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

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

The future mathematician was always lucky with teachers: they were sensitive to the abilities of the young man and helped him in every possible way. One of these mentors was Bartels, who assisted Gauss in obtaining a scholarship from the duke, which proved to be a significant help in teaching the young man in college.

Gauss is also exceptional because 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 at an advanced 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 fell on mathematics.

Already in college, Gauss was able to prove the law of reciprocity of quadratic residues, which was not possible for his famous predecessors - Euler and Legendre. At the same time, Gauss created the method of least squares.

Later, Gauss proved the possibility of constructing a regular 17-gon using a compass and straightedge, and also, in general, substantiated the criterion for such 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 achievement, therefore he published only those studies that he was satisfied with: we will not find unfinished and “raw” results in the works of Gauss. Many of the unpublished ideas have since been resurrected in the writings of other scientists.

Most of the time the mathematician devoted to the development of 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 fugitive planet Ceres. In a few hours, the mathematician did the calculations, which made it possible to accurately indicate the location of the "escaped planet", where it was discovered. Continuing his research, Gauss writes The Theory of Celestial Bodies, where he sets out the theory of taking into account perturbations of orbits. Gauss's calculations made it possible to observe the comet "Fire of Moscow".

The merits of Gauss are also great in geodesy: "Gaussian curvature", the method of conformal mapping, etc.

Gauss conducts research on magnetism with his young friend Weber. Gauss belongs to the discovery of the Gauss gun - one of the varieties of the electromagnetic mass accelerator. Together with Weber Gauss, a working model was also developed the electric telegraph that he himself had created.

The method for solving system equations, discovered by the scientist, was called the Gauss method. The method consists in successive elimination of variables until the equation is reduced to a stepwise form. The solution by the Gauss method is considered classical and is actively used now.

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 thought, for exactingness to himself and genius, the scientist received the title of "king of mathematicians." Gauss' students became no less outstanding scientists than their mentor: Riemann, Dedekind, Bessel, Möbius.

The memory of Gauss remained forever in mathematical and physical terms (Gauss method, Gauss discriminants, direct Gauss, Gauss is a unit of measurement of magnetic induction, etc.). Gauss is named after a lunar crater, a volcano in Antarctica, and a minor planet.

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Mathematician and historian of mathematics Jeremy Gray talks about Gauss and his great contribution to science, about the theory of quadratic forms, the discovery of Ceres, and non-Euclidean geometry*

Portrait of Gauss by Eduard Rietmüller on the Terrace of the Göttingen Observatory // Carl Friedrich Gauss: Titan of Science G. Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohe

Carl Friedrich Gauss was a German mathematician and astronomer. He was born to poor parents in Brunswick in 1777 and died in Göttingen in Germany in 1855, by which time everyone who knew him considered him one of the greatest mathematicians of all time.

Exploring Gauss

How do we study Carl Friedrich Gauss? Well, when it comes to his early life, we have to rely on the family stories shared by his mother when he became famous. Of course, these stories tend to be exaggerated, but his remarkable talent was already evident when Gauss was in his early teens. Since then, we have more and more records of his life.
As Gauss grew up and became noticed, we began to get letters about him from people who knew him, as well as official reports of various kinds. We also have a long biography of his friend based on conversations they had towards the end of Gauss's life. We have his publications, we have a lot of his letters to other people, and he wrote a lot of material, but never published it. And finally, we have obituaries.

Early life and path to mathematics

Gauss's father was engaged in various affairs, he was a worker, a construction site foreman and a merchant's assistant. His mother was intelligent but barely literate, and dedicated herself to Gauss until her death at the age of 97. It appears that Gauss was seen as a gifted student while still at school, at age eleven, his father was persuaded to send him to the local academic school instead of putting him to work. At that time, the Duke of Brunswick sought to modernize his duchy, and attracted talented people to help him in this. When Gauss was fifteen, the duke brought him to the Carolinum College for his higher education, although by that time Gauss had already independently studied Latin and mathematics at the high school level. At the age of eighteen, he entered the University of Göttingen, and at twenty-one he had already written his doctoral dissertation.

Gauss was originally going to study philology, a priority subject in Germany at the time, but he also did extensive research on the algebraic construction of regular polygons. Due to the fact that the vertices of a regular polygon of N sides are given by the solution of the equation (which is numerically equal to . Gauss found that for n = 17 the equation is factorized in such a way that a regular 17-sided polygon can only be built using a ruler and a compass. This was a completely new result, the Greek geometers were unaware of it, and the discovery caused a small sensation - the news of it was even published in the city newspaper. This success, which came when he was barely nineteen, made him decide to study mathematics.

But what made him famous were two completely different phenomena in 1801. The first was the publication of his book entitled "Arithmetic Reasoning", which completely rewrote number theory and led to the fact that it (number theory) became, and still is, one of the central subjects of mathematics. It includes the theory of equations of the form x ^ n - 1, which is both very original and at the same time easily understood, as well as a much more complex theory called the quadratic form theory. This has already attracted the attention of two leading French mathematicians, Joseph Louis Lagrange and Adrien Marie Legendre, who acknowledge that Gauss went very far beyond what they were doing.

The second major development was the rediscovery by Gauss of the first known asteroid. It was found in 1800 by the Italian astronomer Giuseppe Piazzi, who named it Ceres after the Roman goddess of agriculture. He observed her for 41 nights before she disappeared behind the sun. It was a very exciting discovery, and astronomers were keen to know where it would appear again. Only Gauss calculated it correctly, which no other professional did, and this made his name as an astronomer, which he remained for many years to come.

Later life and family

Gauss' first job was as a mathematician in Göttingen, but after the discovery of Ceres and later other asteroids, he gradually switched his interests to astronomy, and in 1815 became director of the Göttingen Observatory, a position he held almost until his death. He also remained a professor of mathematics at the University of Göttingen, but this does not seem to have required much teaching from him, and the record of his contact with the younger generations was rather sparse. In fact, he seems to have been an aloof figure, more comfortable and sociable with astronomers, and the few good mathematicians in his life.

In the 1820s he led a massive exploration of northern Germany and southern Denmark, and in the process rewrote the theory of surface geometry, or differential geometry as it is known today.

Gauss married twice, the first time rather happily, but when his wife Joanna died in childbirth in 1809, he remarried Minna Waldeck, but this marriage was less successful; She died in 1831. He had three sons, two of whom emigrated to the United States, most likely because their relationship with their father was troubled. As a result, there is an active group of people in the States who trace their lineage to Gauss. He also had two daughters, one from each marriage.

Greatest Contribution to Mathematics

Considering Gauss' contribution in this area, we can start with the least squares method of statistics that he invented to understand Piazzi's data and find the asteroid Ceres. This was a breakthrough in averaging a large number of observations, all of which were slightly inaccurate, in order to extract the most reliable information from them. With regard to number theory, you can talk about it for a very long time, but he made wonderful discoveries about what numbers can be expressed in quadratic forms, which are expressions of the form . You may think this is important, but Gauss turned what was a collection of scattered results into a systematic theory and showed that many simple and natural hypotheses have proofs that lie in what is similar to other branches of mathematics in general. Some of the tricks he invented turned out to be important in other areas of mathematics, but Gauss discovered them before those branches were properly studied: group theory is an example.

His work on equations of the form and, more surprisingly, on deep features of the theory of quadratic forms, opened up the use of complex numbers, for example, to prove results on integers. This suggests that much was happening under the surface of the object.

Later, in the 1820s, he discovered that there was a concept of surface curvature that was an integral part of the surface. This explains why some surfaces cannot be exactly copied onto others without transformation, just as we cannot make an accurate map of the Earth on a piece of paper. This freed the study of surfaces from the study of solids: you can have an apple peel without having to imagine an apple underneath.

A surface with negative curvature where the sum of the triangle's angles is less than that of a triangle in the plane //source:Wikipedia

In the 1840s, independently of the English mathematician George Green, he invented the subject of potential theory, which is a huge extension of the calculus of functions of several variables. This is the correct mathematics for studying gravity and electromagnetism and has been used in many areas of applied mathematics ever since.

And we must also remember that Gauss discovered but did not publish quite a lot. No one knows why he did so much for himself, but one theory is that the flood of new ideas he kept in his head was even more exciting. He convinced himself that Euclid's geometry was not necessarily true and that at least one other geometry was logically possible. Glory to this discovery went to two other mathematicians, Boyai in Romania-Hungary and Lobachevsky in Russia, but only after their death - it was so controversial at that time. And he did a lot of work on the so-called elliptic functions - you can think of them as generalizations of the sine and cosine functions of trigonometry, but more precisely, they are complex functions of a complex variable, and Gauss invented a whole theory out of them. Ten years later, Abel and Jacobi became famous for doing the same thing, not knowing that Gauss had already done it.

Work in other areas

After his rediscovery of the first asteroid, Gauss worked hard to find other asteroids and calculate their orbits. It was a difficult job in the pre-computer age, but he turned to his talents, and he seemed to feel that this job allowed him to repay his debt to the prince and the society that had educated him.

In addition, while surveying in northern Germany, he invented the heliotrope for accurate surveying, and in the 1840s he helped design and build the first electric telegraph. If he had thought of amplifiers as well, he might have done this too, since without them the signals could not travel very far.

Enduring Legacy

There are many reasons why Carl Friedrich Gauss is still so relevant today. First of all, number theory has grown into a huge subject with a reputation for being very difficult. Since then, some of the best mathematicians have gravitated towards him, and Gauss gave them a way to approach him. Naturally, some problems that he could not solve attracted attention, so you can say that he created a whole field of research. It turns out that this also has deep connections with the theory of elliptic functions.

In addition, his discovery of the intrinsic concept of curvature enriched the entire study of surfaces and inspired many years of work for later generations. Anyone who studies surfaces, from enterprising modern architects to mathematicians, is indebted to him.

The intrinsic geometry of surfaces extends to the idea of ​​the intrinsic geometry of higher-order objects such as three-dimensional space and four-dimensional spacetime.

Einstein's general theory of relativity and all of modern cosmology, including the study of black holes, were made possible by Gauss's breakthrough. The idea of ​​non-Euclidean geometry, so shocking in its day, made people realize that there could be many kinds of rigorous mathematics, some of which could be more precise or useful - or just interesting - than those we knew about.

Non-Euclidean geometry //

German mathematician, astronomer and physicist, participated in the creation of the first electromagnetic telegraph in Germany. Until old age, he was accustomed to doing most of the calculations in his mind ...

According to family legend, he is already in 3 for a year he knew how to read, write, and even corrected his father’s counting errors in the payroll for workers (his father worked at a construction site, then as a gardener ...).

“At the age of eighteen, he made an amazing discovery regarding the properties of the seventeen-gon; this has not happened in mathematics for 2000 years since the ancient Greeks (this success was decided by the choice of Karl Gauss: what to study further languages ​​​​or mathematics in favor of mathematics - Note by I.L. Vikentiev). His doctoral dissertation on the topic "A new proof that every entire rational function of one variable can be represented by the product of real numbers of the first and second degree" is devoted to the solution of the fundamental theorem of algebra. The theorem itself was known before, but he offered a completely new proof. Glory Gaussian was so great that when in 1807 the French troops approached Göttingen, Napoleon ordered to save the city in which "the greatest mathematician of all time" lives. On the part of Napoleon, this was very kind, but fame has a downside. When the victors imposed an indemnity on Germany, they demanded from Gauss 2000 francs. This equated to about $5,000 today, a fairly large amount for a university professor. Friends offered help Gauss refused; while the bickering was going on, it turned out that the money had already been paid by the famous French mathematician Maurice Pierre de Laplace(1749-1827). Laplace explained his action by the fact that he considers Gauss, who was 29 years younger than him, "the greatest mathematician in the world", that is, he rated him slightly lower than Napoleon. Later, an anonymous admirer sent Gauss 1,000 francs to help him settle accounts with Laplace.

Peter Bernstein, Against the Gods: The Taming of Risk, M., Olimp-Business, 2006, p. 154.

10 year old Carl Gauss very lucky with the assistant teacher of mathematics - Martin Bartels(he was then 17 years old). He not only appreciated the talent of the young Gauss, but managed to get him a scholarship from the Duke of Brunswick to enter the prestigious Collegium Carolinum school. Later, Martin Bartels was a teacher and N.I. Lobachevsky…

“By 1807, Gauss developed a theory of errors (errors), and astronomers began to use it. Although all modern physical measurements require the indication of errors, outside the astronomy of physics not claimed estimates of error up until the 1890s (or even later).”

Ian Hacking, Representation and intervention. Introduction to the philosophy of natural sciences, M., Logos, 1998, p. 242.

“In recent decades, among the problems of the foundations of physics, the problem of physical space has acquired particular importance. Research Gaussian(1816), Bogliai (1823), Lobachevsky(1835) and others led to non-Euclidean geometry, to the realization that until now reigned supreme, the classical geometric system of Euclid is only one of an infinite number of logically equal systems. Thus, the question arose which of these geometries is the geometry of the real space.
Even Gauss wanted to solve this issue by measuring the sum of the angles of a large triangle. Thus, physical geometry has become an empirical science, a branch of physics. These issues were further considered in particular Riemann (1868), Helmholtz(1868) and Poincaré (1904). Poincaré emphasized, in particular, the relationship of physical geometry with all other branches of physics: the question of the nature of real space can only be resolved within the framework of some general system of physics.
Then Einstein found such a general system within which this question was answered, an answer in the spirit of a specific non-Euclidean system.

Rudolf Karnap, Hans Hahn, Otto Neurath, Scientific worldview - Vienna circle, in Sat: Journal "Erkenntnis" ("Knowledge"). Selected / Ed. O.A. Nazarova, M., "Territory of the Future", 2006, p. 70.

In 1832 Carl Gauss“... built a system of units, in which three arbitrary, independent from each other basic units were taken as the basis: length (millimeter), mass (milligram) and time (second). All other (derived) units could be defined using these three. Later, with the development of science and technology, other systems of units of physical quantities appeared, built according to the principle proposed by Gauss. They were based on the metric system of measures, but differed from each other in basic units. The issue of ensuring uniformity in the measurement of quantities that reflect certain phenomena of the material world has always been very important. The lack of such uniformity gave rise to significant difficulties for scientific knowledge. For example, until the 1980s, there was no unity in measuring electrical quantities: 15 different units of electrical resistance, 8 units of electromotive force, 5 units of electric current, etc. were used. The current situation made it very difficult to compare the results of measurements and calculations performed by various researchers.

Golubintsev V.O., Dantsev A.A., Lyubchenko V.C., Philosophy of Science, Rostov-on-Don, "Phoenix", 2007, p. 390-391.

« Carl Gauss, like Issac Newton, often not published scientific results. But all the published works of Karl Gauss contain significant results - there are no raw and passing works among them.

“Here it is necessary to distinguish the very method of research from the presentation and publication of its results. Let's take for example three great - one might say, brilliant - mathematicians: Gauss, Euler and Cauchy. Gauss, before publishing any work, subjected his presentation to the most careful processing, applying extreme care for brevity of presentation, elegance of methods and language, without leaving at the same time, traces of the rough work that he achieved before these methods. He used to say that when a building is built, they do not leave those scaffolding that served for the construction; therefore, he not only did not hurry with the publication of his works, but left them to mature not only for years, but for decades, often returning to this work from time to time in order to bring it to perfection. […] His research on elliptic functions, the main properties of which he discovered 34 years before Abel and Jacobi, he did not bother to publish for 61 years, and they were published in his "Heritage" about 60 years after his death. Euler acted just the opposite of Gauss. He not only did not dismantle the scaffolding around his building, but sometimes even seemed to clutter it up with them. But he can see all the details of the very method of his work, which Gauss is so carefully hidden. Euler did not pursue finishing, he worked immediately clean and published in the form in which the work turned out; but he was far ahead of the printed media of the Academy, so that he himself said that his works would be enough for academic publications for 40 years after his death; but here he was mistaken - they were enough for more than 80 years. Cauchy wrote so many papers, both excellent and hasty, that neither the Paris Academy nor the mathematical journals of that time could accommodate them, and he founded his own mathematical journal, in which he published only his papers. Gauss about the most hasty of them put it this way: "Cauchy suffers from mathematical diarrhea." It is not known whether Cauchy said in retaliation that Gauss suffers from mathematical constipation?

Krylov A.N., My memories, L., "Shipbuilding", 1979, p. 331.

«… Gauss He was a very reserved person and led a reclusive life. He not published a lot of his discoveries, and many of them were rediscovered by other mathematicians. In publications, he paid more attention to the results, not attaching much importance to the methods of obtaining them, and often forcing other mathematicians to spend a lot of effort on proving his conclusions. Eric Temple Bell, one of the biographers Gauss, believes that his lack of sociability delayed the development of mathematics by at least fifty years; half a dozen mathematicians could have become famous if they had obtained results that had been kept in his archive for years, or even decades.

Peter Bernstein, Against the Gods: The Taming of Risk, M., Olimp-Business, 2006, p.156.

The most famous mathematician of all times and peoples is considered to be the famous scientist from Europe, Johann Carl Friedrich Gauss. 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 had prepared for him great glory. The boy already at the age of three showed himself to be a child prodigy, he knew how to count, write, read, even helped his father in his work.


Young talent, of course, was noticed. His curiosity was inherited from his uncle, his mother's brother. Karl 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.

1. Gauss himself claimed that he began to count before he spoke.
2. 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 calculated the earnings of his assistants.
3. Gauss spent quite a short time in the first class, he was very quickly transferred to the second. Teachers immediately recognized him as a talented student.
4. Carl Gauss found it quite easy not only to study numbers, but also to study linguistics. He could speak several languages ​​fluently. A mathematician for quite a long time at a young age could not decide which scientific path he should choose: exact sciences, or philology. Ultimately choosing mathematics as his passion, Gauss later wrote his works in Latin, English, and German.
5. At the age of 62, Gauss began to actively study the Russian language. After reading 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 got acquainted with the concept and tried to either prove it or disprove it himself. Lobachevsky's work was an exception.
6. While studying in college, Gauss was interested in the works of Newton, Lagrange, Euler and other prominent scientists.
7. The most fruitful period in the life of the great European mathematician is considered to be the time of his studies 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.
8. After his studies, Gauss went to live in Braunschweig, where he was awarded a scholarship. In the same place, the mathematician began work on proving the fundamental theorem of algebra.
9. 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 minor planet Ceres, having made a number of complex mathematical calculations. Calculating the trajectory of Ceres mathematically made the name of Gauss known to the entire scientific world.
10. The image of Karl Gauss is on the banknote of Germany in denominations of 10 marks.
11. The name of the great European mathematician is marked on the Earth's satellite - the Moon.
12. Gauss developed an absolute system of units: he took 1 gram for a unit of mass, 1 second for a unit of time, and 1 millimeter for a unit of length.
13. Karl Gauss is known for his research not only in algebra but also in physics, geometry, geodesy and astronomy.
14. In 1836, together with his friend, physicist Wilhelm Weber, Gauss created a society for the study of magnetism.
15. Gauss was very afraid of criticism and misunderstanding from his contemporaries directed at him.
16. There is an opinion among ufologists that the very first person who proposed to establish contact with extraterrestrial civilizations was the great German mathematician - Karl Gauss. He expressed his point of view, according to which it was necessary to cut down a plot in the shape of a triangle in the Siberian forests and sow it with wheat. 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.
17. In 1832, Gauss developed the design of an electric telegraph, which he later finalized and improved together with Wilhelm Weber.
18. The great European mathematician was married twice. He survived his wives, and they, in turn, left him 6 children.
19. Gauss conducted research in the field of optoelectronics and electrostatics.

Gauss is the math king

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

Many scientists considered Gauss by no means 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 the last years of the life of a mathematical genius, pundits gave him glory and honor, but, despite his popularity and world 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, this talented man retained clarity of mind, youthful thirst for knowledge and, at the same time, boundless curiosity.

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

The Little Prince of Mathematics

Carl 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 every 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 insanely proud of his successes. She was a cheerful, intelligent and determined woman, but, due to her simple origin, she was illiterate. Therefore, when little Carl asked to teach him how to write and count, helping him turned out to be a difficult task.

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

Once, when Gerhard again hired a contract for stone work, he paid the workers in the presence of little Karl. An attentive child in his mind managed to count all the amounts voiced by his father, and immediately found an error in his calculations. Gerhard doubted the correctness of his three-year-old son, but, after counting, he really discovered an inaccuracy.

Gingerbread instead of a whip

When Karl turned 7, his parents sent him to the Catherine's Folk School. The middle-aged and strict teacher Byuttner was in charge of all affairs here. His main method of education was corporal punishment (however, as elsewhere at that time). As a deterrent, Buettner carried an impressive whip, which at first hit little Gauss as well.

Carl succeeded in changing his anger to mercy rather quickly. As soon as the first lesson in arithmetic was completed, Buttner 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, Buttner set the task: to add all the numbers from 1 to 100. As soon as the teacher finished explaining the task, Gauss had already handed over his plate with a ready answer. He later explained: “I did not add the numbers in order, but divided them in pairs. If we add 1 and 100, we get 101. If we add 99 and 2, we get 101, and so on. I multiplied 101 by 50 and got the answer." After that, Gauss became a favorite student.

The boy's talents were noticed not only by Buttner, but also by his assistant, Christian Bartels. With his small salary, he bought mathematics textbooks, which he himself studied and taught ten-year-old Karl. These classes 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 Göttingen

The duke was delighted with the young talent and granted Gauss a scholarship of 10 thalers a year. Only thanks to this, the boy from a poor family managed to continue his studies at the most prestigious school - the Carolina 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 a compass. In other words, he solved the equation x17-1 = 0 in quadratic radicals. This seemed to Karl so significant 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 nonagon 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 will 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, the young mathematician does not even think of suspending his scientific activity. On the contrary, the time spent in his native lands became the most fruitful period of his work.

Already in 1799, Gauss proved the basic theorem of algebra: “The number of real and complex roots of a polynomial is equal to its degree”, explores complex roots of unity, quadratic roots and residues, derives and proves the quadratic reciprocity law. From the same year he became Privatdozent at the University of Braunschweig.

In 1801, the book "Arithmetical Investigations" was published, where the scientist shares his discoveries on almost 500 pages. It did 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 was interested in astronomy, or rather, mathematical applications in this area. Thanks to only one correct calculation, Gauss found on paper what astronomers had lost in the sky - the small planet Cirrera (1801, G. Piazzi). Several more planets were found by this method, in particular, Pallas (1802, G.V. Olbers). Later, Carl Friedrich Gauss became the author of an invaluable work called The Theory of 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 meets his first wife, Joanna Osthof. They married on November 22, 1804 and lived happily for five years. Joanna managed to give birth to Gauss 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 has repeatedly stated that these five years in his life were “eternal spring”, which, unfortunately, has ended.

This misfortune in the life of Gauss was not the last. Around the same time, a friend and mentor of the scientist, 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 department 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. August 4, 1810 Gauss marries a girl, but their marriage from the very beginning is accompanied by quarrels and conflicts. Due to his turbulent personal life, Karl even refused a place at the Berlin Academy of Sciences, Minna gave birth to three children to the scientist - two sons and a daughter.

New inventions, discoveries and students

The high post that Gauss held at the university obliged the scientist to a teaching career. His lectures were distinguished by the freshness of his views, and he himself was kind and sympathetic, which evoked a response from the students. However, Gauss himself did not like teaching and felt that teaching others was wasting his time.

In 1818 Carl Friedrich Gauss was one of the first to start work on non-Euclidean geometry. Fearing criticism and ridicule, he never publishes his discoveries, however, he vehemently supports Lobachevsky. The same fate befell the quaternions, which Gauss originally investigated under the name "mutations". The discovery was attributed to Hamilton, who published his work 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 due to Gauss.

A few years later, Gauss takes a great interest in geodesy, surveys the Kingdom of Hanover using the least squares method, describes the actual forms of the earth's surface and invents a new device - the heliotrope. Despite the simplicity of the design (a spotting scope and two flat mirrors), this invention became a new word in geodetic measurements. The result of research in this area were the works of the scientist: "General studies on curved surfaces" (1827) and "Studies 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 makes another discovery that immortalized his name - Gaussian complex numbers. He successfully uses them to solve equations of high degrees, which made it possible 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 to teaching and began to give his students not only lecture hours, but also free time. His work and personal example had a huge impact 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 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 Charles inherited from his father began to crack. Avoiding meetings with representatives of medicine, 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 associates who would later award him the title of king of mathematics.