1816-1855 years. Scientific activity

1816-1855 years

1820: Gauss is commissioned to make a geodetic survey of Hanover. For this purpose, he developed appropriate computational methods (including the method of practical application of his method of least squares), which led to the creation of a new scientific direction — higher geodesy, and organized the survey of the area and mapping[9].

1821: in connection with the 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. 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 " Studies concerning curved surfaces" (1822). It was freely used in General curvilinear coordinates on the surface. Gauss developed the method of conformal mapping, which preserves angles in cartography (but distorts distances); it is also used in Aero-, hydrodynamics, and electrostatics.

1824: elected a 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 high-degree comparisons.

1829: in a remarkable work " On a new General law of mechanics", consisting of only four pages, Gauss justifies [17] a new variational principle of mechanics — the principle of least compulsion. The principle applies to mechanical systems with ideal connections and is formulated by Gauss as follows: " the movement of a system of material points connected to each other in an arbitrary way and subject to any influence, at each moment occurs in the most perfect possible agreement with the movement that these points would have if they all became free, that is, occurs with the least possible compulsion, if as a measure of compulsion applied during an infinitesimal instant, take the sum of the products of the mass of each point by the square of its deviation from the position it would occupy if it were free" [18].

1831: his second wife died, and Gauss developed severe insomnia. The 27-year-old talented physicist Wilhelm Weber, whom Gauss met in 1828 while visiting Humboldt, came to gö ttingen on Gauss's initiative. The two science enthusiasts become friends, despite their age difference, and begin a cycle of research on electromagnetism.

1832: " the Theory of biquadratic deductions". Using the same integer complex Gaussian numbers, 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 this point on becomes generally accepted.

1833: Gauss invents the electric Telegraph and (with Weber) builds a working model of it. One thousand eight hundred thirty seven: Weber is fired for refusing to take the oath of office to the new king of Hanover. Gauss is left alone again.

Russian Russian language in 1839: 62-year-old Gauss mastered the Russian language and in letters to the St. Petersburg Academy asked to send him Russian magazines and books, in particular " the Captain's daughter" by Pushkin. It is assumed that this is due to Gauss's interest in the works of Lobachevsky, who in 1842, on the recommendation of Gauss, was elected a foreign corresponding member of the Royal society of gö ttingen.

In the same 1839 year, Gauss in his essay " General theory of forces of attraction and repulsion acting inversely proportional to the square of distance" outlined the basics of potential theory, including a number of fundamental propositions and theorems — for example, the basic theorem of electrostatics (Gauss's theorem) [19].

1840: in the work " Dioptric studies" Gauss developed a theory of image construction in complex optical systems[19].

Gauss died on 23 February 1855 in gö ttingen. King George V of Hanover ordered a medal to be minted in honor of Gauss, which was engraved with a portrait of Gauss and the honorary title " Mathematicorum Princeps" — " king of mathematicians".

Scientific activity

Gauss ' name is associated with fundamental research in almost all major areas of mathematics: algebra, number theory, differential and non-Euclidean geometry, mathematical analysis, the theory of functions of a complex variable, probability theory, as well as in analytical and celestial mechanics, astronomy, physics and geodesy[9]. " In each area, the depth of insight into the material, the boldness of thought, and the significance of the result were striking. Gauss was called the " king of mathematicians" " [20] (Latin: Princeps mathematicorum).

Gauss was extremely strict about his printed works and never published even outstanding results if he considered his work on this topic incomplete. On his personal seal was an image of a tree with several fruits, under the motto: " Pauca sed matura" (a little, but Mature) [21]. A study of the Gauss archive showed that he was slow to publish a number of his discoveries, and as a result he was outpaced by other mathematicians. Here is an incomplete list of priorities that he missed.

• Non-Euclidean geometry, where he was ahead of Lobachevsky and Boyai, but did not dare to publish his results[22].

* Elliptical functions, where he also went far, but did not have time to print anything, and after the work of Jacobi and Abel, there was no need for publication.

* A substantial outline of the theory of quaternions, independently discovered by Hamilton 20 years later.

• The least squares method, rediscovered later by Legendre.

• The law of distribution of Prime numbers, with which it was also preceded by Legendre's publication.

Several students, students of Gauss, became outstanding mathematicians, for example: Riemann, Dedekind, Bessel, Moebius.

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