Mathematician Gauss was an introverted person. Eric Temple Bell, who studied his biography, believes that if Gauss published all his studies and discoveries in full and on time, he could have become famous with half a dozen mathematicians. And so they had to spend the lion's share of the time to find out how the scientist received this or that data. After all, he rarely published methods; he was always interested only in the result. An outstanding mathematician, a strange person and an inimitable personality - these are all Karl Friedrich Gauss.
early years
The future mathematician Gauss was born on 04/30/1777. This, of course, is a strange phenomenon, but outstanding people are most often born in poor families. So it happened this time. His grandfather was an ordinary peasant, and his father worked in the Duchy of Braunschweig as a gardener, bricklayer or plumber. Parents learned that their child was a child prodigy when the baby was two years old. A year later, Karl already knows how to count, write and read.
The teacher noticed his ability at school when he gave the task to calculate the sum of numbers from 1 to 100. Gauss quickly managed to understand that all the extreme numbers in the pair were 101, and in seconds he solved this equation by multiplying 101 by 50.
The young mathematician was incredibly lucky with the teacher. He helped him in everything, even strove for a scholarship to be paid to the beginning talent. With her help, Karl managed to graduate from college (1795).
Student years
After college, Gauss studies at the University of Gottingen. Biographers designate this period of life as the most fruitful. At this time, he managed to prove that it was possible to draw a regular seventeenthagon using only compasses. He assures: you can draw not only the seventeenthagon, but also other regular polygons, using only a compass and a ruler.
At the university, Gauss begins to keep a special notebook, where he enters all the notes that relate to his research. Most of them were hidden from the public eye. For friends, he always repeated that he would not be able to publish a study or formula in which he was not 100% sure. For this reason, most of his ideas were discovered by other mathematicians after 30 years.
"Arithmetic studies"
Along with graduation, the mathematician Gauss completed his outstanding work Arithmetic Studies (1798), but it was only published two years later.
This extensive composition determined the further development of mathematics (in particular, algebra and higher arithmetic). The bulk of the work is focused on describing the abiogenesis of quadratic forms. Biographers claim that it was with him that Gauss's discoveries in mathematics begin. After all, he was the first mathematician who managed to calculate fractions and translate them into functions.
Also in the book you can find the full paradigm of the equalities of the division of the circle. Gauss skillfully applies this theory, trying to solve the problem of drawing polygons using a ruler and a compass. Proving this probability, Karl Gauss (mathematician) introduces a series of numbers called Gauss numbers (3, 5, 17, 257, 65337). This means that with the help of simple stationery, you can build a 3-gon, 5-gon, 17-gon, etc. But the 7-gon cannot be built, because 7 is not a âGaussian numberâ. To âhisâ numbers, mathematicians also include deuces that are multiplied by any degree of his series of numbers (2 3 , 2 5 , etc.)
This result can be called a "pure existence theorem." As already stated at the beginning, Gauss liked to publish the final results, but never specified methods. Itâs the same in this case: the mathematician claims that itâs quite possible to build a regular polygon , but doesnât specify how to do it.
Astronomy and the Queen of Sciences
in 1799, Karl Gauss (mathematician) received the title of privat-docent of the University of Braunschwein. Two years later, he is given a place at the St. Petersburg Academy of Sciences, where he acts as a correspondent. He still continues to study number theory, but his interests expand after the discovery of a small planet. Gauss tries to calculate and indicate its exact location. Many people wonder what the name of the planet was called the mathematician Gauss. However, few people know that Ceres is not the only planet with which the scientist worked.
In 1801, a new celestial body was first discovered. It happened unexpectedly and suddenly, just as unexpectedly the planet was lost. Gauss tried to discover her using mathematical methods, and, oddly enough, she was exactly where the scientist pointed out.
The scientist has been engaged in astronomy for more than two decades. The Gauss method (a mathematician who owns many discoveries) for determining the orbit with the help of three observations receives worldwide fame. Three observations - this is the place where the planet is located at a different time period. Using these indicators, Ceres was again found. In exactly the same way, another planet was discovered. Since 1802, the question, what is the name of the planet discovered by the mathematician Gauss, could be answered: "Pallas." Looking a little ahead, it is worth noting that in 1923 a large asteroid orbiting Mars was named after the famous mathematician. Gauss, or asteroid 1001, is the officially recognized planet of the mathematician Gauss.
These were the first studies in astronomy. Perhaps the contemplation of the starry sky has become the reason that a person, passionate about numbers, decides to start a family. In 1805, he married Johann Osthof. In this union, a couple has three children, but the youngest son dies in infancy.
In 1806, the duke died, who patronized mathematics. European countries are vying to invite Gauss to their place. From 1807 until his last days, Gauss headed the department at the University of Gottingen.
In 1809, the first wife of a mathematician dies, in the same year, Gauss publishes his new creation - a book entitled "The paradigm of the movement of celestial bodies." The methods for calculating the orbits of the planets, which are described in this work, are relevant today (though with minor corrections).
The main theorem of algebra
Germany met the beginning of the 19th century in a state of anarchy and decline. These years were difficult for the mathematician, but he continues to live on. In 1810, Gauss for the second time tied the knot - with Minna Waldeck. In this union, he has three more children: Teresa, Wilhelm and Eugen. Also, 1810 was marked by the receipt of a prestigious award and a gold medal.
Gauss continues his work in the fields of astronomy and mathematics, exploring more and more unknown components of these sciences. His first publication on the basic theorem of algebra dates from 1815. The main idea is this: the number of roots of a polynomial is directly proportional to its degree. Later, the statement took on a slightly different form: any number in a degree not equal to zero, a priori, has at least one root.
He first proved it back in 1799, but was not happy with his work, so the publication was published 16 years later, with some amendments, additions and calculations.
Non-Euclidean theory
According to the data, in 1818, Gauss was the first to build a base for non-Euclidean geometry, the theorems of which would be possible in reality. Non-Euclidean geometry is a field of science distinguishable from Euclidean. The main feature of Euclidean geometry is the presence of axioms and theorems that do not require confirmation. In his book, "Beginnings," Euclid came up with statements that must be accepted without evidence, because they cannot be changed. Gauss was the first to prove that Euclidean theories cannot always be perceived without justification, because in certain cases they do not have a solid evidence base that satisfies all the requirements of the experiment. So non-Euclidean geometry appeared. Of course, the basic geometric systems were discovered by Lobachevsky and Riemann, but the Gauss method - a mathematician who knows how to look deeper and find the truth - laid the foundation for this section of geometry.
Geodesy
In 1818, the Hanoverian government decided that it was time to measure the kingdom, and this task was given to Karl Friedrich Gauss. Discoveries in mathematics did not end there, but only acquired a new connotation. He develops the computational combinations necessary to complete the task. These included the Gaussian âsmall squaresâ technique, which raised geodesy to a new level.
He had to make maps and organize a survey of the area. This made it possible to acquire new knowledge and put new experiments, so in 1821 he began to write a work on geodesy. This work of Gauss was published in 1827, under the title "General analysis of uneven planes." This work was based on ambushes of internal geometry. The mathematician believed that it is necessary to consider objects that are on the surface as properties of the surface itself, paying attention to the length of the curves, while ignoring the data of the surrounding space. Somewhat later, this theory was supplemented by the works of B. Riman and A. Alexandrov.
Thanks to this work, the concept of âGaussian curvatureâ began to appear in scientific circles (it determines the degree of curvature of a plane at a certain point). Differential geometry begins to exist. And so that the observation results are reliable, Karl Friedrich Gauss (mathematician) introduces new methods for obtaining quantities with a high level of probability.
Mechanics
In 1824, Gauss was in absentia included in the membership of the St. Petersburg Academy of Sciences. His achievements do not end there, he is still stubbornly engaged in mathematics and presents a new discovery: "Gaussian integers." By them we mean numbers having an imaginary and real part, which are integers. In essence, Gaussian numbers resemble ordinary integers in their properties, but those small distinguishing characteristics make it possible to prove the biquadratic reciprocity law.
At any time, he was inimitable. Gauss - a mathematician whose discoveries are so closely intertwined with life - in 1829 made new adjustments even to mechanics. At this time, his little work On the New Universal Principle of Mechanics was published. In it, Gauss proves that the principle of small impact can rightfully be considered the new paradigm of mechanics. The scientist assures that this principle can be applied to all mechanical systems that are interconnected.
Physics
Since 1831, Gauss begins to suffer from severe insomnia. The disease manifested itself after the death of the second wife. He seeks solace in new studies and acquaintances. So, thanks to his invitation, W. Weber came to Göttingen. With a young talented person, Gauss quickly finds a common language. They are both passionate about science, and the thirst for knowledge has to be quenched by exchanging their best practices, guesses and experience. These enthusiasts quickly get to work, devoting their time to the study of electromagnetism.
Gauss, a mathematician whose biography is of great scientific value, in 1832 created absolute units that are still used in physics today. He distinguished three main positions: time, weight and distance (length). Along with this discovery in 1833, thanks to joint research with the physicist Weber, Gauss managed to invent the electromagnetic telegraph.
The year 1839 was marked by the release of yet another work - "On the general abiogenesis of gravitational and repulsive forces, which act in direct proportion to distance." The pages describe in detail the famous Gauss law (also known as the Gauss-Ostrogradsky theorem, or simply the Gauss theorem). This law is one of the main ones in electrodynamics. It determines the relationship between the electric flux and the sum of the surface charge, divisible by the electric constant.
In the same year, Gauss mastered the Russian language. He sends letters to St. Petersburg with a request to send him Russian books and magazines, he especially wanted to get acquainted with the work âThe Captain's Daughterâ. This fact of the biography proves that, in addition to computational abilities, Gauss had many other interests and hobbies.
Just a man
Gauss was never in a hurry to publish. He long and painstakingly checked his every work. For the mathematician, everything mattered: from the correctness of the formula to the grace and simplicity of the syllable. He loved to repeat that his work was like a newly built house. The owner is shown only the final result of the work, and not the remnants of the forest that used to be at the place of the dwelling. Also with his works: Gauss was sure that no one should show rough draft studies, only ready-made data, theories, formulas.
Gauss always showed a keen interest in the sciences, but he was especially interested in mathematics, which he considered "the queen of all sciences." And nature did not deprive him of his mind and talents. Even at an advanced age, as usual, he carried out most of the complex calculations in his mind. The mathematician never spread about his work in advance. Like every person, he was afraid that his contemporaries would not understand him. In one of his letters, Karl says that he was tired of always balancing on the brink: on the one hand, he would gladly support science, but, on the other, he did not want to tidy up the "horny nest of the dull."
Gauss spent his whole life in Göttingen, only once he managed to visit a scientific conference in Berlin. He could conduct research, experiments, calculations, or measurements for a long time, but he really did not like to give lectures. He considered this process only to be an unfortunate necessity, but if talented students appeared in his group, he spared neither time nor energy for them and for many years supported correspondence discussing important scientific issues.
Karl Friedrich Gauss, a mathematician whose photo is featured in this article, was a truly amazing person. He could boast of outstanding knowledge not only in the field of mathematics, but also âmade friendsâ with foreign languages. He spoke fluently in Latin, English and French, and even mastered Russian. The mathematician read not only scientific memoirs, but also ordinary fiction. He especially liked the works of Dickens, Swift and Walter Scott. After his younger sons emigrated to the United States, Gauss became interested in American writers. Over time, addicted to Danish, Swedish, Italian and Spanish books. The mathematician certainly read all the works in the original.
Gauss took a very conservative position in public life. From an early age, he felt addicted to people in power. Even when in 1837 a protest against the king began at the university, which curtailed the professors, Karl did not intervene.
Last years
In 1849, Gauss celebrates the 50th anniversary of his doctorate. Well- known mathematicians came to him , and this pleased him much more than the awarding of another award. In the last years of his life, Karl Gauss was already sick a lot. It was difficult for mathematicians to move around, but the clarity and sharpness of the mind did not suffer from this.
Shortly before death, Gauss's health deteriorated. Doctors diagnosed heart disease and nervous strain. Medications did not help much.
The mathematician Gauss died on February 23, 1855, at the age of seventy-eight. The famous scientist was buried in Göttingen, and, according to his last will, a regular seventeen hexagon was engraved on a tombstone. Later, his portraits will be printed on postage stamps and banknotes, the country will forever remember his best thinker.
That was Karl Friedrich Gauss - strange, smart and enthusiastic. And if they ask what the name of the Gaussian mathematics planet is, you can slowly answer: âCalculations!â, Because he devoted all his life to them.