For the creativity of Gauss is characterized by an organic association between theoretical and practical arithmetic, the depth of the problems. Gauss's works had a huge impact on the formation of algebra (confirmation of the main axioms of this science), the solution of linear equations of number theory (internal geometric surface), mathematical physics (Gauss principle), the theory of electricity and magnetism, geodesy (the development of a method of smaller squares) and almost all sections astronomy.
"Arithmetic studies"
The first of its kind, the vast creation of Gauss - "Arithmetic Studies" (published in 1801), which lasted almost all the years of his life. The next formation is the fundamental sections of arithmetic - number theory and higher mathematics, which includes the solution of linear equations.
Of the large number of fundamental and small results cited in the "Arithmetic Studies", it is necessary to note the complete concept of quadratic forms and the first confirmation of the quadratic reciprocity law. At the end of his life, Gauss gives a perfect concept of the equations of separation of a circle, indicating their associations with the tasks of constructing polygons, already proven in ancient times about the ability to construct a true polygon with a compass and a ruler with the correct number of sides.
Gauss showed all the numbers at which building a regular polygon using a compass and a ruler can be simple. These are the so-called “five different Gaussian ordinary numbers”: three and five, seventeen and two hundred fifty seven and 65237, and also multiplied by a different level of two Gaussian numbers. For example, using a stationery to build a correct (3x5x17) - a square is allowed, but a true 7-gon is impossible, since the figure is not Gaussian, it has the usual number.
The main axiom of algebra
The main axiom of algebra is also associated with the name of Gauss, according to which the number of roots of the polynomial (real and complex) is the same (when converting numerical roots, the complex root will be taken into account as many times as its level). Gauss made the first confirmation of the main axiom of algebra in 1799, and later proposed some more proofs.
Observation Processing
Unsuitable meaning for all sciences dealing with such a system as the methods for solving systems of equations developed by Gauss are able to obtain more potential values of measurements of quantities. Especially widespread was the one made by Gauss in 1821. way of smaller squares. Scientists also laid the foundations of the theory of errors.
The meaning of Gauss studies
Almost all, as it turned out now, the great studies of Carl Gauss did not publish during his lifetime. They are preserved in the form of sketches, essays that corresponded with his comrades. The research of these works was carried out by the Göttingen scientific community, which managed to publish twelve volumes of Gauss's works. A more fascinating and popular work “Solving linear equations” was published late, as he accidentally found his diary with these entries.
Karl’s scientific work was based on solving linear equations. Applied mathematics was fully implemented in the basic part of science, it was given with great difficulty. It was necessary to fight for ideas; there were many scientists who wanted to become famous for the topic of solving linear equations.
Arithmetic research has had a big impact on the upcoming formation of number theory and algebra. The laws of reciprocity to this day occupy one of the most important places in algebra. This great scientist did not have the literature needed to work on such works as “Arithmetic studies”, “Solving a matrix by the Gauss method”, and “Solving linear equations”, he took all the knowledge from his head, as they say.