Gauss (1777~1855) was born in Brunswick, located in what is now central and northern Germany. His grandfather was a farmer, his father was a plasterer, and his mother was the daughter of a mason. He had a very smart younger brother, Gauss. This uncle took great care of little Gauss and occasionally gave him some guidance. His father can be said to be a " "Big boss" believes that only strength can make money, and knowledge is of no use to the poor.

Gauss showed his extraordinary talent very early. At the age of three, he was able to point out errors in his father's account books. When I was seven years old, I entered primary school. I had classes in a dilapidated classroom. The teacher was not kind to the students. He often thought that he was underappreciating his talents by teaching in a remote area. When Gauss was ten years old, his teacher took the famous "adding from one to a hundred" test and finally discovered Gauss's talent. He knew that his ability was not enough to teach Gauss, so he bought a deeper mathematics book from Hamburg. Read to Gauss. At the same time, Gauss became very familiar with Bartels, an assistant teacher who was almost ten years older than him. Bartels was also much more capable than his teacher. He later became a university professor and taught Gauss more and deeper mathematics.

The teacher and teaching assistant visited Gauss’s father and asked him to let Gauss receive a higher education. However, Gauss’s father believed that his son should be a plasterer like him, and he had no money for Gauss to continue studying. The final conclusion is - find rich and powerful people to be Gauss's sponsors, although they don't know where to look. After this visit, Gauss was exempted from the work of weaving every night and discussed mathematics with Bartels every day, but before long, Bartels had nothing to teach Gauss.

In 1788, Gauss entered higher education despite his father's opposition. After seeing Gauss's homework, the math teacher asked him to stop taking math classes, and his Latin soon became better than the rest of the class.

In 1791, Gauss finally found a sponsor, Duke Ferdinand of Brunswick (Braunschweig), who promised to help him in every possible way. Gauss's father no longer had any reason to object. The following year, Gauss entered the Braunschweig Academy. This year, Gauss was fifteen years old. There, Gauss began to conduct research on advanced mathematics. He also independently discovered the general form of the binomial theorem, the "Law of Quadratic Reciprocity" in number theory, the prime numer theorem, and the arithmetic-geometric mean.

In 1795, Gauss entered the University of G?ttingen. Because he was extremely talented in languages ??and mathematics, he worried for a while about whether to specialize in classical Chinese or mathematics in the future. By 1796, the seventeen-year-old Gauss obtained a very important result in the history of mathematics. The most well-known thing, and what led him to embark on the path of mathematics, is the theory and method of drawing regular heptagonal rulers and compasses.

Mathematicians in the Greek era already knew how to use a ruler and compass to make a regular 2m×3n×5p polygon, where m is a positive integer, and n and p can only be 0 or 1. But for two thousand years, no one knew the rules and compasses for drawing regular seven-, nine-, and eleven-sided polygons. And Gauss proved:

A regular n-sided polygon can be drawn with a ruler and compass if and only if n is one of the following two forms:

1. n = 2k, k = 2, 3,…

2. n = 2k × (the product of several different “Fermat prime numbers”), k = 0,1,2,…

Fermat prime number is a prime number of the form Fk = 22k. Like F0 = 3, F1 = 5, F2 = 17, F3 = 257, F4 = 65537, all prime numbers. Gauss used algebraic methods to solve geometric problems for more than 2,000 years. He also regarded this as his proud work. He also confessed that he would engrave a regular heptagon on his tombstone, but later it was not inscribed on his tombstone. Instead of a seventeen-pointed star, the sculptor responsible for engraving the stele believed that the regular heptadagon looked too similar to a circle and people would not be able to tell them apart.

In 1799 Gauss presented his doctoral thesis, which proved an important theorem of algebra:

Any polynomial has (complex number) roots.

This result is called the Fundamental Theorem of Algebra.

In fact, many mathematicians before Gauss believed that they had given proof of this result, but none of the proofs was rigorous. Gauss pointed out the deficiencies of previous proofs one by one, and then put forward his own opinions. He gave four different proofs in one go in his life.

In 1801, when Gauss was twenty-four years old, he published "Disquesitiones Arithmeticae". This book was written in Latin and originally had eight chapters. Due to lack of money, seven chapters had to be printed.

Except for Chapter 7, which introduces the basic theorems of algebra, the rest of this book is devoted to number theory. It can be said to be the first systematic work on number theory. Gauss introduced "Congruent" for the first time. concept. "Quadratic reciprocity theorem" is also included.

Starting at the age of twenty-four, Gauss gave up his research in pure mathematics and studied astronomy for several years.

The astronomical community at that time was troubled by the huge gap between Mars and Jupiter, believing that there should be undiscovered planets between Mars and Jupiter. In 1801, the Italian astronomer Piazzi discovered a new star between Mars and Jupiter. It was named "Cere". We now know that it was one of the asteroid belts of Mars and Jupiter, but at that time there was a lot of debate in the astronomical community. Some said it was a planet, and some said it was a comet. We must continue to observe to judge, but Piazzi could only observe its 9-degree orbit, and then it disappeared behind the sun. Therefore, its orbit cannot be known, and it cannot be determined whether it is a planet or a comet.

Gauss became interested in this problem at this time, and he decided to solve the problem of this elusive star trajectory. Gauss himself created a unique method that can calculate the orbit of a planet with just three observations. He could predict the positions of the planets with great accuracy. Sure enough, Ceres appeared exactly where Gauss predicted. This method - although he did not announce it at the time - was the "Method of Least Square".

In 1802, he accurately predicted the position of asteroid 2, Pallas. At this time, his reputation spread far and wide, and honors rolled in. He was elected as a member of the Russian Academy of Sciences in St. Petersburg. , the astronomer Olbers who discovered Pallas asked him to be the director of the G?ttingen Observatory. He did not agree immediately, and did not go to G?ttingen until 1807 to take up the post.

In 1809 he wrote two volumes of "Theory of the Motion of Celestial Bodies". The first volume included differential equations, conical intercepts and elliptical orbits, and the second volume showed how to estimate the orbits of planets. Most of Gauss's contributions to astronomy were made before 1817, but he continued to make observations until he was seventy years old. While working at the observatory, he still found time to do other research. In order to use integrals to solve the differential force range of celestial motion, he considered infinite series and studied the convergence problem of the series. In 1812, he studied the hypergeometric series (Hypergeometric Series) and wrote the research results into a monograph, which he presented To the Royal Academy of Sciences G?ttingen.

Between 1820 and 1830, Gauss began to do geodesy work in order to map the principality of Hanover (where Gauss lived). He wrote a book about geodesy. Needed, he invented the Heliotrope. In order to study the surface of the earth, he began to study the geometric properties of some curved surfaces.

In 1827, he published "Disquisitiones generales circa superficies curva" (Disquisitiones generales circa superficies curva), which covered part of the "differential geometry" now studied in universities.

Between 1830 and 1840, Gauss worked on magnetic research with a young physicist, Withelm Weber, who was 27 years younger than him. Their cooperation was ideal: Weber conducted experiments , Gauss's research theory, Weber aroused Gauss's interest in physical problems, and Gauss used mathematical tools to deal with physical problems, which influenced Weber's thinking and working methods.

In 1833, Gauss pulled an 8,000-foot wire from his observatory across the roofs of many houses to Weber's laboratory. Using a volt battery as a power source, he constructed the world's first Telegraph machine.

In 1835, Gauss set up a magnetic observatory in the observatory and organized the "Magnetic Association" to publish the research results, which led to research and measurement of geomagnetism in vast areas of the world.

Gauss had obtained the precise theory of geomagnetism. In order to obtain experimental data to prove it, his book "General Theory of Geomagnetism" was not published until 1839.

In 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. In 1841, 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 excellence and he is very strict with his research results. He himself once said: "I would rather publish less, but what I publish is mature results." Many contemporary mathematicians asked him not to take it too seriously, but to write down and publish the results, which is very helpful to the development of mathematics. One famous example concerns the development of non-Euclidean geometry. There are three founders of non-Euclidean geometry, Gauss, Lobatchevsky (1793～1856), and Bolyai (1802～1860). Among them, Bolyai's father was a classmate of Gauss University. He once wanted to try to prove the parallel axiom. Although his father objected to him continuing to engage in this seemingly hopeless research, little Bolyai was still addicted to the parallel axiom. Finally, non-Euclidean geometry was developed and the research results were published in 1832-1833. The old Bolyai sent his son's results to his old classmate Gauss. Unexpectedly, Gauss wrote back:

to praise it would mean to praise myself. I cannot praise him, because praising him is equivalent to praising myself.

As early as decades ago, Gauss had obtained the same result, but he did not publish it because he was afraid that it would not be accepted by the world.

The famous American mathematician E.T. Bell once criticized Gauss in his book "Men of Mathematics":

In Gauss After his death, it became known that he had foreseen some nineteenth-century mathematics and had anticipated their appearance before 1800. If he could have leaked some of what he knows, it is likely that mathematics would be half a century or more more advanced than it is today. Abel and Jacobi could start from where Gauss left off, rather than spending their best efforts discovering what Gauss already knew when they were born. The creators of non-Euclidean geometry could apply their genius to other forces.

In the early morning of February 23, 1855, Gauss died peacefully in his sleep.

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On April 30, 1777, Gauss was born in Braunscheig (Braunscheig) in Lower Saxony, Germany. No one among the ancestors can explain why a genius like Gauss came into being. Gauss's father was an ordinary laborer. He worked as a stonemason, a tracker, and a flower farmer. ?⑶ Rui Jun of Xinyuan died at the age of 7, and Gauss was her only adopted son. It is said that when Gauss was 3 years old, he discovered an error in his father's account books. When Gauss was 9 years old, he was studying in a public elementary school. One time, in order to keep the students busy, his teacher asked them to add up the numbers from 1 to 100. Gauss almost immediately put the slate with the results written face down on his desk. When all the slates were finally turned over, the teacher was surprised to find that only Gauss came up with the correct answer: 5050, but there was no calculation process. Gauss had already summed up this arithmetic series in his mind. He noticed that 1+100=101, 2+99=101, 3+98=101... In this way, it is equivalent to the addition of 50 101s, so the answer is 5050. In his later years, Gauss often humorously claimed that he could calculate before he could speak. He also said that he learned to read by himself after asking adults how to pronounce letters.

Gauss's precocity attracted the attention of the Duke of Brunswick, who was an enthusiastic patron. Gauss entered the Braunschweig Academy at the age of 14 and the University of G?ttingen at the age of 18. At that time, G?ttingen was still unknown. The arrival of Gauss made this world-famous university become important. At first, Gauss was hesitant between becoming a linguist or a mathematician. It was March 30, 1796, that he decided to devote himself to mathematics. When he was one month short of turning 19, he made amazing contributions to the Euclidean construction theory of regular polygons (using only compasses and unscaled rulers). In particular, he discovered the seventeen-sided construction of regular polygons. This is a mathematical unsolved problem with a history of more than 2,000 years. Gauss was already proficient when he was just starting out, and he maintained this level for the next fifty years. The era in which Gauss lived was the era when German Romanticism was prevalent. Gauss was influenced by fashion, and his personal letters and narratives were full of beautiful words. Gauss said: "Mathematics is the queen of science, and number theory is the queen of mathematics." People of that era also called Gauss the "Prince of Mathematics." In fact, looking at Gauss's entire life's work, it seems that there is also a romantic overtone.

Fascination with natural numbers

Number theory is one of the oldest branches of mathematics, which mainly studies the properties and interrelationships of natural numbers. Since the time of Pythagoras, people have been obsessed with discovering the mysterious relationship of numbers. Beauty, simplicity, and wisdom are the characteristics of this science. Like other mathematical prodigies, Gauss was first fascinated by natural numbers. Gauss said in 1808: "Anyone who has spent a little time studying number theory will inevitably feel a special kind of passion and enthusiasm." The last "know-it-all" in modern mathematics - the biography of David Hilbert When the author talks about the masters abandoning the theory of algebraic invariants and turning to the study of number theory, he points out: "There is no field in mathematics that can attract the best of mathematicians with its beauty - an irresistible force like number theory." Painter Wa Cili Kandinsky also believed: “Number is the ultimate abstract expression of all kinds of art.

"I noticed that some great mathematicians who had never studied number theory, such as Pascal, Descartes, Newton and Leibniz, all devoted the rest of their lives to philosophy or religion. Only Fermat and Euler and Gauss, three mathematicians who made outstanding contributions to number theory, did not need any philosophy or religion throughout their lives, because they already had the purest and most essential art in their hearts - number theory.

Here I would like to quote the story of the Indian mathematical genius Ramanujan to illustrate the "friendship" between number theorists and natural numbers. This compatriot of Rabindranath Tagore came from Tamil Nadu, the southernmost state of India. He was a poor clerk who had never received higher education. , but he had the amazing talent of quickly and profoundly seeing the relationships between complex numbers. The famous British mathematician G. H. Hardy "discovered" him in 1913 and invited him to England to study in Cambridge the following year. University. When Hardy once visited the sick Ramanujan, he told him that the taxi number 1729 he just took seemed to have no meaning, but he hoped it was not an ominous omen. Ramanujan replied: " No, this is a very interesting number. 1729 is the smallest number that can be expressed in two ways as the sum of two natural numbers cubed (it is equal to 1 cubed plus 12 cubed, and it is equal to 9 cubed plus 10 cubed). Hardy asked again, what is the smallest number for the fourth power? Ramanujan thought for a while and replied: "This number is very large. The answer is 635318657." (It is equal to 59 to the fourth power plus 158 to the fourth power, and it is equal to 133 to the fourth power plus 134 to the fourth power. power)

"Arithmetic Research": the code of number theory

In 1801, Gauss, who was only 24 years old, published "Arithmetic Research", thus creating a new era of modern number theory. The book contains the drawing of regular polygons, convenient congruence notation, and the first proof of the beautiful quadratic reciprocity law. This great work was sent to the French Academy of Sciences and rejected, but Gauss published it himself. Like Gauss's earlier works, it was written in Latin, which was the Esperanto of the scientific community at the time. However, due to the influence of nationalism in the early nineteenth century, Gauss later switched to German. If he and other researchers had stuck to Latin, perhaps we would be free of language troubles today. At the end of that century, Cantor, the founder of set theory, commented: "Investigations of Arithmetic" is the charter of number theory. The benefit to science that Gauss was always slow to publish his work is that his printed work remains as correct and important today as it was when it was first published, and his publication is the Codex. It is superior to other human codes, because no fault has ever been found in it at any time and anywhere. This can be understood when Gauss said in his later years when he talked about the first masterpiece of his youth: ""Arithmetic Research" is history. Wealth." His complacency at that time was quite reasonable.

Regarding "Arithmetic Research", there is also a story circulating. On July 16, 1849, the University of G?ttingen held a celebration for the 50th anniversary of Gauss's doctorate. When a certain procedure was carried out, Gauss was about to light a cigarette with a manuscript of "Arithmetic Research". The mathematician Dirichlet (who later succeeded Gauss's position) who was present at the time ate a piece of it as if he had witnessed an act of sacrilege. Shocked, he immediately snatched the page from Gauss and treasured it for the rest of his life; his editor found the original manuscript among his papers after his death.

Like an artist, Gauss hoped that what he left behind would be perfect art treasures, and any slight change would destroy its internal balance. He often said: "When a building is completed, the scaffolding should be removed." Gauss also had very strict requirements for rigor, which made it take a long time for a theorem to go from an intuitive form to a complete mathematical proof. . In addition, Gauss was very particular about organizational structure. He hoped to establish a consistent and universal theory in every field to connect different theorems. For these reasons, Gauss was reluctant to publish his work publicly. His famous aphorism is: I would rather be less, but be mature. For this reason, Gauss paid a high price, including giving up the invention rights of non-Euclidean geometry and the method of least squares to Lobachevsky, Boyer and Legendre, just like Fermat gave up the invention of analytic geometry and differential equations. The invention of integral points was given to Descartes, Newton, and Leibniz.

From the day he made his discovery about regular polygons, Gauss started a famous mathematical diary. He recorded many great mathematical discoveries in coded words. Gauss's diary was not found until 1898. It contains 146 short notes, including numerical calculation results and simple mathematical theorems. For example, regarding the problem of drawing regular polygons, Gauss wrote in his diary:

The law of division of a circle, how to geometrically divide a circle into seventeen equal parts.

Another example is the record on July 10, 1796,

num＝△＋△＋△

It means "Every natural number is three triangles The sum of numbers". Like Mozart, Gauss's turbulent whims as a young man left him with no time to finish one thing before another appeared.

Versatile

Gauss was not only a mathematician, but also one of the greatest physicists and astronomers of his time. In the same year that "Arithmetic Investigations" came out, that is, on New Year's Day 1801, an Italian astronomer observed in Sicily a star with a luminosity of 8th magnitude moving near the constellation Aries. This star is now called Ceres. The asteroid (Ceres) appeared in the sky for 41 days. After sweeping across an octave angle, it disappeared under the rays of the sun. At the time, astronomers were unable to determine whether the nova was a comet or a planet, and the issue quickly became a focus of academic attention and even a philosophical question. Hegel once wrote an article mocking astronomers, saying that there is no need to be so enthusiastic about finding the eighth planet. He believed that his logical method could be used to prove that there are exactly seven planets in the solar system, no more and no less. Gauss was also fascinated by this star. He used the observation data provided by astronomers to calculate its trajectory calmly. No matter how unhappy Hegel was, a few months later, the first discovered and still the largest asteroid to date appeared on time at the location designated by Gauss. Since then, asteroids and large planets (Neptune and Pluto) have been discovered one after another.

Gauss's most notable achievement in physics was the invention of the wire telegraph with the physicist Weber in 1833, which brought Gauss's reputation beyond the academic circle and into the public society. In addition, Gauss has made outstanding contributions in mechanics, geodesy, hydraulics, electrodynamics, magnetism and optics. Even in terms of mathematics, we are talking about only a small part of the work he did in the field of number theory when he was young. During his long life, he had pioneering work in almost every field of mathematics. For example, about a century after he published "General Investigations on the Theory of Surfaces," Einstein commented: "Gauss's contribution to the development of modern physics, especially to the mathematical basis of the theory of relativity (referring to the theory of surfaces), Its importance is beyond all and unparalleled."

It's always cold at the top

In Gauss's time, there were few people who could share his ideas or provide him with new ideas. concept. Whenever he discovered a new theory, he had no one to discuss it with. This feeling of loneliness, accumulated over the years, resulted in his aloof and cold state of mind. This kind of intellectual loneliness has been experienced by only a few great men in history. Gauss never participated in public debates. He always hated debates. He believed that they could easily turn into stupid shouting. This may be a psychological rebellion against his rough and authoritarian father since he was a child. After Gauss became famous, he rarely left G?ttingen. He repeatedly rejected invitations from the Academy of Sciences in Berlin, St. Petersburg and other places. Gauss even hated teaching and was not keen on cultivating and discovering young people. Naturally, he could not talk about founding any school of thought. This was mainly due to Gauss's excellent talent and his spiritual isolation. But this does not mean that Gauss did not have outstanding students. Riemann and Dirichlet were both great mathematicians, and Detkin and Eisenstein also made outstanding contributions to mathematics. However, due to Gauss's rise to the top, among these people, only Riemann (who succeeded Gauss after Dirichlet's death) is considered to be relatively close to Gauss.

The great mathematicians Jacobi and Abel, both of Gauss's contemporaries, complained that Gauss ignored their achievements. Jacobi was a very thoughtful man. He had a famous saying that has been passed down to this day: "The only purpose of science is to glorify the human spirit." He was a compatriot of Gauss and the father-in-law of Dirichlet, but he had never been able to develop a close friendship with Gauss.

At the celebration in G?ttingen in 1849, Jacobi, who came from Berlin, sat in the honorary seat next to Gauss. When he wanted to find a topic to talk about mathematics, Gauss ignored him. This may be the wrong time. At that time After drinking several glasses of sweet wine, Gauss felt a little unable to control himself; but even if the situation were different, the result would probably be the same. In a letter to his brother about the banquet, Jacobi wrote, "You must know that in these twenty years, he (Gauss) never mentioned me and Dirichlet..."

Abel's fate was tragic. Like his later compatriots Ibsen, Grieg and Munch, he was the only Norwegian to achieve world-wide achievements in his own field. He was a great genius, but he lived a life of poverty, unknown to his contemporaries. When Abel was 20 years old, he solved a big problem in the history of mathematics, that is, he proved the impossibility of using radicals to solve general quintic equations. He sent just six pages of "unsolvable" proof to some famous European mathematicians. Gauss naturally also received a copy. In his introduction, Abel was confident that mathematicians would accept the paper favorably. Soon, Abel, the son of a country pastor, started the only hike in his life. At that time, he wanted to use this article as a stepping stone. Abel's biggest wish during this trip was to visit Gauss, but Gauss was out of reach. He only glanced at a few lines of the paper and then threw it aside, still concentrating on his own research work. Abel had to make an increasingly painful detour around G?ttingen on his journey from Paris to Berlin.

Although Gauss was aloof, what is surprising is that he spent his middle-class life proudly without suffering the blow of cold reality; this kind of blow is often ruthlessly imposed on everyone who breaks away. People living in real environment. Perhaps Gauss's pragmatic and perfectionist nature helped him grasp the simple realities of life. Gauss received his doctorate at the age of 22, was elected as a foreign academician of the St. Petersburg Academy of Sciences at the age of 25, and became a professor of mathematics and director of the Observatory at the University of G?ttingen at the age of 30. Although Gauss did not like glitz and glory, these things fell on him like raindrops in the fifty years after he became famous. Almost the whole of Europe was involved in this awarding trend. He won 75 awards in his lifetime. Various honors, including the title of "Senator" conferred by King George III in 1818, and the title of "Chief Senator" in 1845. Gauss's two marriages were also very happy. After his first wife died in childbirth, within ten months, Gauss married a second wife. There is a common phenomenon in psychology and physiology. People who live a happy married life often remarry soon after being widowed. The same is true for the musician Johann Sebastian Bach who lived in poverty all his life.

A great cultural crystal

Gauss has never forgotten the kindness of the Duke of Brunswick. He has always been grudged by the tragic death of his patron at the hands of Napoleon in 1806. Huai, therefore refused to accept the creed of the French Revolution and the influence of the democratic thoughts arising from it. His students called him a conservative. From this point of view, Gauss can be said to be the last - and the greatest - cultural crystallization in the aristocratic autocratic social system. Gauss liked literature very much. He had read all of Goethe's works, but he didn't admire them very much. Because of his innate language expertise, Gauss was very good at reading foreign languages. He was fluent in English, French, Russian, Danish, and had some knowledge of Italian, Spanish, and Swedish. His private diary was written in Latin. When Gauss was 50 years old, he began to learn Russian again, partly to read the original works of the young poet Pushkin. However, Gauss's language talent is not the most outstanding among mathematicians. Hamilton, the Irish prodigy who is famous in the field of mathematics, was able to speak 13 foreign languages ??fluently when he was 13 years old. Gauss loved to read the works of Montaigne, Rousseau and others, but did not like Shakespeare's tragedies very much. However, he chose two lines of poems in "King Lear" as his motto,

Nature, My goddess,

I am willing to devote myself to you forever.

The English writer whom Gauss most admired was Scott, and he read almost all of his works. On one occasion, Gauss was ecstatic when he found an error in Sir Scott's description of the natural landscape (the full moon rose from the northwest). Not only did he correct it in his own book, he also went to the G?ttingen bookstore and corrected all the other unsold books.

Like all great mathematicians, abstract symbols were not unreal to Gauss.

Once he said: "The satisfaction of the soul is a higher state, and material satisfaction is superfluous. As for my application of mathematics to a planet made of several pieces of mud, or to purely mathematical problems, this does not matter. Not important. But the latter often brings me greater satisfaction." Gauss had always been in good health and did not spend time on religion or spirituality until he was struck by illness in his later years. Heart disease continued to destroy his will. In 1848, Gauss wrote to his closest friend: "Although the life I have experienced is like a ribbon flying across the world, it also has its painful side. This feeling is felt by the elderly. I am even more unable to control myself at this time, and I am happy to admit that if someone else were to live my life, I might be much happier. On the other hand, this makes me realize the emptiness of life. Everyone who is approaching the end of life will feel the same. There must be this feeling..." He added: "If some questions can be answered, I think they have more transcendent value than solving mathematical problems, such as the relationship between humans and gods, our destiny, our future, etc. etc. The answers to these questions are far beyond our ability and cannot be achieved within the scope of science." In the early morning of February 23, 1855, Gauss died peacefully in his sleep at the age of 77. He once asked for a regular heptagon to be engraved on his tombstone, but contrary to his wishes, what was engraved on the Gauss Memorial Tower in Brunswick was a star with seventeen points, because the carver believed that the seventeen-pointed star was engraved on it. The edge shape is almost exactly the same as the circle after it is carved out.

Gauss was once described as: "A genius who can grasp the stars and esoteric mathematics from a certain point of view from the height of the sky." He combined his several talents-creative intuition, excellent calculation Ability, rigorous logical reasoning, perfect experiments - harmoniously combined, this combination of abilities makes Gauss outstanding and has few rivals in human history. He is conventionally compared to Archimedes and Newton, both of whom were extremely versatile. As a theorist, Einstein was on the same level, but he was somewhat limited because he was not an experimentalist.