Hilbert David (1862-1943) is a great German mathematician. David Hilbert is world famous for his fundamental works in very different fields of mathematics. In 1900 he was invited to second Congress of mathematicians held in Paris. On the eve of this congress, for a short time and with great brevity he reconstructed axiomatics of Euclid geometry. The axiomatics offered for Euclid geometry was perfect. Furthermore, in the succeeding century he decided to draw attention of scientists to problems determining the development of mathematics. Among Hilbert’s 23 problems alongside with specific problems there are general problems that determine the direction of development of mathematics.
Only one of Hilbert’s problems (III problem) concerned secondary school geometry. The fact that when calculating the square of a triangle the notion of limit is not necessary, when calculating the volume of a triangular pyramid it is impossible to do without limit, attracted Hilbert’s attention.
In 1900 M.Den answered to this question having solved Hilbert’s third problem, he proved that a cube and a regular tetrahedron of the same size are not homogeneous, i.e. in order to construct volume theory of polyhedrons it is impossible to do without limit (see figures of same size).
After the Congress the scientist is interested in mathematical analysis and as it always has been, he demonstrates mysterious approach. To his mind, the functions are the points of infinite-dimensional space. Analytic results are obtained in absolutely analytic term.
He solves Varing’s known problem in number theory and proves that any natural number may be represented in the form of the sum of powers of numbers. Any natural number may be represented the form of the sum of four squares, nine cubes, nineteenth, fourth degree, etc.
The University where Hilbert has worked, was one of the great centers of world mathematical thinking in the first third of the XX century.
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