Carl Gauss his discoveries briefly. Karl Gauss short biography
Johann Carl Friedrich Gauss is called the king of mathematicians. His discoveries in algebra and geometry gave direction to the development of science in the 19th century. In addition, he made significant contributions to astronomy, geodesy and physics.
Karl Gauss was born on April 30, 1777 in the German Duchy of Brunswick in the family of a poor canal caretaker. It is noteworthy that his parents did not remember the exact date of birth - Karl himself brought it out in the future.
Already at the age of 2, the boy’s relatives recognized him as a genius. At age 3, he read, wrote, and corrected his father's calculation errors. Gauss later recalled that he learned to count before he could talk.
At school, the boy’s genius was noticed by his teacher Martin Bartels, who later taught Nikolai Lobachevsky. The teacher sent a petition to the Duke of Brunswick and obtained a scholarship for the young man at the largest technical university in Germany.
From 1792 to 1795, Karl Gauss spent time at the University of Braunschweig, where he studied the works of Lagrange, Newton, and Euler. He spent the next 3 years studying at the University of Göttingen. His teacher was the outstanding German mathematician Abraham Kästner.
In the second year of study, the scientist begins to keep a diary of observations. Later biographers will draw from him many discoveries that Gauss did not disclose during his lifetime.
In 1798, Karl returned to his homeland. The Duke pays for the publication of the scientist's doctoral dissertation and grants him a scholarship. Gauss remained in Brunswick until 1807. During this period, he held the position of private assistant professor at a local university.
In 1806, the patron of the young scientist died in the war. But Carl Gauss had already made a name for himself. He is vying with each other for invitations to different European countries. The mathematician goes to work in the German university city of Göttingen.
In his new place, he receives the position of professor and director of the observatory. Here he remains until his death.
Carl Gauss received wide recognition during his lifetime. He was a corresponding member of the Academy of Sciences in St. Petersburg, awarded the prize of the Paris Academy of Sciences, the gold medal of the Royal Society of London, became a laureate of the Copley medal and a member of the Swedish Academy of Sciences.
Mathematical discoveries
Carl Gauss made fundamental discoveries in almost all areas of algebra and geometry. The most fruitful period is considered to be the time of his studies at the University of Göttingen.
While in collegiate college he proved the law of reciprocity of quadratic residues. And at the university, the mathematician managed to construct a regular seventeen-sided polygon using a ruler and compass and solved the problem of constructing regular polygons. The scientist valued this achievement most of all. So much so that he wanted to engrave a circle on his posthumous monument, which would contain a figure with 17 corners.
In 1801, Klaus published his work Arithmetic Studies. After 30 years, another masterpiece of the German mathematician will appear - “The Theory of Biquadratic Residues.” It provides proofs of important arithmetic theorems for real and complex numbers.
Gauss became the first to provide proofs of the fundamental theorem of algebra and began to study the internal geometry of surfaces. He also discovered the ring of complex Gaussian integers, solved many mathematical problems, developed the theory of congruences, and laid the foundations of Riemannian geometry.
Achievements in other scientific fields
Vice-heliotrope. Brass, gold, glass, mahogany (created before 1801). With a handwritten inscription: “Property of Mr. Gauss.” Located at the University of Göttingen, First Physics Institute.
Carl Gauss became truly famous for his calculations, with the help of which he determined the position of the plant, discovered in 1801.
Subsequently, the scientist repeatedly returned to astronomical research. In 1811, he calculated the orbit of the newly discovered comet and made calculations to determine the location of the comet of the “Fire of Moscow” in 1812.
In the 20s of the 19th century, Gauss worked in the field of geodesy. It was he who created a new science - higher geodesy. He also develops computational methods for geodetic surveying and publishes a series of works on the theory of surfaces, included in the publication “Research on Curved Surfaces” in 1822.
The scientist also turns to physics. He develops the theories of capillarity and lens systems, lays the foundations of electromagnetism. Together with Wilhelm Weber, he invents the electric telegraph.
Personality of Karl Gauss
Karl Gauss was a maximalist. He never published raw, even brilliant works, considering them imperfect. Because of this, other mathematicians were ahead of him in a number of discoveries.
The scientist was also a polyglot. He spoke and wrote fluently in Latin, English, and French. And at the age of 62, he mastered Russian in order to read the works of Lobachevsky in the original.
Gauss was married twice and became the father of six children. Unfortunately, both spouses died early, and one of the children died in infancy.
Karl Gauss died in Göttingen on February 23, 1855. In his honor, by order of King George V of Hanover, a medal was minted with a portrait of the scientist and his title - “King of Mathematicians”.
On the first night of the 19th century, Italian astronomer Giuseppe Piazzi discovered the first of the small planets - Ceres (it turned out to be the largest of almost two thousand discovered to this day - its diameter is about 800 km).
The planet was observed for some time. However, soon the path of Ceres approached the Sun, in whose rays it was impossible to notice the planet. And then astronomers for a long time could not find the planet in the starry sky.
The solution to a difficult task for those times - determining the elliptical orbit of a planet from three observations (that is, knowing its position in the sky at three different moments in time) - was undertaken by the young German mathematician Carl Friedrich Gauss. He carried out the work very thoroughly, and soon astronomers discovered Ceres in exact accordance with the calculations.
Calculating the trajectory of Ceres made Gauss's name, known until then only in a narrow circle of scientists, is available to the general public. The methods he developed remained the basis for calculating planetary orbits for a century and a half. It was possible to simplify and speed up these calculations only with the help of a computer.
Gauss's essay "Theory of the motion of celestial bodies" appeared in 1809. By this time, Gauss was already known as the author of several works, including a serious work on number theory, Arithmetic Studies (1801).
The first mention of the great mathematician, physicist, astronomer and surveyor Carl Friedrich Gauss was an entry in a church book dated May 4, 1777:
“Gebhard Dietrich Gauss and his wife Dorothea born. Bence gave birth to a son on April 30, 1777... The child was named: Johann Friedrich Karl...”
The father of the future scientist was a mason, then a gardener, then a plumber. According to Gauss’s recollections, “my father wrote and counted well” and was very proud when Leipzig and Brunswick merchants invited him during fairs to keep accounts.
Young Karl Friedrich, in his own words, “learned to count before speaking.” They say that when his father was once loudly calculating the earnings of his assistants, three-year-old Karl audibly noticed an error in the calculations and pointed it out to his father.
In 1784, seven-year-old Karl began studying at a local one-class (that is, with one teacher) school. The first biographer of Gauss, Göttingen professor von Waltershausen writes:
“...A stuffy room with a low ceiling and an uneven, cracked floor. From one window there is a view of the Gothic towers of the Church of St. Katarina, from the other - to the stables. Among hundreds of students from seven to fifteen years of age, teacher Büttner walks back and forth with a whip in his hands. The teacher used this merciless argument for his method of education quite often - according to his mood and need. In this school, as if torn out of the distant Middle Ages, young Gauss studied for two years without any incident, and then was transferred to the “arithmetic class.”
However, the “transfer” was only expressed in the fact that the nine-year-old boy was moved from one row of benches to another. The same teacher Büttner gave the students in this row fewer spelling assignments and more arithmetic assignments. The student who was the first to complete a given calculation usually placed his slate on a large table; a second board was placed on top of it, and so on in order. Then the pile of boards was turned over. The teacher started the test from the board of the one who solved it first.
Soon after nine-year-old Gauss was transferred to arithmetic class, the teacher gave him an assignment: add all the natural numbers from 1 to 100.
“The task had barely been formulated,” continues von Waltershausen, “when young Karl announced: “I laid down my board.” And while the rest of the schoolchildren were diligently adding and multiplying numbers, teacher Büttner, full of dignity, walked around the class, casting sarcastic glances from time to time at the youngest of the students, who had long completed the task. And he smiled calmly, imbued with unshakable confidence in the correctness of the result obtained - this confidence took possession of Gauss after the completion of every major work throughout his life... At the end of the lesson, a single number was discovered on Gauss’s slate board, which, to everyone’s amazement, was the correct answer to the problem, while many other answers turned out to be incorrect and were subject to “correction with a whip.”
“Instead of adding sequentially 1+2=3; 3+3=6; 6+4=10; 10 + 5 = 15, etc., which would be natural for any normal schoolchild of that age,” wrote Leipzig specialist in the history of mathematics, Professor Hans Wusing, recently, “Gauss had the idea to combine numbers in pairs from different ends of a given series: 1+ 100=101; 2+99 = 101, etc. There were 50 such pairs. Then all that remained was to perform the multiplication 101x50=5050. There is nothing to be surprised about: it did not take Gauss much time to write this singular number on his board.”
Büttner noticed the extraordinary abilities of his student and obtained additional manuals for him. Great help was provided by the young assistant teacher Martin Bartels, who was also partial to mathematics (later Bartels became a professor of mathematics and, in particular, was one of N.I. Lobachevsky’s teachers at Kazan University). Despite the eight-year age difference, Gauss and Bartels quickly became close over their shared passion for mathematics. Büttner and Bartels convinced Father Gauss to send his son to the gymnasium and promised to obtain financial support: the poor artisan did not have the opportunity to pay for his son’s education at the gymnasium.
In 1788 Gauss was accepted - an unprecedented case! - straight to the second grade of the gymnasium. He especially impressed his teachers with his brilliant abilities in Greek and Latin - these ancient languages, along with history, were considered the most important in humanitarian gymnasium education. The capable young man was introduced to the Duke, the ruler of Brunswick, who awarded him a scholarship to study at the gymnasium and at the university.
In those days, children of peasants and artisans very rarely went to gymnasiums and even more so to universities - education and obtaining “privileged” professions were practically inaccessible to the lower classes of society. Gauss turned out to be a happy exception.
Citizens of the Duchy of Brunswick usually studied at “their” Helmigged University. Gauss chose Gottingen, known for the high level of development of physical and mathematical sciences and a rich library. In 1795 he was enrolled there as a student. By order of the Duke, he was provided with “free food and 158 thalers a year for expenses.” Gauss had not yet chosen a specialty and hesitated between classical linguistics and mathematics.
The choice was made only the following year, when a 19-year-old student solved a problem that had not been solved for more than two thousand years.
Mathematicians have long tried to answer the question: what regular polygons can be constructed using a compass and ruler?
The construction of an equilateral triangle and a square is known to every schoolchild. Even in the time of Euclid, they were able to build a pentagram - a regular pentagon; by elementary constructions they also obtained a regular 15-gon and polygons containing 3 * 2 n; 5*2 n ; 15*2 n sides (for example, 6-gon, 20-gon, etc.). Attempts to construct other regular polygons were unsuccessful.
Carl Friedrich Gauss (1777-1855).
Gauss took advantage of the fact that constructing a regular n-gon inscribed in a circle is equivalent to solving the binomial equation x n - 1 = 0 in radicals. The result he obtained states: the construction is possible only if n is a prime number of the form
With k = 0, 1, 2, 3, 4, we get n = 3, 5, 17, 257, 65537, respectively, which means that it is possible to construct regular polygons with such a number of sides (the method of construction itself is a completely different question, in which there are many technical difficulties ). When k = 5, the number m turns out to be composite (back in 1732, L. Euler found that it is divisible by 641), therefore it is impossible to construct a regular polygon with such a number of sides using a compass and a ruler. It is not yet known which of the further terms of the series will be simple.
Gauss published a statement about his research:
“Everyone who has begun to study geometry knows that it is possible to construct geometrically various regular polygons, namely a triangle, a pentagon, a fifteen-gon, as well as those that are obtained from them by doubling the number of sides. All this was known back in the time of Euclid; As far as I know, it has not been possible to expand this list since then. All the more noteworthy is the message that it is possible to construct other regular polygons, for example, a decagon.
This discovery is part of an extensive theory not yet completed, which will be published after its completion.
K. F. Gauss, student of mathematics in Göttingen."
“It is noteworthy that Mr. Gauss is only 18 years old and that he studies philosophy and classical linguistics with the same success as mathematics.
E. A. W. Zimmerman, professor.”
It was a confession. Gauss became the pride of the university - professors and students extolled his abilities and successes. In 1799, Gauss was the first to rigorously prove the fundamental theorem of classical algebra - the possibility of decomposing any integer polynomial into factors of the first and second degree with real coefficients (further expansion of a quadratic trinomial with complex roots was considered inappropriate in those years). For this discovery, Helmstedt University awarded Gauss a doctorate in absentia and offered him an assistant professorship.
Gauss's book was published in 1801"Arithmetic Studies". In addition to a clear and consistent presentation of many important information, it contained 3 major discoveries of Gauss himself: the proof of the quadratic reciprocity law in the theory of algebraic numbers, research on the composition of classes in the theory of number fields and a detailed study of the binomial equation x n - 1 = 0, which made up a section of one of the basic algebraic theories, later created by Evariste Galois. Each of these discoveries alone would glorify the name of any mathematician. And what’s surprising is that the author was only a little over twenty!
As already mentioned, the calculation of the trajectory of Ceres brought Gauss the widest fame. On August 31, 1802, the secretary of the St. Petersburg Academy read a letter from the Berlin astronomer Professor Bode about his observation of Ceres in accordance with the indication of its position by Gauss. “The ellipse of Dr. Gauss still gives the position of this planet with amazing accuracy,” the letter said. Then the secretary, with the consent of the president, proposed to elect Dr. Karl Friedrich Gauss from Braunschweig as a corresponding member of the academy. Gauss was elected unanimously.
Soon, the secretary of the academy, N. I. Fuss (Nikolai Ivanovich Fuss, mathematician, one of L. Euler’s students.) sent a letter to Gauss. An associate professor at Helmstedt University was asked to move to St. Petersburg to conduct astronomical observations and be elected a member of the academy. Gauss was flattered. He asked for a deferment and began to study Russian.
A year later, Fuss repeated the invitation, promising an apartment and a salary of 1000 rubles a year (a lot of money at that time - much more than the 96 thalers salary of an assistant professor). But suddenly His Excellency the Duke heard about the invitation. He immediately ordered Gauss's salary to be increased fourfold and ordered the construction of an observatory for the scientist in Braunschweig. Gauss hesitated and decided to stay.
In 1806, the Duke of Brunswick was wounded in battle and died soon after. The unfinished observatory was destroyed during hostilities. Gauss, his wife and small child were left without service. He wrote several letters to St. Petersburg, but due to hostilities in Europe they did not arrive. Only a letter sent at the end of 1807 through M. Bartels, who was traveling to Russia, reached the academy. But in it, Gauss already announced that he accepted the invitation of the University of Göttingen. In the fall of 1808, he gave his first lecture in Göttingen: on the use of astronomy in navigation and in the service of precise time. From now on until the end of his life he is a professor and director of the astronomical observatory of the University of Göttingen. Soon, thanks to Gauss, this university and the Göttingen Scientific Royal Society occupy a leading position in Europe in the field of physical and mathematical sciences.
belong to Gauss deep and fundamental research in almost all the main areas of mathematics: number theory, geometry, probability theory, analysis, algebra, as well as important research in astronomy, geodesy, mechanics and the theory of magnetism, said Academician I.M. Vinogradov in his speech at the ceremonial meeting dedicated to the 100th anniversary of the death of Gauss. - All general mathematical ideas appeared in Gauss in connection with the solution of very specific problems.
The solution of practical problems of geodetic measurements prompted Gauss to discover fundamental theorems about the internal geometry of surfaces (“Gaussian curvature”).
Extensive processing of observations and measurements in practical problems of astronomy and geodesy forced the development of the least squares method and the study of statistical distribution laws (“Gaussian distribution”).
Work on the study of terrestrial magnetism led Gauss to the discovery of important theorems of potential theory...
Having taken up geodesy (Gauss was commissioned to conduct a geodetic survey and draw up a map of the Kingdom of Hanover), he created a new field of geometry for that time - the general theory of surfaces. Specially designated officers (and among them the son of K.F. Gauss, Joseph) took measurements on the ground using the heliotrope constructed by Gauss. Gauss himself performed numerous calculations.
Initially, the measurements were made with large errors, but Gauss insisted on clarifying the triangulation and achieved unprecedented accuracy at that time: the sum of the angles of any triangle could differ from 180 degrees by no more than 2 arc seconds! According to rough estimates, Gauss and his assistants processed in the process of calculations over a million initial data - distances, angles, coordinates - and, moreover, manually, without the help of an adding machine or other calculating devices. The titanic work ended only in 1848 - the geographical coordinates of all 2578 trigonometric points of the Kingdom of Hanover were determined very accurately.
In 1829, Gauss met Wilhelm Weber- physicist from Halle. Later, in 1831, Weber was invited to the University of Göttingen, where Gauss and Weber conducted fruitful joint research in the field of terrestrial magnetism and clarified the position of the Earth's magnetic poles. At the same time, they conducted research in the fields of electricity, electromagnetism, electrodynamics and induction and, in particular, developed the theoretical foundations of the electromagnetic telegraph. And in 1836, Gauss and Weber founded the International Society for the Study of Magnetism in Göttingen.
Gauss's interest in the exact sciences was truly inexhaustible. But his favorite brainchild remained the theory of numbers, which he considered the “queen of mathematics.” Gauss laid the foundations for many modern areas of this science.
Ideas related to the foundations of geometry occupy a special position in Gauss’s work. While still a student, he thought a lot about the postulates formulated by Euclid and whether the fifth postulate (the axiom of parallels) was independent or could be deduced from the remaining axioms.
The possibility of the existence in a plane of two different lines, parallel to a given line and passing through a point not lying on this line, contradicts our usual ideas. However, by 1816, Gauss had become convinced that geometry, in which Euclid's parallel axiom was replaced by another axiom, was consistent. Gauss did not agree with Kant's assertion that our familiar space is Euclidean. However, he adhered to Kantian agnosticism:
“I am coming to the conviction that geometry cannot be proven, at least by human reason and for human reason,” wrote Gauss in 1817. “Perhaps in another life we will come to other views on the nature of space that are now inaccessible to us.” ..."
Gauss was pleased with Lobachevsky's discovery, which corresponded to his inner convictions. He highly appreciated the achievement of the Russian scientist and achieved his election as a corresponding member of the Gottingen scientist of the Royal Society. However, Gauss himself never came out officially, much less in print, with the recognition of non-Euclidean geometry or with his thoughts about it.
Excerpts from Gauss's letters will make it possible to understand the reasons why he did not consider it possible to announce not only his ideas (Gauss never developed these ideas with sufficient clarity), but also his attitude towards the possibility of a “new” geometry.
“The wasps whose nest you destroy will rise above your head,” wrote Gauss in 1818 to a student and friend who was going to express doubts about the validity of the fifth postulate in the new edition of his book.
“If non-Euclidean geometry were true... we would have a priori an absolute measure of length,” he wrote in 1824. “But you must look at this as a private communication that should not be published.”
“It will probably be a while before I can process my research so that it can be published. It is even possible that I will not dare to do this all my life, because I am afraid of the cry of the Boeotians,” wrote Gauss in 1829, 3 years after Lobachevsky publicly announced his discovery.
Gauss was afraid of being misunderstood by his contemporaries. He wavered between the desire to support scientific truth and the danger of disturbing the hornet's nest of those who do not understand.
Gauss lived constantly in Göttingen. Only once, at the invitation of A. Humboldt, he took part in the Berlin Congress of Naturalists. He could conduct very lengthy and tedious research, experiments, experiments, but he was very reluctant to give lectures, considering teaching groups of students a necessary but unpleasant duty. However, he willingly gave his strength, time, and ideas to some of his favorite students, and maintained correspondence with them on scientific problems for decades.
Gauss was fluent in Latin, French, English. He enjoyed reading the original works of Dickens, Swift, Richardson, Milton and especially Walter Scott, the great French enlighteners - Montaigne, Rousseau, Condorcet, Voltaire. Gauss's two youngest sons emigrated to the United States - and Gauss became interested in American literature. He also read Danish, Swedish, Spanish, and Italian. In his youth, he studied Russian a little; at the age of 63, wanting to become more familiar with the works of Lobachevsky, he began to intensively study the Russian language. “I began to read Russian fluently and received great pleasure from it,” he wrote to one of his students. 57 books in Russian were subsequently discovered in Gauss’s personal library, including an eight-volume edition of Pushkin.
Oddly enough, Gauss was very conservative in public life. Even in his youth, he felt completely dependent on the powers that be, and in particular on the Duke, who awarded him a scholarship, and later a high salary.
In 1837, after King Ernst August of Hanover abolished the already scanty constitution, seven professors at the University of Göttingen made an official protest. Among these scientists were Gauss's friend, the physicist Weber, the famous philologists the Brothers Grimm, and Gauss's son-in-law, Professor Ewald. The king rejected the protest, cynically declaring that he could “support dancers, prostitutes and professors for his own money” - as many as he wanted. Three of those who signed the protest were asked to leave the kingdom within three days, the rest were expelled from the university. The prestige of the University of Göttingen fell sharply after this scandalous story and was restored only after several decades.
Gauss was not affected by all these events. He firmly adhered to the principle of not interfering in politics.
In 1849, celebrations took place to mark the fiftieth anniversary of Gauss's doctorate. Famous mathematicians arrived in Göttingen: P. Dirichlet (later Gauss's successor at the University of Göttingen), K. Jacobi and others. These honors pleased Gauss much more than all sorts of panegyrics in the press and messages about his election as an honorary member of scientific societies and academies.
In recent years, Gauss was overcome by apathy. He moved little and with difficulty, but retained clarity of speech and thinking. In February 1851, he wrote to Alexander Humboldt: “Although I have not suffered from any illness for many years, I always feel unwell and constantly drowsy. This is associated with increased irritability and the need to constantly take care, as well as a monotonous way of life...”
Gauss wore a light black cap, a long brown frock coat and gray trousers,” said one of Gauss’s last students, Richard Dedekind. “He mostly sat in a comfortable position, leaning slightly forward. He spoke freely, very simply and clearly. When he wanted to emphasize his point and used special terms, he leaned towards his interlocutor and looked directly at him with the piercing gaze of his beautiful blue eyes... For numerical examples, to which he always attached great importance, he had small pieces of paper with the necessary numbers.
With age, my health began to decline. Doctors noted overexertion and expansion of the heart. Medicines brought only some relief. In June 1854, the carriage in which 77-year-old Gauss was traveling with his daughter capsized. This incident shocked Gauss, although neither he nor his daughter received a single scratch.
Gauss died on February 23, 1855. He was buried in the cemetery in Göttingen. In accordance with the last will of the scientist, a regular 17-gon inscribed in a circle is engraved on his tombstone. The memory of Gauss was immortalized by a medal embossed by royal decree with the Latin inscription “ Carl Friedrich Gauss - King of Mathematicians».
GAUSS, CARL FRIEDRICH(Gauss, Carl Friedrich) (1777–1855), German mathematician, astronomer and physicist. Born April 30, 1777 in Brunswick. In 1788, with the support of the Duke of Brunswick, Gauss entered the closed school Collegium Carolinum, and then the University of Göttingen, where he studied from 1795 to 1798. In 1796, Gauss managed to solve a problem that had defied the efforts of geometers since the time of Euclid: he found a way to construct using compass and ruler regular 17-gon. Gauss himself was so impressed by this result that he decided to devote himself to the study of mathematics, and not classical languages, as he initially assumed. In 1799 he defended his doctoral dissertation at the University of Helmstadt, in which he first gave a rigorous proof of the so-called. fundamental theorem of algebra, and in 1801 he published the famous Arithmetic studies (Disquisitiones arithmeticae), considered the beginning of modern number theory. The central place in the book is occupied by the theory of quadratic forms, residues and comparisons of the second degree, and the highest achievement is the law of quadratic reciprocity - the “golden theorem”, the first complete proof of which was given by Gauss.
In January 1801, astronomer G. Piazzi, who was compiling a star catalogue, discovered an unknown star of 8th magnitude. He managed to trace its path only over an arc of 9° (1/40 of the orbit), and the task arose of determining the full elliptical trajectory of the body from the available data, all the more interesting since, apparently, in fact, we were talking about the long-supposed between Mars and Jupiter to the minor planet. In September 1801, Gauss began calculating the orbit, in November the calculations were completed, the results were published in December, and on the night of December 31 to January 1, the famous German astronomer Olbers, using Gauss’s data, found the planet (it was called Ceres). In March 1802, another similar planet, Pallas, was discovered, and Gauss immediately calculated its orbit. He outlined his methods for calculating orbits in the famous Theories of the motion of celestial bodies (Theoria motus corporum coelestium, 1809). The book describes the least squares method he used, which to this day remains one of the most common methods for processing experimental data.
In 1807, Gauss headed the department of mathematics and astronomy at the University of Göttingen and received the post of director of the Göttingen Astronomical Observatory. In subsequent years, he worked on the theory of hypergeometric series (the first systematic study of the convergence of series), mechanical quadratures, secular perturbations of planetary orbits, and differential geometry.
In 1818–1848, geodesy was the center of Gauss's scientific interests. He carried out both practical work (geodetic survey and drawing up a detailed map of the Kingdom of Hanover, measuring the arc of the Göttingen-Altona meridian, undertaken to determine the true compression of the Earth), and theoretical research. He laid the foundations of higher geodesy and created the theory of the so-called. internal geometry of surfaces. In 1828, Gauss's main geometric treatise was published. General studies regarding curved surfaces (Disquisitiones generales circa superficies curvas). In particular, it mentions a surface of rotation of constant negative curvature, the internal geometry of which, as was later discovered, is the geometry of Lobachevsky.
Research in the field of physics, which Gauss was engaged in since the early 1830s, belongs to different branches of this science. In 1832 he created an absolute system of measures, introducing three basic units: 1 sec, 1 mm and 1 kg. In 1833, together with W. Weber, he built the first electromagnetic telegraph in Germany, connecting the observatory and the physical institute in Göttingen, carried out extensive experimental work on terrestrial magnetism, invented a unipolar magnetometer, and then a bifilar one (also together with W. Weber), created the foundations of potential theory , in particular, formulated the fundamental theorem of electrostatics (the Gauss–Ostrogradsky theorem). In 1840 he developed the theory of constructing images in complex optical systems. In 1835 he created a magnetic observatory at the Göttingen Astronomical Observatory.
In 1845, the university instructed Gauss to reorganize the Fund for the Support of Widows and Children of Professors. Gauss not only did an excellent job of this task, but also made important contributions to the theory of insurance along the way. On July 16, 1849, the University of Göttingen solemnly celebrated the golden anniversary of Gauss's dissertation. In the anniversary lecture, the scientist returned to the topic of his dissertation, offering the fourth proof of the main theorem of algebra.
Carl Gauss (1777-1855), - German mathematician, astronomer and physicist. He created the theory of “primordial” roots from which the construction of the 17-gon flowed. One of the greatest mathematicians of all time.
Carl Friedrich Gauss was born on April 30, 1777 in Brunswick. He inherited good health from his father's family, and a bright intellect from his mother's family.
At the age of seven, Karl Friedrich entered the Catherine Folk School. Since they started counting there in the third grade, they did not pay attention to little Gauss for the first two years. Students usually entered third grade at the age of ten and studied there until confirmation (age fifteen). Teacher Büttner had to work with children of different ages and different levels of training at the same time. Therefore, he usually gave some of the students long calculation tasks in order to be able to talk with other students. Once a group of students, among whom was Gauss, was asked to sum the natural numbers from 1 to 100. As they completed the task, the students had to place their slates on the teacher's table. The order of the boards was taken into account when grading. Ten-year-old Karl put down his board as soon as Büttner finished dictating the task. To everyone's surprise, only he had the correct answer. The secret was simple: the task was dictated for now. Gauss managed to rediscover the formula for the sum of an arithmetic progression! The fame of the miracle child spread throughout little Brunswick.
In 1788, Gauss entered the gymnasium. However, it does not teach mathematics. Classical languages are studied here. Gauss enjoys studying languages and makes such progress that he does not even know what he wants to become - a mathematician or a philologist.
Gauss is known at court. In 1791 he was introduced to Karl Wilhelm Ferdinand, Duke of Brunswick. The boy visits the palace and entertains the courtiers with the art of counting. Thanks to the Duke's patronage, Gauss was able to enter the University of Göttingen in October 1795. At first, he listens to lectures on philology and almost never attends lectures on mathematics. But this does not mean that he does not do mathematics.
In 1795, Gauss developed a passionate interest in integers. Unfamiliar with any literature, he had to create everything for himself. And here he again shows himself as an extraordinary calculator, paving the way into the unknown. In the autumn of the same year, Gauss moved to Göttingen and literally devoured the literature that he first came across: Euler and Lagrange.
“March 30, 1796 comes for him the day of creative baptism. - writes F. Klein. - Gauss had already been studying for some time the grouping of roots of unity on the basis of his theory of “primitive” roots. And then one morning, waking up, he suddenly clearly and distinctly realized that the construction of a 17-gon follows from his theory... This event was the turning point in Gauss's life. He decides to devote himself not to philology, but exclusively to mathematics.”
Gauss's work became an unattainable example of mathematical discovery for a long time. One of the creators of non-Euclidean geometry, János Bolyai, called it “the most brilliant discovery of our time, or even of all time.” How difficult it was to comprehend this discovery. Thanks to letters to the homeland of the great Norwegian mathematician Abel, who proved the unsolvability of equations of the fifth degree in radicals, we know about the difficult path that he went through while studying Gauss's theory. In 1825, Abel writes from Germany: “Even if Gauss is the greatest genius, he obviously did not strive for everyone to understand this at once...” Gauss’s work inspires Abel to build a theory in which “there are so many wonderful theorems that it is simply impossible to I believe it." There is no doubt that Gauss also influenced Galois.
Gauss himself retained a touching love for his first discovery throughout his life.
“They say that Archimedes bequeathed to build a monument in the form of a ball and a cylinder over his grave in memory of the fact that he found the ratio of the volumes of a cylinder and a ball inscribed in it to be 3:2. Like Archimedes, Gauss expressed the desire to have a decagon immortalized in the monument on his grave. This shows the importance Gauss himself attached to his discovery. This drawing is not on Gauss’s gravestone; the monument erected to Gauss in Brunswick stands on a seventeen-sided pedestal, although barely noticeable to the viewer,” wrote G. Weber.
On March 30, 1796, the day when the regular 17-gon was built, Gauss's diary begins - a chronicle of his remarkable discoveries. The next entry in the diary appeared on April 8. It reported on the proof of the quadratic reciprocity theorem, which he called the “golden” theorem. Special cases of this statement were proved by Ferm, Euler, and Lagrange. Euler formulated a general hypothesis, an incomplete proof of which was given by Legendre. On April 8, Gauss found a complete proof of Euler's conjecture. However, Gauss did not yet know about the work of his great predecessors. He walked the entire difficult path to the “golden theorem” on his own!
Gauss made two great discoveries in just ten days, a month before he turned 19! One of the most amazing aspects of the “Gauss phenomenon” is that in his first works he practically did not rely on the achievements of his predecessors, rediscovering, as it were, in a short period of time what had been done in number theory over a century and a half through the works of major mathematicians.
In 1801, Gauss's famous "Arithmetic Studies" were published. This huge book (over 500 large format pages) contains Gauss's main results. The book was published at the expense of the Duke and dedicated to him. In its published form, the book consisted of seven parts. There wasn't enough money for an eighth of it. In this part, we were supposed to talk about the generalization of the reciprocity law to degrees higher than the second, in particular, about the biquadratic reciprocity law. Gauss found a complete proof of the biquadratic law only on October 23, 1813, and in his diaries he noted that this coincided with the birth of his son.
Outside of the Arithmetic Studies, Gauss essentially no longer studied number theory. He only thought through and completed what was planned in those years.
“Arithmetic studies” had a huge impact on the further development of number theory and algebra. The laws of reciprocity still occupy one of the central places in algebraic number theory. In Braunschweig, Gauss did not have the literature necessary to work on Arithmetical Research." Therefore, he often traveled to neighboring Helmstadt, where there was a good library. Here, in 1798, Gauss prepared a dissertation devoted to the proof of the Fundamental Theorem of Algebra - the statement that every algebraic equation has a root, which can be a real or imaginary number, in one word - complex. Gauss critically examines all previous experiments and evidence and with great care carries out the idea to Lambert. An impeccable proof still did not work out, since there was a lack of a strict theory of continuity. Subsequently, Gauss came up with three more proofs of the Fundamental Theorem (the last time in 1848).
Gauss's "mathematical age" is less than ten years old. At the same time, most of the time was occupied by works that remained unknown to contemporaries (elliptic functions).
Gauss believed that he could not rush to publish his results, and this was the case for thirty years. But in 1827, two young mathematicians at once - Abel and Jacobi - published much of what they had obtained.
Gauss's work on non-Euclidean geometry became known only with the publication of a posthumous archive. Thus, Gauss provided himself with the opportunity to work calmly by refusing to make his great discovery public, causing ongoing debate to this day about the admissibility of the position he took.
With the advent of the new century, Gauss's scientific interests decisively shifted away from pure mathematics. He will occasionally turn to it many times, and each time he will get results worthy of a genius. In 1812 he published a paper on the hypergeometric function. Gauss's contribution to the geometric interpretation of complex numbers is widely known.
Gauss's new hobby was astronomy. One of the reasons he took up the new science was prosaic. Gauss occupied the modest position of privatdozent in Braunschweig, receiving 6 thalers a month.
A pension of 400 thalers from the patron duke did not improve his situation enough to support his family, and he was thinking about marriage. It was not easy to get a chair in mathematics somewhere, and Gauss was not very keen on active teaching. The expanding network of observatories made a career as an astronomer more accessible, and Gauss began to become interested in astronomy while still in Göttingen. He carried out some observations in Brunswick, and he spent part of the ducal pension on the purchase of a sextant. He is looking for a worthy computing problem.
A scientist calculates the trajectory of a proposed new large planet. The German astronomer Olbers, relying on Gauss's calculations, found a planet (it was called Ceres). It was a real sensation!
On March 25, 1802, Olbers discovers another planet - Pallas. Gauss quickly calculates its orbit, showing that it too is located between Mars and Jupiter. The effectiveness of Gauss's computational methods became undeniable for astronomers.
Recognition comes to Gauss. One of the signs of this was his election as a corresponding member of the St. Petersburg Academy of Sciences. Soon he was invited to take the place of director of the St. Petersburg Observatory. At the same time, Olbers makes efforts to save Gauss for Germany. Back in 1802, he proposed to the curator of the University of Göttingen to invite Gauss to the post of director of the newly organized observatory. Olbers writes at the same time that Gauss “has a positive aversion to the department of mathematics.” Consent was given, but the move took place only at the end of 1807. During this time, Gauss married. “Life seems to me like spring with always new bright colors,” he exclaims. In 1806, the Duke, to whom Gauss apparently was sincerely attached, dies of his wounds. Now nothing is keeping him in Brunswick.
Gauss's life in Göttingen was not easy. In 1809, after the birth of his son, his wife died, and then the child himself. In addition, Napoleon imposed a heavy indemnity on Göttingen. Gauss himself had to pay an exorbitant tax of 2,000 francs. Olbers and, right in Paris, Laplace tried to pay for him. Both times Gauss proudly refused.
However, another benefactor was found, this time anonymous, and there was no one to return the money to. Only much later did they learn that it was the Elector of Mainz, a friend of Goethe. “Death is dearer to me than such a life,” writes Gauss between notes on the theory of elliptic functions. Those around him did not appreciate his work; they considered him, to say the least, an eccentric. Olbers reassures Gauss, saying that one should not count on people’s understanding: “they must be pitied and served.”
In 1809, the famous “Theory of the motion of celestial bodies revolving around the Sun along conical sections” was published. Gauss outlines his methods for calculating orbits. To ensure the power of his method, he repeats the calculation of the orbit of the 1769 comet, which Euler had calculated in three days of intense calculation. It took Gauss an hour to do this. The book outlined the least squares method, which remains to this day one of the most common methods for processing observational results.
1810 saw a large number of honors: Gauss received the prize of the Paris Academy of Sciences and the gold medal of the Royal Society of London, and was elected to several academies.
Regular studies in astronomy continued almost until his death. The famous comet of 1812 (which “foreshadowed” the fire of Moscow!) was observed everywhere using Gauss’s calculations. On August 28, 1851, Gauss observed a solar eclipse. Gauss had many astronomer students: Schumacher, Gerling, Nikolai, Struve. The greatest German geometers Möbius and Staudt studied from him not geometry, but astronomy. He was in active correspondence with many astronomers on a regular basis.
By 1820, the center of Gauss's practical interests had shifted to geodesy. We owe it to geodesy that for a relatively short time Mathematics again became one of Gauss’s main concerns. In 1816, he thinks about generalizing the basic problem of cartography - the problem of mapping one surface onto another "so that the mapping is similar to the one depicted in the smallest detail."
In 1828, Gauss's main geometric memoir, General Studies on Curved Surfaces, was published. The memoir is devoted to the internal geometry of a surface, that is, to what is associated with the structure of this surface itself, and not with its position in space.
It turns out that “without leaving the surface” you can find out whether it is curved or not. A “real” curved surface cannot be turned onto a plane by any bending. Gauss proposed a numerical characteristic of the measure of surface curvature.
By the end of the twenties, Gauss, who had passed the fifty-year mark, began to search for new areas of scientific activity. This is evidenced by two publications from 1829 and 1830. The first of them bears the stamp of reflection on the general principles of mechanics (Gauss’s “principle of least constraint” is built here); the other is devoted to the study of capillary phenomena. Gauss decides to study physics, but his narrow interests have not yet been determined.
In 1831 he tried to study crystallography. This is a very difficult year in the life of Gauss,” his second wife dies, he begins to suffer from severe insomnia. In the same year, 27-year-old physicist Wilhelm Weber, invited on Gauss’ initiative, comes to Göttingen. Gauss met him in 1828 in Humboldt’s house. Gauss was 54 years old. , his reticence was legendary, and yet in Weber he found a scientific companion such as he had never had before.
The interests of Gauss and Weber lay in the field of electrodynamics and terrestrial magnetism. Their activities had not only theoretical, but also practical results. In 1833 they invent the electromagnetic telegraph. The first telegraph connected the magnetic observatory with the city of Neuburg.
The study of terrestrial magnetism was based both on observations at the magnetic observatory established in Göttingen, and on materials that were collected in different countries by the “Union for the Observation of Terrestrial Magnetism,” created by Humboldt after returning from South America. At the same time, Gauss created one of the most important chapters of mathematical physics - potential theory.
The joint studies of Gauss and Weber were interrupted in 1843, when Weber, along with six other professors, was expelled from Göttingen for signing a letter to the king, which indicated the latter’s violations of the constitution (Gauss did not sign the letter). Weber returned to Göttingen only in 1849, when Gauss was already 72 years old.
Gauss Karl Friedrich (1777-1855)
I have known my results for a long time, I just don’t know how I will arrive at them.
The science of mathematics is the queen of all sciences.
K. Gauss
German mathematician and astronomer
Carl Friedrich Gauss was born on April 30, 1777 in Germany, in the city of Brunswick, into the family of a craftsman. The father, Gerhard Diederich Gauss, had many different professions, since due to lack of money he had to do everything from installing fountains to gardening. Karl's mother, Dorothea, was also from a simple family of stonemasons. She was distinguished by her cheerful character, she was an intelligent, cheerful and determined woman, she loved her only son and was proud of him.
As a child, Gauss learned to count very early. One summer, his father took three-year-old Karl to work in a quarry. When the workers finished work, Gerhard, Karl's father, began to make payments to each worker. After tedious calculations, which took into account the number of hours, output, working conditions, etc., the father read out a statement from which it followed who was owed how much. And suddenly little Karl said that the count was incorrect, that there was a mistake. They checked, and the boy was right. They began to say that little Gauss learned to count before he spoke.
When Karl was 7 years old, he was assigned to the Catherine School, which was headed by Büttner. He immediately paid attention to the boy who solved the examples the fastest. At school, Gauss met and became friends with a young man, Buettner's assistant, whose name was Johann Martin Christian Bartels. Together with Bartels, 10-year-old Gauss took up mathematical transformation and the study of classical works. Thanks to Bartels, Duke Karl Wilhelm Ferdinand and the nobles of Brunswick drew attention to the young talent. Johann Martin Christian Bartels subsequently studied at Helmstedt and Göttingen universities, and subsequently came to Russia and was a professor at Kazan University, Nikolai Ivanovich Lobachevsky listened to his lectures.
Meanwhile, Karl Gauss entered the Catherine Gymnasium in 1788. The poor boy would never have been able to study at the gymnasium, and then at the university, without the help and patronage of the Duke of Brunswick, to whom Gauss was devoted and grateful throughout his life. The Duke always remembered the shy young man of extraordinary abilities. Karl Wilhelm Ferdinand provided the necessary funds to continue the young man’s education at the Karolinska College, which prepared him for entering the university.
In 1795, Karl Gauss entered the University of Göttingen to study. Among the young mathematician's university friends was Farkas Bolyai, the father of János Bolyai, the great Hungarian mathematician. In 1798 he graduated from the university and returned to his homeland.
In his native Braunschweig, for ten years, Gauss experienced a kind of “Boldino autumn” - a period of ebullient creativity and great discoveries. The area of mathematics in which he works is called the “three great As”: arithmetic, algebra and analysis.
It all started with the art of counting. Gauss counts constantly, he performs calculations with decimal numbers with an incredible number of decimal places. Over the course of his life, he becomes a virtuoso in numerical calculations. Gauss accumulates information about various sums of numbers, calculations of infinite series. It's like a game where the genius of a scientist comes up with hypotheses and discoveries. He is like a brilliant prospector, he feels when his pickaxe hits a gold nugget.
Gauss compiles tables of reciprocals. He decided to trace how the period of the decimal fraction changes depending on the natural number p.
He proved that a regular 17-gon can be constructed using a compass and ruler, i.e. that the equation is:
or equation
solvable in quadratic radicals.
He gave a complete solution to the problem of constructing regular heptagons and ninegons. Scientists have been working on this problem for 2000 years.
Gauss begins to keep a diary. Reading it, we see how a fascinating mathematical action begins to unfold, the scientist’s masterpiece, his “Arithmetic Studies,” is born.
He proved the fundamental theorem of algebra, in number theory he proved the law of reciprocity, which was discovered by the great Leonhard Euler, but he could not prove it. Carl Gauss deals with the theory of surfaces in geometry, from which it follows that geometry is constructed on any surface, and not just on a plane, as in Euclidean planimetry or spherical geometry. He managed to construct lines on the surface that play the role of straight lines, and was able to measure distances on the surface.
Applied astronomy is firmly within the scope of his scientific interests. This is an experimental and mathematical work consisting of observations, studies of experimental points, mathematical methods for processing observation results, and numerical calculations. Gauss's interest in practical astronomy was known, and he did not trust anyone with tedious calculations.
The discovery of the small planet Ceres brought him fame as the most famous astronomer in Europe. And it was like this. First, D. Piazzi discovered a small planet and named it Ceres. But he was unable to determine its exact location, since the celestial body was hidden behind dense clouds. Gauss, at the tip of his pen, rediscovered Ceres at his desk. He calculated the orbit of the small planet and, in a letter to Piazzi, indicated where and when Ceres could be observed. When astronomers pointed their telescopes at the indicated point, they saw Ceres, which reappeared. There was no end to their amazement.
The young scientist is tipped to become the director of the Göttingen Observatory. The following was written about him: “Gauss’s fame is well deserved, and the young 25-year-old man is already ahead of all modern mathematicians...”.
On November 22, 1804, Karl Gauss married Joanna Osthoff from Brunswick. He wrote to his friend Bolyai: “Life seems to me like an eternal spring with all new bright flowers.” He is happy, but it doesn't last long. Five years later, Joanna dies after the birth of her third child, son Louis, who, in turn, did not live long, only six months. Karl Gauss is left alone with two children - son Joseph and daughter Minna. And then another misfortune happened: the Duke of Brunswick, an influential friend and patron, suddenly died. The Duke died from wounds received in battles, which he lost, at Auerstedt and Jena.
Meanwhile, the scientist is invited by the University of Göttingen. Thirty-year-old Gauss received the chair of mathematics and astronomy, and then the post of director of the Göttingen Astronomical Observatory, which he held until the end of his life.
On August 4, 1810, he married his late wife’s beloved friend, the daughter of the Göttingen councilor Wal-dec. Her name was Minna, she gave birth to Gauss a daughter and two sons. At home, Karl was a strict conservative who did not tolerate any innovations. He had an iron character, and his outstanding abilities and genius were combined with truly childish modesty. He was deeply religious and firmly believed in an afterlife. Throughout his life as a scientist, the furnishings of his small office spoke of the unpretentious tastes of its owner: a small desk, a desk painted with white oil paint, a narrow sofa and a single armchair. The candle burns dimly, the temperature in the room is very moderate. This is the abode of the “king of mathematicians,” as Gauss was called, the “Göttingen colossus.”
The scientist’s creative personality has a very strong humanitarian component: he is interested in languages, history, philosophy and politics. He learned the Russian language, in letters to friends in St. Petersburg he asked to send him books and magazines in Russian and even Pushkin’s “The Captain’s Daughter.”
Karl Gauss was offered to take a chair at the Berlin Academy of Sciences, but he was so overwhelmed by his personal life and its problems (after all, he had just become engaged to his second wife) that he refused the tempting offer. After only a short stay in Göttingen, Gauss formed a circle of students; they idolized their teacher, worshiped him, and subsequently became famous scientists themselves. These are Schumacher, Gerlin, Nicolai, Möbius, Struve and Encke. The friendship arose in the field of applied astronomy. They all become directors of observatories.
Karl Gauss's work at the university was, of course, related to teaching. Oddly enough, his attitude towards this activity is very, very negative. He believed that this was a waste of time, which was taken away from scientific work and research. However, everyone noted the high quality of his lectures and their scientific value. And since by nature Karl Gauss was a kind, sympathetic and attentive person, the students paid him with respect and love.
His studies in dioptrics and practical astronomy led him to practical applications, particularly how to improve the telescope. He carried out the necessary calculations, but no one paid attention to them. Half a century passed, and Steingel used the calculations and formulas of Gauss and created an improved telescope design.
In 1816, a new observatory was built and Gauss moved into a new apartment as director of the Göttingen Observatory. Now the manager has important concerns - he needs to replace instruments that have long been obsolete, especially telescopes. Gauss ordered the famous masters Reichenbach, Frauenhofer, Utzschneider and Ertel two new meridian instruments, which were ready in 1819 and 1821. The Gottingen Observatory, under the leadership of Gauss, begins to make the most accurate measurements.
The scientist invented the heliotron. This is a simple and cheap device, consisting of a telescope and two flat mirrors, placed normally. They say that everything ingenious is simple, and this also applies to the heliotron. The device turned out to be absolutely necessary for geodetic measurements.
Gauss calculates the effect of gravity on the surfaces of planets. It turns out that only very small creatures can live on the Sun, since the force of gravity there is 28 times greater than that on Earth.
In physics, he is interested in magnetism and electricity. In 1833, the electromagnetic telegraph invented by him was demonstrated. It was the prototype of the modern telegraph. The conductor through which the signal passed was made of iron 2 or 3 millimeters thick. On this first telegraph, individual words were first transmitted, and then entire phrases. Public interest in Gauss's electromagnetic telegraph was very great. The Duke of Cambridge specially came to Göttingen to meet him.
“If there were money,” Gauss wrote to Schumacher, “then electromagnetic telegraphy could be brought to such perfection and to such dimensions that the imagination is simply horrified.” After successful experiments in Göttingen, the Saxon Minister of State Lindenau invited Leipzig professor Ernst Heinrich Weber, who together with Gauss demonstrated the telegraph, to present a report on “the construction of an electromagnetic telegraph between Dresden and Leipzig.” Ernst Heinrich Weber's report contained prophetic words: “...if the earth is ever covered with a network of railways with telegraph lines, it will resemble the nervous system in the human body...”. Weber took an active part in the project, made many improvements, and the first Gauss-Weber telegraph lasted ten years, until on December 16, 1845, after a strong lightning strike, most of its wire line burned out. The remaining piece of wire became a museum exhibit and is stored in Göttingen.
Gauss and Weber conducted famous experiments in the field of magnetic and electrical units and the measurement of magnetic fields. The results of their research formed the basis of the theory of potential, the basis of the modern theory of errors.
While Gauss was studying crystallography, he invented a device that could be used to measure the angles of a crystal with high precision using a 12-inch Reichenbach theodolite, and he also invented a new way to designate crystals.
An interesting page of his heritage is connected with the foundations of geometry. They said that the great Gauss studied the theory of parallel lines and came to a new, completely different geometry. Gradually, a group of mathematicians formed around him and exchanged ideas in this area. It all started with the fact that young Gauss, like other mathematicians, tried to prove the parallel theorem based on axioms. Having rejected all pseudo-evidence, he realized that nothing could be created along this path. The non-Euclidean hypothesis frightened him. These thoughts cannot be published - the scientist would be anathematized. But the thought cannot be stopped, and Gaussian non-Euclidean geometry - here it is in front of us, in the diaries. This is his secret, hidden from the general public, but known to his closest friends, since mathematicians have a tradition of correspondence, a tradition of exchanging thoughts and ideas.
Farkas Bolyai, a professor of mathematics, a friend of Gauss, while raising his son Janos, a talented mathematician, persuaded him not to study the theory of parallels in geometry, saying that this topic was cursed in mathematics and, except for misfortune, it would bring nothing. And what Karl Gauss did not say was later said by Lobachevsky and Bolyai. Therefore, absolute non-Euclidean geometry is named after them.
Over the years, Gauss's reluctance to teach and lecture disappears. By this time, he is surrounded by students and friends. On July 16, 1849, the fiftieth anniversary of Gauss receiving his doctorate was celebrated in Göttingen. Numerous students and admirers, colleagues and friends gathered. He was awarded diplomas of honorary citizen of Göttingen and Braunschweig, orders of various states. A gala dinner took place, at which he said that in Göttingen there are all conditions for the development of talent, they help in everyday difficulties and in science, and also that “... banal phrases have never had power in Göttingen.”
Carl Gauss has aged. Now he works less intensively, but his range of activities is still wide: convergence of series, practical astronomy, physics.
The winter of 1852 was very difficult for him, his health deteriorated sharply. He never went to doctors because he did not trust medical science. His friend, Professor Baum, examined the scientist and said that the situation was very serious and it was associated with heart failure. The health of the great mathematician steadily deteriorated, he stopped walking and died on February 23, 1855.
Contemporaries of Karl Gauss felt the superiority of genius. The medal, minted in 1855, is engraved: Mathematicorum princeps (Princeps of Mathematicians). In astronomy, his memory remains in the name of one of the fundamental constants, a system of units, a theorem, a principle, formulas - all of this bears the name of Karl Gauss.
