Biography of Friedrich Gauss. Historical essay about the great mathematician Carl Friedrich Gauss. Start of work

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 far from easy Russian language to familiarize yourself with Lobachevsky’s works 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 a method least squares.

Later, Gauss proved the possibility of constructing a regular 17-gon using a compass and ruler, and also generally substantiated the criterion for such a construction 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 Many of the unpublished ideas were later resurrected in the works of other scientists.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, investigated quadratic forms and roots of unity, the properties of quadratic residues are outlined, 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 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 Gauss method solution 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.). Named after Gauss lunar crater, a volcano in Antarctica and a small planet.

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Carl Friedrich Gauss, the son of a poor man and an uneducated mother, independently solved the riddle of the date of his own birth and determined it as April 30, 1777. From childhood, Gauss showed all the signs of genius. The young man completed the main work of his life, “Arithmetic Research,” back in 1798, when he was only 21 years old, although it would not be published until 1801. This work was of paramount importance for improving the theory of numbers as scientific discipline, and presented this field of knowledge as we know it today. Gauss's amazing abilities so impressed the Duke of Brunswick that he sent Charles to study at the Charles College (now the Technical University of Brunswick), which Gauss attended from 1792 to 1795. In 1795-1798. Gauss moves to the University of Götting. During his university years, the mathematician proved many significant theorems.

Start of work

1796 turns out to be the most successful year both for Gauss himself and for his theory of numbers. One after another, he does important discoveries. On March 30, for example, he reveals the rules for constructing a regular heptagon. It improves modular arithmetic and greatly simplifies manipulations in number theory. April 8 Gauss proves the law of reciprocity of quadratic residues, which allows mathematicians to find a solution to any quadratic equation of modular arithmetic. On May 31, he proposes the prime number theorem, thereby providing an accessible explanation of how prime numbers distributed among integers. On July 10, a scientist makes the discovery that any whole positive number can be expressed as the sum of no more than three triangular numbers.

In 1799, Gauss defended his dissertation in absentia, in which he presented new proofs of the theorem stating that every entire rational algebraic function with one variable can be represented by the product real numbers first and second degrees. It confirms the fundamental theorem of algebra, which states that every non-constant polynomial in one variable with complex coefficients has at least one complex root. His efforts greatly simplify the concept of complex numbers.

Meanwhile, Italian astronomer Giuseppe Piazzi discovers the dwarf planet Ceres, which instantly disappears in the solar glow, but a few months later, when Piazzi expects to see it again in the sky, Ceres does not appear. Gauss, who had just turned 23 years old, having learned about the astronomer's problem, took up the task of solving it. In December 1801, after three months of hard work, he determined the position of Ceres on starry sky with an error of only half a degree.

In 1807, the brilliant scientist Gauss received the post of professor of astronomy and head astronomical observatory Gottingen, which he will occupy for the rest of his life.

Later years

In 1831, Gauss met professor of physics Wilhelm Weber, and this acquaintance turned out to be fruitful. Their joint work leads to new discoveries in the field of magnetism and the establishment of Kirchhoff's rules in the field of electricity. Gauss formulated the law own name. In 1833, Weber and Gauss invented the first electromechanical telegraph, which connected the observatory with the Göttingen Institute of Physics. Following this, in the courtyard of the astronomical observatory, a magnetic observatory was built, in which Gauss, together with Weber, founded the “Magnetic Club”, which was engaged in measurements magnetic field Lands in different points planets. Gauss also successfully developed a technique for determining the horizontal component of the Earth's magnetic field.

Personal life

Gauss's personal life was a succession of tragedies, beginning with the premature death of his first wife, Joanna Ostoff, in 1809, and the subsequent death of one of their children, Louis. Gauss marries again, to the best friend of his first wife, Frederica Wilhelmina Waldeck, but she, too, dies after a long illness. Gauss had six children from two marriages.

Death and legacy

Gauss died in 1855 in Göttingen, Hanover (now Lower Saxony in Germany). His body was cremated and buried in Albanifridhof. According to the study of his brain by Rudolf Wagner, Gauss's brain had a mass of 1.492 g and a brain cross-sectional area of ​​219.588 mm² (34.362 square inches), which scientifically proves that Gauss was a genius.

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German mathematician, astronomer and physicist, participated in the creation of Germany's first electromagnetic telegraph. Until his old age, he got used to doing most of the calculations in his head...

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

"At eighteen he did amazing discovery, concerning the properties of the decagon; 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 next: languages ​​or mathematics in favor of mathematics - Note by I.L. Vikentyev). His doctoral dissertation was on the topic “New evidence that every whole rational function one variable can be represented by the product of real numbers of the first and second degrees” is devoted to solving the fundamental theorem of algebra. The theorem itself was known before, but he proposed a completely new proof. Glory Gauss was so great that when French troops approached Göttingen in 1807, Napoleon ordered to take care of the city in which “the greatest mathematician of all time” lives. This was very kind of Napoleon, but fame also has a downside. When the victors imposed an indemnity on Germany, they demanded from Gauss 2000 francs This corresponded to approximately 5,000 today's dollars - quite a large sum 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 saying that he considered 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 1000 francs to help him pay off Laplace.”

Peter Bernstein, Against the Gods: Taming Risk, M., Olympus Business, 2006, p. 154.

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

“By 1807, Gauss had developed a theory of errors (errors), and astronomers began to use it. Although in all modern physical measurements error indication required, outside of astronomy physics Not error estimates were reported 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 Gauss(1816), Bolyai (1823), Lobachevsky(1835) and others led to non-Euclidean geometry, to the realization that the classical geometric system of Euclid, which has so far reigned supreme, is only one of an infinite number of logically equal systems. Thus, the question arose which of these geometries is the geometry of real space.
Gauss also wanted to solve this issue by measuring the sum of angles big triangle. Thus, physical geometry turned into an empirical science, a branch of physics. These problems were further considered in particular Riemann (1868), Helmholtz(1868) and Poincare (1904). Poincare emphasized, in particular, the relationship between physical geometry and 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 one common system, within the framework of which this question was answered, an answer in the spirit of a specific non-Euclidean system."

Rudolf Carnap, Hans Hahn, Otto Neurath, Scientific worldview - Vienna circle, in Collection: Journal “Erkenntnis” (“Knowledge”). Favorites / 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 a 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 appeared physical quantities, built according to the principle proposed by Gauss. They were based on metric system measures, but differed from each other in basic units. The question of ensuring uniformity in the measurement of quantities reflecting certain phenomena material world, has always been very important. The lack of such uniformity created significant difficulties for scientific knowledge. For example, until the 80s of the 19th century there was no unity in the measurement electrical quantities: 15 different units of electrical resistance were used, 8 units electromotive force, 5 units electric current etc. 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 B.S., Philosophy of Science, Rostov-on-Don, “Phoenix”, 2007, p. 390-391.

« Carl Gauss, like Isaac Newton, often Not published scientific results. But all the published works of Carl Gauss contain significant results - there are no crude or pass-through works among them.

“Here it is necessary to distinguish the research method itself from the presentation and publication of its results. Let's take as an 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, exerting extreme care for the brevity of the presentation, the 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 the scaffolding that served for the construction; therefore, he not only was in no hurry to publish his works, but left them to mature not just for years, but for decades, often returning to this work from time to time in order to bring it to perfection. […] He did not bother to publish his studies on elliptic functions, the main properties of which he discovered 34 years before Abel and Jacobi, for 61 years, and they were published in his “Heritage” approximately another 60 years after his death. Euler did exactly the opposite of Gauss. Not only did he not dismantle the scaffolding around his building, but sometimes he even seemed to clutter it up with them. But he shows all the details of the very method of his work, which is so carefully hidden in Gauss. Euler did not bother with finishing; he worked straight away and published it as the work turned out; but he was far ahead of the Academy's printed media, so that he himself said that academic publications would have enough of his works for 40 years after his death; but here he was wrong - they lasted more than 80 years. Cauchy He wrote so many works, both excellent and hasty, that neither the Paris Academy nor the mathematical journals of that time could contain them, and he founded his own mathematical journal, in which he published only his works. Gauss put it this way about the most hasty of them: “Cauchy suffers from mathematical diarrhea.” It is not known whether Cauchy said in retaliation that Gauss suffered from mathematical constipation?

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

«… Gauss was a very reserved person and led a reclusive lifestyle. He Not published a lot of his discoveries, and many of them were re-done by other mathematicians. In his publications, he paid more attention to the results, without attaching much importance to the methods for 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 unsociability delayed the development of mathematics for at least fifty years; half a dozen mathematicians could have become famous if they had obtained the results that had been kept in his archive for years, or even decades.”

Peter Bernstein, Against the Gods: Taming Risk, M., Olympus Business, 2006, p.156.

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 in the largest technical university 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. They vying with each other to invite him to different countries Europe. 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”.

Carl Friedrich Gauss(German: Carl Friedrich Gauß) - an outstanding German mathematician, astronomer and physicist, considered one of the greatest mathematicians of all time.

Carl Friedrich Gauss was born on April 30, 1777. in the Duchy of Brunswick. Gauss's grandfather was a poor peasant, his father was a gardener, mason, and canal caretaker. Gauss's early age showed extraordinary talent for mathematics. One day, while doing his father's calculations, his three-year-old son noticed an error in the calculations. The calculation was checked, and the number indicated by the boy was correct. Little Karl was lucky with his teacher: M. Bartels appreciated the exceptional talent of young Gauss and managed to get him a scholarship from the Duke of Brunswick.

This helped Gauss finish college, where he studied Newton, Euler, and Lagrange. Already there, Gaus made several discoveries in higher mathematics, including proving the law of reciprocity of quadratic residues. Legendre, however, discovered this most important law earlier, but failed to strictly prove it, and Euler also failed to do so.

From 1795 to 1798, Gauss studied at the University of Göttingen. This is the most fruitful period in Gauss's life. In 1796, Carl Friedrich Gauss proved the possibility of constructing a regular 17-gon 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 regular n-gon using a compass and ruler: if n is a prime number, then it should be of the form n=2^(2^k)+1 (Fermat number). Gauss treasured this discovery very much and bequeathed that a regular 17-gon inscribed in a circle should be depicted on his grave.

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. Gauss made two discoveries in just ten days, a month before he turned 19 years old.

Since 1799, Gauss has been a privatdozent at the University of Braunschweig. The Duke continued to patronize the young genius. He paid for the publication of his doctoral dissertation (1799) and awarded him a good scholarship. After 1801, Gauss, without breaking with number theory, expanded his range of interests to include the natural sciences.

Carl Gauss gained worldwide fame after developing a method for calculating the elliptical orbit of a planet. according to three observations. The application of this method to the minor planet Ceres made it possible to find it again in the sky after it had been lost.

On the night of December 31 to January 1, the famous German astronomer Olbers, using data from Gauss, discovered a planet called Ceres. In March 1802, another similar planet, Pallas, was discovered, and Gauss immediately calculated its orbit.

Karl Gauss outlined his methods for calculating orbits in his famous Theories of the motion of celestial bodies(lat. 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 1806, his generous patron, the Duke of Brunswick, died from a wound received in the war with Napoleon. Several countries vied with each other to invite Gauss to serve. 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.

Associated with the name Gauss basic research in almost all basic areas of mathematics: algebra, mathematical analysis, theory of functions of a complex variable, differential and non-Euclidean geometry, probability theory, as well as in astronomy, geodesy and mechanics.

Published in 1809 Gauss's new masterpiece - "The Theory of the Motion of Celestial Bodies", where the canonical theory of accounting for orbital perturbations is outlined.

In 1810, Gauss received the Prize of the Paris Academy of Sciences and gold medal Royal Society of London, was elected to several academies. The famous comet of 1812 was observed everywhere using Gauss's calculations. In 1828, Gauss's main geometric memoir was published. General studies about curved surfaces." 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.

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 V. Weber, he built the first electromagnetic telegraph in Germany, connecting the observatory and physical institute in Göttingen, completed a large experimental work on terrestrial magnetism, invented a unipolar magnetometer, and then a bifilar one (also together with V. Weber), created the foundations of potential theory, in particular, formulated the basic theorem of electrostatics (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 every scientific field, his depth of penetration into the material, the courage of his thought and the significance of the result were amazing. Gauss was called the “king of mathematicians.” He discovered the ring of complex Gaussian integers, created a theory of divisibility for them, and with their help solved many algebraic problems.

Gauss died on February 23, 1855 in Göttingen. Contemporaries remember Gauss as a cheerful, friendly person with an excellent sense of humor. The following names were named in honor of Gauss: a crater on the Moon, minor planet No. 1001 (Gaussia), a unit of measurement of magnetic induction in the GHS system, and the Gaussberg volcano in Antarctica.