl of water is flat", which can't be flatter.

There may be many solutions to this problem, and the following is just one of them. Suppose the number of children is X and the total amount of property is Y. According to the meaning of the question, the share of the first son is: the share of the second son is: the share of the third son is; By analogy, we can see the difference between the eldest and the second (the second and the third, the third and the fourth, and so on). According to the meaning of the question, the difference should be 0, so that we can get a one-dimensional equation: the result of the solution is

X = 900, so y=8 100. So my father has nine children, and he * * * has 8 100 kronor, and each person gives 900 kronor.

Below we might as well list two interesting questions raised by Euler, and interested readers can think about it:

1. Mules and donkeys carry hundreds of pounds each, and they complain about each other. The donkey said to the mule, "Just give me the weight on your back 100 Jin, and I can carry twice as much as you." The mule replied, "Yes! But if you give me the hundred pounds you carry, I will carry three times as much as you. " Ask them how many catties they each carried.

2. Three people play some kind of game together. At the end of the first game, what A lost to the other two people was equal to everything in their hands. At the end of the second game, what B lost to A and Xi was exactly equal to everything they had at that time. At the end of the third game, it was C's turn to be the loser. What he lost to A and B was exactly what they had at that time. They ended the game and finally found that the three people's things were exactly the same, all of which were 24. How many things did these three people have before the game?

3. German mathematician David Hilbert.

Hilbert (David, 1862 ~ 1943) is a German mathematician.

1900 On August 8th, at the Second International Congress of Mathematicians held in Paris, he put forward 23 mathematical problems that mathematicians should strive to solve in the new century, which were considered as the commanding heights of mathematics in the 20th century. The study of these problems strongly promoted the development of mathematics in the 20th century and had a far-reaching impact in the world. The school of mathematics led by Hilbert was a banner of mathematics at the end of 19 and the beginning of the 20th century. Hilbert is called "the uncrowned king of mathematics".

(The famous Goldbach conjecture is also one of the problems. The mathematicians in China, represented by Chen Jingrun, have made great breakthroughs, but they have not been completely solved. )

Hilbert

He was born in Lao Wei near Konigsberg in East Prussia (Kaliningrad, the former Soviet Union), and was a studious student in middle school. He showed great interest in science, especially mathematics, and was good at mastering and applying the contents of the teacher's lectures flexibly and profoundly. 1880, against his father's wishes, he asked him to study law, entered the university of konigsberg to study mathematics, and obtained his doctorate in 1884, then stayed in school to obtain the qualification of lecturer and was promoted to associate professor. 1893 was hired as a full professor, 1895 was transferred to the University of G? ttingen as a professor, and has been living and working in G? ttingen ever since. He retired on 1930. During this period, he became a member of the School of Communication of the Berlin Academy of Sciences, and won the Steiner Prize, the Lobachevsky Prize and the Boyle Prize. 1930 won the science prize of Swedish Academy in Mittag-Leffler, and 1942 became an honorary academician of Berlin Academy of Sciences. Hilbert is an upright scientist. On the eve of the First World War, he refused to sign the book To the Civilized World published by the German government for deceptive propaganda. During the war, he dared to publish an article in memory of "enemy mathematician" Dabu. After Hitler came to power, he resisted and wrote against the Nazi government's policy of excluding and persecuting Jewish scientists. Due to the increasingly reactionary policies of the Nazi government, many scientists were forced to emigrate, and the once-flourishing Gottingen School declined, and Hilbert died alone in 1943.

Hilbert is one of the mathematicians who had a profound influence on mathematics in the 20th century. He led the famous Gottingen School, made the University of Gottingen an important mathematical research center in the world at that time, trained a group of outstanding mathematicians and made great contributions to the development of modern mathematics. Hilbert's mathematical work can be divided into several different periods, and in each period he almost devoted himself to one kind of problems. In chronological order, his main research contents include: invariant theory, algebraic number field theory, geometric foundation, integral equation, physics and general mathematical foundation. His research topics are interspersed with Dirichlet principle and variational method, Welling problem, eigenvalue problem and "Hilbert space". In these fields, he has made great or pioneering contributions. Hilbert believes that science has its own problems in every era, and the solution of these problems is of far-reaching significance to the development of science. He pointed out: "As long as a branch of science can raise a large number of questions, it is full of vitality, and the lack of questions indicates the decline and termination of independent development."

At the 1900 International Congress of Mathematicians held in Paris, Hilbert gave a famous speech entitled "Mathematical Problems". According to the achievements and development trend of mathematical research in the past, especially in the 19th century, he put forward 23 most important mathematical problems. These 23 problems, collectively called Hilbert problems, later became the difficulties that many mathematicians tried to overcome, which had a far-reaching impact on the research and development of modern mathematics and played a positive role in promoting it. Some Hilbert problems have been satisfactorily solved, while others have not yet been solved. The belief that every mathematical problem can be solved in his speech is a great encouragement to mathematicians. He said: "among us, we often hear such a voice: here is a math problem, find out its answer!" " You can find it through pure thinking, because there is no unknowability in mathematics. Thirty years later, 1930, in his speech accepting the title of honorary citizen of Konigsberg, he declared confidently again: "We must know, and we will know. "

Hilbert's Fundamentals of Geometry (1899) is a masterpiece of axiomatic thought. Euclidean geometry is sorted out in the book and becomes a pure deductive system based on a set of simple axioms, and the relationship between axioms and the logical structure of the whole deductive system are discussed. 1904 began to study the basic problems of mathematics. After years of deliberation, in the early 1920s, he put forward a scheme on how to demonstrate the consistency of number theory, set theory or mathematical analysis. He suggested formalizing mathematics from several formal axioms into a symbolic language system, and establishing a corresponding logical system from the point of view of never assuming infinite reality. Then, the logical properties of this formal language system are studied, so as to establish meta-mathematics and proof theory. Hilbert's purpose is to try to give an absolute proof that the formal language system is not contradictory, so as to overcome the crisis caused by paradox and eliminate the doubt on the reliability of mathematical foundation and mathematical reasoning method once and for all. However, in 1930, the young Austrian mathematical logician Godel (K.G.? Del, 1906 ~ 1978) gets a negative result, which proves that Hilbert scheme is impossible to realize. However, as Godel said, Hilbert's scheme based on mathematics "still retains its importance and continues to arouse people's high interest". Hilbert's works include The Complete Works of Hilbert (three volumes, including his famous Report on Number Theory), Fundamentals of Geometry, and General Theoretical Foundations of Linear Integral Equations. He co-authored Methods of Mathematical Physics, Fundamentals of Theoretical Logic, Intuitive Geometry and Fundamentals of Mathematics.

4. Swiss mathematician Jacob Bernoulli

Bernoulli, J. (Bernoulli, Jacob) 1654 12.27 was born in Basel, Switzerland; 1705 August 16 died in Basel. Mathematics, mechanics, astronomy.

Jacob Bernoulli (Jacob

Bernoulli) was born in a merchant family. His grandfather was a drug dealer in Amsterdam, the Netherlands, and moved to Basel 1622. His father took over the thriving business of medicinal materials and became a member of the city Council and a local administrator. His mother is the daughter of a city councilman and banker. Jacob married the daughter of a wealthy businessman and his son Nicholas in 1684. NikolausBernoulli is an artist, a member of the Basel City Council and chairman of the Art Guild.

Jacob graduated from university of basel, 167 1 master of arts. Art here refers to "free art", including the basics of arithmetic, geometry, astronomy and mathematical music, as well as seven categories of grammar, rhetoric and eloquence. In accordance with my father's wishes, I obtained my master's degree in theology at 1676. At the same time, he has a strong interest in mathematics, but his interest in mathematics was opposed by his father. He taught himself mathematics and astronomy against his father's wishes. 65438-0676, went to Geneva to be a tutor. Starting from 1677, he began to write rich meditation articles here. 1678, Jacob made his first study trip. He visited France, Holland, England and Germany and established extensive correspondence with mathematicians. Then he stayed in France for two years, during which he began to study mathematical problems. At first, he didn't know the work of Newton and Leibniz. He first became familiar with Descartes and his followers' scientific methodology, and studied Descartes' geometry (La

Géometrie), J. Wallis's Infinite Arithmetic (Arithmetic A.

Infinitorum) and i. Barrow's geometry lecture notes (Geometrical

Later, he gradually became familiar with Leibniz's work. During1681-1682, he made his second research trip and met many mathematicians and scientists, such as J. Hudde, R. Boyle, R. Hooke and C. Huygens. By visiting and reading literature, he enriched his knowledge and broadened his personal interests. During this trip, his direct scientific gains were the publication of Incomplete Theory of Comets (1682) and the highly respected Theory of Gravity (1683). After returning to Basel from 1683, Jacob gave some experimental lectures on liquid and solid mechanics for the learned journal.

des

Scavans) and Actaeruditorum have written some articles on scientific and technological issues and are continuing to study mathematical works. 1687, Jacob published his method of dividing the area of a triangle into four parts with two vertical lines in Teacher's Magazine. After the popularization and application, these achievements were published as an appendix to Geometry edited by F.V. Schooten.

After 1684, Jacob turned to sophistry logic. 1685 published his earliest article on probability theory. Influenced by Wallis and Barrow's materials about mathematics, optics and astronomy, he turned to differential geometry. Meanwhile, his brother John. Bernoulli (John

Bernoulli) has been studying mathematics with him. Jacob became a professor of mathematics in university of basel from 65438 to 0687 until his death from 65438 to 0705. During this period, he kept in touch with Leibniz.

1699 Jacob was elected as a foreign academician of the Paris Academy of Sciences, and 170 1 was accepted as a member of the Berlin Science Association (later Berlin Academy of Sciences) in.

Jacob Bernoulli was one of the important members of the Bernoulli family who made special contributions to mathematics in the European continent during the17-18th century. His contributions to mathematics include calculus, analytic geometry, probability theory and variational method.

5. An "unjust case" in the history of mathematics

Humans have mastered the solution of quadratic equation with one variable for a long time, but the research on cubic equation with one variable has made slow progress. Mathematicians in ancient China, Greek, Indian and other places have tried their best to study the cubic equation of one yuan, but the solution they invented can only solve the cubic equation in a special form, but it is not suitable for the cubic equation in a general form.

16th century Europe, with the development of mathematics, the cubic equation of one variable has a fixed solution. In many mathematical documents, the formula for finding the root of cubic equation is called "cardano formula", which is obviously to commemorate the first Italian mathematician cardano who published the formula for the root of cubic equation with one variable in the world. So, was the general solution of the univariate cubic equation first discovered by cardano? This is not a historical fact.

In the history of mathematics, the first person to find the general solution of a cubic equation is/kloc-another Italian mathematician in the 6th century, Hotel Nigro fontana.

Fontana was born in poverty, lost his father, and there was no condition for him to study at home. However, through hard work, he finally became one of the most accomplished Italian scholars in the16th century. Because Vontana suffers from stuttering, people nicknamed him "Tarta".

In Italian, it means "stuttering". Later, in many math books, Feng Tana was directly called "Tarta Riya".

After years of exploration and research, Fontana found a method to find the root of a cubic equation in a general form with a very clever method. This achievement made him win a great victory in several open mathematics competitions and became famous in Europe. But Feng Tana didn't want to make this important discovery public.

Cardano, another Italian mathematician and doctor at that time, was very interested in Feng Tana's discovery. He sincerely visited several times for advice, hoping to get Fontana's roots. But Fontana kept her mouth shut. Although cardano was frustrated many times, he was extremely persistent and tried to "dig the secret" from Feng Tana. Later, Vontana finally "revealed" the solution of the cubic equation to cardano in incantation-like obscure language. Feng Tana thought it was difficult for cardano to break his "magic spell", but cardano's understanding was great. Through the comparative practice of solving cubic equations, he quickly cracked Fontana's secret completely.

Cardano wrote Feng Tana's cubic equation root formula into his academic book Dafa, but did not mention Feng Tana's name. With the advent of European Dafa, people realized the general solution of cubic equation. Because the first person who published the formula for finding the root of cubic equation was really cardano, later generations called this solution "cardano formula".

Cardano stole other people's academic achievements and took them for himself, leaving a disgraceful page in the history of human mathematics. This result is of course unfair to Fontana who has worked hard. However, Feng Tana's insistence on not disclosing his research results is incorrect, at least for the development of human science, and it is an irresponsible attitude.