The great mathematician Gauss: biography, photos, discoveries. Carl Gauss - interesting data and facts What Gauss discovered

Gauss Karl Friedrich
Born: April 30, 1777.
Died: February 23, 1855.

Biography

Johann Carl Friedrich Gauss (German: Johann Carl Friedrich Gauß; April 30, 1777, Braunschweig - February 23, 1855, Göttingen) - German mathematician, mechanic, physicist, astronomer and surveyor. Considered one of the greatest mathematicians of all time, the "King of Mathematicians". Laureate of the Copley Medal (1838), foreign member of the Swedish (1821) and Russian (1824) Academies of Sciences, and the English Royal Society.

1777-1798

Gauss's grandfather was a poor peasant, his father was a gardener, mason, and canal supervisor in the Duchy of Brunswick. Already at the age of two, the boy showed himself to be a child prodigy. At the age of three he could read and write, even correcting his father’s calculation mistakes. According to legend, the school math teacher, in order to keep the children busy, for a long time, asked them to count the sum of numbers from 1 to 100. Young Gauss noticed that the pairwise sums from opposite ends are the same: 1+100=101, 2+99=101, etc., and instantly got the result: 50 \times 101= 5050. Until his old age, he was accustomed to doing most of his calculations in his head.

He was lucky with his teacher: M. Bartels (later Lobachevsky’s teacher) appreciated the exceptional talent of young Gauss and managed to get him a scholarship from the Duke of Brunswick. This helped Gauss graduate from the Collegium Carolinum in Brunswick (1792-1795).

Fluent in many languages, Gauss hesitated for some time between philology and mathematics, but chose the latter. He loved the Latin language very much and wrote a significant part of his works in Latin; loved English, French and Russian literature. At the age of 62, Gauss began to study Russian in order to familiarize himself with the works of Lobachevsky, and was quite successful in this matter.

In college Gauss studied the works of Newton, Euler, Lagrange. Already there he made several discoveries in number theory, including proving the law of reciprocity of quadratic residues. Legendre, however, discovered this most important law earlier, but was unable to strictly prove it; Euler also failed to do this. In addition, Gauss created the “least squares method” (also independently discovered by Legendre) and began research in the field of “normal error distribution.”

From 1795 to 1798, Gauss studied at the University of Göttingen, where his teacher was A. G. Kästner. This is the most fruitful period in Gauss's life.

1796: Gauss proved the possibility of constructing a regular seventeen-sided triangle using a compass and ruler. Moreover, he solved the problem of constructing regular polygons to the end and found a criterion for the possibility of constructing a regular n-gon using a compass and ruler: if n is a prime number, then it must be of the form n=2^(2^k)+1 (the number Farm). Gauss treasured this discovery very much and bequeathed that a regular 17-gon inscribed in a circle should be depicted on his grave.

Since 1796, Gauss has kept a short diary of his discoveries. He, like Newton, did not publish many things, although these were results of exceptional importance (elliptic functions, non-Euclidean geometry, etc.). He explained to his friends that he publishes only those results that he is satisfied with and considers complete. Many ideas that he put aside or abandoned were later resurrected in the works of Abel, Jacobi, Cauchy, Lobachevsky and others. He also discovered quaternions 30 years before Hamilton (calling them “mutations”).

1798: the masterpiece “Arithmetic Investigations” (Latin: Disquisitiones Arithmeticae) was completed, published only in 1801.

In this work, the theory of comparisons is presented in detail in modern (introduced by him) notation, comparisons of arbitrary order are solved, quadratic forms are deeply studied, complex roots of unity are used to construct regular n-gons, the properties of quadratic residues are outlined, a proof of the quadratic reciprocity law is given, etc. D. Gauss liked to say that mathematics is the queen of sciences, and number theory is the queen of mathematics.

1798-1816

In 1798, Gauss returned to Brunswick and lived there until 1807.

The Duke continued to patronize the young genius. He paid for the printing of his doctoral dissertation (1799) and awarded him a good scholarship. In his doctoral work, Gauss first proved the fundamental theorem of algebra. Before Gauss, there were many attempts to do this; D'Alembert came closest to the goal. Gauss repeatedly returned to this theorem and gave 4 different proofs of it.

Since 1799, Gauss has been a privatdozent at the University of Braunschweig.

1801: elected corresponding member of the St. Petersburg Academy of Sciences.

After 1801, Gauss, without breaking with number theory, expanded the range of his interests, including natural Sciences. The catalyst was the discovery of the minor planet Ceres (1801), which was lost shortly after discovery. 24-year-old Gauss performed (in a few hours) the most complex calculations, using a new computational method he had developed, and with great accuracy indicated the place where to look for the “fugitive”; There she was, to everyone's delight, soon discovered.

Gauss's fame becomes pan-European. Many scientific societies in Europe elect Gauss as a member, the Duke increases his allowance, and Gauss's interest in astronomy increases even more.

1805: Gauss married Johanna Osthoff. They had three children.

1806: his generous patron, the Duke, dies from a wound received in the war with Napoleon. Several countries vied with each other to invite Gauss to serve (including in St. Petersburg). On the recommendation of Alexander von Humboldt, Gauss was appointed professor in Göttingen and director of the Göttingen Observatory. He held this position until his death.

1807: Napoleonic troops occupy Göttingen. All citizens are subject to indemnity, including a huge amount - 2000 francs - required to be paid to Gauss. Olbers and Laplace immediately come to his aid, but Gauss rejects their money; then an unknown person from Frankfurt sends him 1000 guilders, and this gift has to be accepted. Only much later did they learn that the unknown person was the Elector of Mainz, a friend of Goethe.

1809: new masterpiece, “The Theory of the Motion of Celestial Bodies.” The canonical theory of taking into account orbital perturbations is presented.

Just on their fourth wedding anniversary, Johanna dies, shortly after the birth of her third child. There is devastation and anarchy in Germany. These are the most difficult years for Gauss.

1810: new marriage - to Minna Waldeck, Johanna's friend. The number of Gauss children soon increases to six.

1810: new honors. Gauss received the Prize of the Paris Academy of Sciences and the Gold Medal of the Royal Society of London.

1811: A new comet appears. Gauss quickly and very accurately calculates its orbit. Begins work on complex analysis, discovers (but does not publish) a theorem, later rediscovered by Cauchy and Weierstrass: the integral of an analytic function over a closed loop is equal to zero.

1812: study of the hypergeometric series, generalizing the expansion of almost all functions known at that time.

The famous comet of the “Fire of Moscow” (1812) is observed everywhere using Gauss’s calculations.

1815: Publishes the first rigorous proof of the Fundamental Theorem of Algebra.

1816-1855

1820: Gauss is commissioned to carry out a geodetic survey of Hanover. For this, he developed appropriate computational methods (including the technique practical application his method of least squares), which led to the creation of a new scientific direction - higher geodesy, and organized surveying of the area and drawing up maps.

1821: in connection with his work on geodesy, Gauss begins a historical cycle of work on the theory of surfaces. Science includes the concept of “Gaussian curvature.” The beginning of differential geometry was laid. It was Gauss's results that inspired Riemann to write his classic dissertation on "Riemannian geometry."

The result of Gauss's research was the work “Research on Curved Surfaces” (1822). It freely used general curvilinear coordinates on the surface. Gauss greatly developed the method of conformal mapping, which in cartography preserves angles (but distorts distances); it is also used in aerodynamics, hydrodynamics and electrostatics.

1824: elected foreign honorary member of the St. Petersburg Academy of Sciences.

1825: discovers Gaussian complex integers, builds a theory of divisibility and comparisons for them. Successfully applies them to solve comparisons of high degrees.

1829: in the remarkable work “On a New General Law of Mechanics,” consisting of only four pages, Gauss substantiates a new variational principle of mechanics - the principle of least constraint. The principle is applicable to mechanical systems with ideal connections and was formulated by Gauss as follows: “the movement of a system of material points, interconnected in an arbitrary manner and subject to any influence, at every moment occurs in the most perfect possible agreement with the movement that these points, if they all became free, i.e., occurs with the least possible coercion, if as a measure of coercion applied during an infinitesimal instant, we take the sum of the products of the mass of each point by the square of the magnitude of its deviation from the position it occupied I would if I were free."

1831: his second wife dies, Gauss begins to suffer from severe insomnia. The 27-year-old talented physicist Wilhelm Weber, whom Gauss met in 1828 while visiting Humboldt, comes to Gottingen, invited on the initiative of Gauss. Both science enthusiasts became friends, despite the difference in age, and began a series of studies of electromagnetism.

1832: “The Theory of Biquadratic Residues.” Using the same complex Gaussian integers, important arithmetic theorems are proved not only for complex numbers, but also for real numbers. Here Gauss gives a geometric interpretation of complex numbers, which from that moment on becomes generally accepted.

1833: Gauss invents the electric telegraph and (together with Weber) builds a working model of it.

1837: Weber is fired for refusing to swear allegiance to the new king of Hanover. Gauss is left alone again.

1839: 62-year-old Gauss masters the Russian language and in letters to the St. Petersburg Academy asked to send him Russian magazines and books, in particular “ Captain's daughter» Pushkin. It is believed that this is due to Gauss’s interest in the work of Lobachevsky, who in 1842, on the recommendation of Gauss, was elected a foreign corresponding member of the Royal Society of Göttingen.

In the same 1839, Gauss, in his essay “The General Theory of Attractive and Repulsive Forces Acting Inversely Proportional to the Square of the Distance,” outlined the foundations of potential theory, including a number of fundamental provisions and theorems - for example, the fundamental theorem of electrostatics (Gauss’s theorem).

1840: In his work “Dioptric Studies,” Gauss developed the theory of constructing images in complex optical systems.

Contemporaries remember Gauss as a cheerful, friendly person with an excellent sense of humor.

Perpetuation of memory

Named after Gauss:
crater on the Moon;
minor planet No. 1001 (Gaussia);
Gauss is a unit of measurement of magnetic induction in the CGS system; this system of units itself is often called Gaussian;
one of the fundamental astronomical constants is the Gaussian constant;
Gaussberg volcano in Antarctica.

The name of Gauss is associated with many theorems and scientific terms in mathematics, astronomy and physics, some of them:
Gaussian algorithm for calculating the date of Easter
Gaussian curvature
Gaussian integers
Hypergeometric Gaussian function
Gaussian interpolation formula
Gauss-Laguerre quadrature formula
Gauss method for solving systems of linear equations.
Gauss-Jordan method
Gauss-Seidel method
Gauss method (numerical integration)
Normal distribution or Gaussian distribution
Gaussian mapping
Gaussian test
Gauss-Kruger projection
Straight Gaussian
Gauss gun
Gauss series
Gaussian system of units for measuring electromagnetic quantities.
The Gauss-Wanzel theorem on the construction of regular polygons and Fermat numbers.
The Gauss-Ostrogradsky theorem in vector analysis.
The Gauss-Lucas theorem on the roots of a complex polynomial.
Gauss-Bonnet formula on Gaussian curvature.

The famous European scientist Johann Carl Friedrich Gauss is considered to be the greatest mathematician of all times. Despite the fact that Gauss himself came from the poorest strata of society: his father was a plumber and his grandfather was a peasant, fate destined him for great fame. The boy already at the age of three showed himself to be a child prodigy; he could count, write, read, and even helped his father in his work.

The young talent, of course, was noticed. His curiosity was inherited from his uncle, his mother's brother. Carl Gauss, the son of a poor German, not only received a college education, but already at the age of 19 was considered the best European mathematician of that time.

Gauss himself claimed that he began to count before he spoke.
The great mathematician had a well-developed auditory perception: once, at the age of 3, he identified by ear an error in the calculations performed by his father when he was calculating the earnings of his assistants.
Gauss spent quite a short time in the first class, he was very quickly transferred to the second. The teachers immediately recognized him as a talented student.
Karl Gauss found it quite easy not only to study numbers, but also to study linguistics. He could speak several languages fluently. For quite a long time at a young age, the mathematician could not decide which academic path he should choose: exact sciences or philology. Ultimately choosing mathematics as his hobby, Gauss later wrote his works in Latin, English, and German.
At the age of 62, Gauss began to actively study the Russian language. Having become familiar with the works of the great Russian mathematician Nikolai Lobachevsky, he wanted to read them in the original. Contemporaries noted the fact that Gauss, having become famous, never read the works of other mathematicians: he usually became familiar with the concept and himself tried to either prove or disprove it. Lobachevsky's work was an exception.
While studying in college, Gauss was interested in the works of Newton, Lagrange, Euler and other other outstanding scientists.
The most fruitful period in the life of the great European mathematician is considered to be his time in college, where he created the law of reciprocity of quadratic residues and the method of least squares, and also began work on the study of the normal distribution of errors.
After his studies, Gauss went to live in Brunswick, where he was awarded a scholarship. There, the mathematician began work on proving the fundamental theorem of algebra.
Karl Gauss was a corresponding member of the St. Petersburg Academy of Sciences. He received this honorary title after he discovered the location of the small planet Ceres, making a series of complex mathematical calculations. Calculating the trajectory of Ceres mathematically made the name of Gauss known to the entire scientific world.
The image of Karl Gauss appears on the German 10 mark banknote.
The name of the great European mathematician is marked on the Earth’s satellite – the Moon.
Gauss developed an absolute system of units: he took 1 gram as a unit of mass, 1 second as a unit of time, and 1 millimeter as a unit of length.
Carl Gauss is famous for his research not only in algebra, but also in physics, geometry, geodesy and astronomy.
In 1836, together with his friend physicist Wilhelm Weber, Gauss created a society for the study of magnetism.
Gauss was very afraid of criticism and misunderstanding from his contemporaries directed at him.
There is an opinion among ufologists that the very first person to propose establishing contact with extraterrestrial civilizations was the great German mathematician Carl Gauss. He expressed his point of view, according to which it was necessary to cut down an area in the shape of a triangle in the Siberian forests and sow it with wheat. The aliens, seeing such an unusual field in the form of a neat geometric figure, should have understood that intelligent beings live on planet Earth. But it is not known for certain whether Gauss actually made such a statement, or whether this story is someone’s invention.
In 1832, Gauss developed the design of an electric telegraph, which he later refined and improved together with Wilhelm Weber.
The great European mathematician was married twice. He outlived his wives, and they, in turn, left him 6 children.
Gauss conducted research in the field of optoelectronics and electrostatics.

Gauss - the king of mathematics

The life of young Karl was influenced by his mother’s desire to make him not a rude and uncouth person like his father was, but intelligent and versatile personality. She sincerely rejoiced at her son's success and idolized him until the end of her life.

Many scientists considered Gauss not to be the mathematical king of Europe; he was called the king of the world for all the research, works, hypotheses, and proofs created by him.

IN last years life mathematical genius pundits gave him glory and honor, but, despite his popularity and worldwide fame, Gauss never found full happiness. However, according to the memoirs of his contemporaries, the great mathematician appears as a positive, friendly and cheerful person.

Gauss worked almost until his death - 1855. Until his death talented person retained clarity of mind, a youthful thirst for knowledge and at the same time boundless curiosity.

How many outstanding mathematicians can you remember without thinking? Can you name those of them who during their lifetime received the well-deserved title “King of Mathematicians”? One of the few to receive this honor Carl Gauss was a German mathematician, physicist and astronomer.

The boy, who grew up in a poor family, showed extraordinary abilities as a child prodigy from the age of two. At three years old, the child counted perfectly and even helped his father identify inaccuracies in the mathematical operations performed. According to legend, a mathematics teacher asked schoolchildren the task of counting the sum of numbers from 1 to 100 in order to keep the children occupied. Little Gauss coped with this task brilliantly, noticing that the pairwise sums at opposite ends are the same. Since childhood, Gauss began the habit of carrying out any calculations in his head.

The future mathematician was always lucky with his teachers: they were sensitive to the young man’s abilities and helped him in every possible way. One of these mentors was Bartels, who helped Gauss obtain a scholarship from the Duke, which turned out to be a significant help in the young man’s college education.

Gauss is also exceptional in that for a long time he tried to make a choice between philology and mathematics. Gauss spoke many languages (and especially loved Latin) and could quickly learn any of them; he understood literature; already in old age, the mathematician was able to learn the far from easy Russian language in order to familiarize himself with the works of Lobachevsky in the original. As we know, Gauss's choice ultimately fell on mathematics.

Already in college, Gauss was able to prove the law of reciprocity of quadratic residues, which his famous predecessors, Euler and Legendre, failed to do. At the same time, Gauss created the least squares method.

Later, Gauss proved the possibility of constructing a regular 17-gon using a compass and a ruler, and also generally substantiated the criterion for such a construction of regular polygons. This discovery was especially dear to the scientist, so he bequeathed to depict a 17-gon inscribed in a circle on his grave.

The mathematician was demanding about his achievements, so he published only those studies with which he was satisfied: we will not find unfinished and “raw” results in Gauss’s works. Many of the unpublished ideas were later resurrected in the works of other scientists.

The mathematician devoted most of his time to developing number theory, which he considered the “queen of mathematics.” As part of his research, he substantiated the theory of comparisons, studied quadratic forms and roots of unity, outlined the properties of quadratic residues, etc.

In his doctoral dissertation, Gauss proved the fundamental theorem of algebra, and later developed 3 more proofs of it in different ways.

Gauss the astronomer became famous for his “search” for the runaway planet Ceres. In a few hours, the mathematician made calculations that made it possible to accurately indicate the location of the “escaped planet”, where it was discovered. Continuing his research, Gauss wrote “The Theory of Celestial Bodies,” where he sets out the theory of taking into account orbital disturbances. Gauss's calculations made it possible to observe the "Fire of Moscow" comet.

Gauss also made great achievements in geodesy: “Gaussian curvature”, the method of conformal mapping, etc.

Gauss conducts research on magnetism with his young friend Weber. Gauss was responsible for the discovery of the Gauss gun - one of the types of electromagnetic mass accelerator. Together with Weber Gauss, a working model of the design was also developed the electric telegraph he created.

The method for solving system equations discovered by the scientist was called the Gauss method. The method consists of sequentially eliminating variables until the equation is reduced to a stepwise form. The solution by the Gaussian method is considered classic and is still actively used today.

The name of Gauss is known in almost all areas of mathematics, as well as in geodesy, astronomy, and mechanics. For the depth and originality of his thoughts, for his self-demandingness and genius, the scientist received the title “king of mathematicians.” Gauss's students became no less outstanding scientists than their mentor: Riemann, Dedekind, Bessel, Mobius.

The memory of Gauss forever remained in mathematical and physical terms (Gauss method, Gauss discriminants, Gauss straight line, Gauss - a unit of measurement of magnetic induction, etc.). A lunar crater, a volcano in Antarctica and a small planet are named after Gauss.

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From his early years, Gauss was distinguished by his phenomenal memory and outstanding abilities in the exact sciences. All his life he improved his knowledge and counting system, which brought mankind many great inventions and immortal works.

The little prince of mathematics

Karl was born in Braunschweig, in Northern Germany. This event took place on April 30, 1777 in the family of a poor worker Gerhard Diederich Gauss. Although Karl was the first and only child in the family, his father rarely had time to raise the boy. In order to somehow feed his family, he had to grab any opportunity to earn money: arranging fountains, gardening, stone work.

Gauss spent most of his childhood with his mother Dorothea. The woman doted on her only son and, in the future, was incredibly proud of his successes. She was a cheerful, intelligent and determined woman, but, due to her simple origin, - illiterate. Therefore, when little Karl asked to be taught how to write and count, helping him turned out to be a difficult task.

However, the boy did not lose his enthusiasm. At every convenient opportunity, he asked adults: “What kind of icon is this?”, “What letter is this?”, “How to read this?” In this simple way, he was able to learn the entire alphabet and all the numbers at the age of three. At the same time, the simplest counting operations succumbed to him: addition and subtraction.

One day, when Gerhard again took out a contract for stone work, he paid the workers in the presence of little Karl. The attentive child managed to count in his mind all the amounts announced by his father, and immediately found an error in his calculations. Gerhard doubted the correctness of his three-year-old son, but after recounting, he actually discovered an inaccuracy.

Gingerbread instead of stick

When Karl turned 7, his parents sent him to the Catherine People's School. All affairs here were managed by the middle-aged and strict teacher Büttner. His main method of education was corporal punishment (as was the case everywhere else at that time). As a deterrent, Büttner carried an impressive whip, which at first also hit little Gauss.

Karl managed to change his anger to mercy quite quickly. As soon as he completed his first lesson in arithmetic, Büttner radically changed his attitude towards the smart boy. Gauss was able to solve complex examples literally on the fly, using original and non-standard methods.

So at the next lesson, Büttner set a task: adding up all the numbers from 1 to 100. As soon as the teacher finished explaining the task, Gauss had already handed over his tablet with the ready answer. He later explained: “I did not add the numbers in order, but divided them in pairs. If you add 1 and 100, you get 101. If you add 99 and 2, you also get 101, and so on. I multiplied 101 by 50 and got the answer.” After this, Gauss became a favorite student.

The boy’s talents were noticed not only by Büttner, but also by his assistant, Christian Bartels. With his small salary, he bought mathematics textbooks, from which he studied himself and taught ten-year-old Karl. These studies led to stunning results - already in 1791 the boy was introduced to the Duke of Brunswick and his entourage as one of the most talented and promising students.

Compasses, ruler and Gottingen

The Duke was delighted with the young talent and granted Gauss a scholarship of 10 thalers per year. Only thanks to this, a boy from a poor family was able to continue his studies at the most prestigious school - the Karolinska College. There he received the necessary training and in 1895 easily entered the University of Göttingen.

Here Gauss makes one of his greatest discoveries (according to the scientist himself). The young man managed to calculate the construction of a 17-gon and reproduce it using a ruler and compass. In other words, he solved the equation x17- 1 = 0 in quadratic radicals. This seemed so significant to Karl that on the same day he began to keep a diary in which he bequeathed to draw a 17-gon on his tombstone.

Working in the same direction, Gauss manages to construct a regular heptagon and a ninegon and prove that it is possible to construct polygons with 3, 5, 17, 257 and 65337 sides, as well as with any of these numbers multiplied by a power of two. Later these numbers would be called “simple Gaussian”.

Stars on the tip of a pencil

In 1798, Karl left the university for unknown reasons and returned to his native Braunschweig. At the same time, your scientific activity The young mathematician does not even think about stopping. On the contrary, the time spent in his native land became the most fruitful period of his work.

Already in 1799, Gauss proved the fundamental theorem of algebra: “The number of real and complex roots of a polynomial is equal to its degree,” explored complex roots of unity, quadratic roots and residues, and derived and proved the quadratic reciprocity law. From the same year he became a private assistant professor at the University of Braunschweig.

In 1801, the book “Arithmetic Research” was published, where the scientist shares his discoveries on almost 500 pages. It does not include a single unfinished study or raw material - all data is as accurate as possible and brought to a logical conclusion.

At the same time, he became interested in issues of astronomy, or rather mathematical applications in this area. Thanks to just one correct calculation, Gauss found on paper what astronomers had lost in the sky - the small planet Zirrera (1801, G. Piazzi). Several more planets were found using this method, in particular, Pallas (1802, G.V. Olbers). Later, Carl Friedrich Gauss would become the author of an invaluable work entitled “The Theory of the Motion of Celestial Bodies” (1809) and many studies in the field of the hypergeometric function and the convergence of infinite series.

Marriages without calculation

Here, in Braunschweig, Karl met his first wife, Joanna Osthoff. They married on November 22, 1804 and lived happily for five years. Joanna managed to give birth to Gauss's son Joseph and daughter Minna. During the birth of her third child, Louis, the woman died. Soon the baby himself died, and Karl was left alone with two children. In letters to his comrades, the mathematician repeatedly stated that these five years in his life were an “eternal spring”, which, unfortunately, ended.

This misfortune in Gauss's life was not the last. Around the same time, the scientist’s friend and mentor, the Duke of Brunswick, dies from mortal wounds. With a heavy heart, Karl leaves his homeland and returns to the university, where he accepts the chair of mathematics and the post of director of the astronomical laboratory.

In Göttingen, he becomes close to the daughter of a local councilor, Minna, who was a good friend of his late wife. On August 4, 1810, Gauss married a girl, but their marriage was accompanied by quarrels and conflicts from the very beginning. Due to his stormy personal life, Karl even refused a place at the Berlin Academy of Sciences. Minna gave birth to the scientist three children - two sons and a daughter.

New inventions, discoveries and students

The high position that Gauss held at the university obliged the scientist to a teaching career. His lectures were fresh and he was kind and helpful, which resonated with students. However, Gauss himself did not like teaching and believed that by teaching others he was wasting his time.

In 1818, Carl Friedrich Gauss was one of the first to begin work related to non-Euclidean geometry. Fearing criticism and ridicule, he never publishes his discoveries, however, he ardently supports Lobachevsky. The same fate befell quaternions, which Gauss originally studied under the name “mutations.” The discovery was attributed to Hamilton, who published his works 30 years after the death of the German scientist. Elliptic functions first appeared in the work of Jacobi, Abel and Cauchy, although the main contribution was made by Gauss.

A few years later, Gauss became interested in geodesy, surveyed the Kingdom of Hanover using the least squares method, and described real forms earth's surface and invents a new device - heliotrope. Despite the simplicity of the design (spotting scope and two flat mirrors), this invention became a new word in geodetic measurements. The result of research in this area was the scientist’s works: “General Studies on Curved Surfaces” (1827) and “Research on the Subjects of Higher Geodesy” (1842-47), as well as the concept of “Gaussian curvature”, which gave rise to differential geometry.

In 1825, Karl Friedrich made another discovery that immortalized his name - Gaussian complex numbers. He successfully uses them to solve high-degree equations, which allowed him to conduct a number of studies in the field of real numbers. The main result was the work “The Theory of Biquadratic Residues.”

Towards the end of his life, Gauss changed his attitude towards teaching and began to devote not only lecture hours to his students, but also free time. His work and personal example had a huge influence on young mathematicians: Riemann and Weber. Friendship with the first led to the creation of “Riemannian geometry”, and with the second - to the invention of the electromagnetic telegraph (1833).

In 1849, for his services to the university, Gauss was awarded the title of "honorary citizen of Göttingen". By this time, his circle of friends already included such famous scientists as Lobachevsky, Laplace, Olbers, Humboldt, Bartels and Baum.

Since 1852, the good health that Karl inherited from his father began to crack. Avoiding meetings with medical representatives, Gauss hoped to cope with the disease himself, but this time his calculation turned out to be wrong. He died on February 23, 1855, in Göttingen, surrounded by friends and like-minded people, who would later award him the title of King of Mathematics.