David Hilbert is a famous mathematician and teacher of the highest class, never tired, persistent in his intentions, inspiring and generous, one of the greats of his time.

Creative power, original originality of thinking, amazing insight and versatility of interests made David a pioneer in most areas of the exact sciences.

## Gilbert David: short biography

David was born in the city of Velau, located near Königsberg (Prussia). Born on January 23, 1862, he was the first child of a married couple, Otto and Maria. Gilbert was not a child prodigy; in turn setting himself the goal of fully exploring each area of mathematics, he solved the problems that interested him. With the completion of the creative impulse, David left the studied field of activity to his students. Moreover, he left them in absolute order, teaching them the appropriate course and publishing a good textbook for followers.

Hilbert could have acted differently: he announced for the new academic year a special course in a field of mathematics he had not studied and conquered it together with the students recruited. Getting into such a course was considered a huge success, although in reality, studying on it was a huge test.

## Gilbert and students

David Gilbert, whose biography is interesting to the modern generation, was caring and polite with students in whom he felt potential. If the spark faded, the scientist politely recommended that they try themselves in another kind of activity. Some of Hilbert's students followed the teacher's advice and became engineers, physicists, and even writers. The professor did not understand loafers and considered them inferior people. Being a highly respected man of science, David had his own characteristics. In warm weather, he came to lectures in a short-sleeved shirt with an open collar, which was not at all befitting a professor, or delivered flower bouquets to numerous passions. Could ahead on a bicycle, like some kind of gift, to carry a container of fertilizer.

However, despite his cheerfulness, David Hilbert was a rather tough person and could rudely criticize someone who did not meet his standards (too difficult to calculate, where it could be made easier, or explain clearly enough, as for high school level).

## Hilbert's first studies

His abilities for the exact sciences David Gilbert, whose brief biography is described in ourarticle, I felt back in Königsberg, where the profession of mathematics was little revered. Therefore, having opted for the quiet Göttingen, the gathering place for German mathematicians, Hilbert moved there in 1895 and successfully worked until 1933, when Adolf Hitler came to power.

Hilbert read his lectures slowly, without unnecessary embellishments, with frequent repetitions so that everyone would understand him. David also always repeated the previous material. Hilbert's lectures always attracted a large number of people: several hundred people could crowd into the hall, even sitting on the windowsills.

Research David started with algebra, more precisely - with transformations in number theory. A report on this topic became the basis of his textbook.

## Gilbert Family

Fortunate in friendship, David was unlucky in his family. They got along well with his wife Kete, but their only son was born demented. Therefore, Hilbert found an outlet in communication with numerous students - representatives of European and American countries. The mathematician often organized hiking trips and arranged joint tea parties, during which reasoning on mathematical topics smoothly turned into ordinary conversations on various topics. The prim German professors did not recognize this style of communication; it was the authority of David Hilbert that made it the norm, which was spread around the world by students of mathematics.

Soon, the algebraic interests of the mathematician moved to geometry, namely, to infinite-dimensional spaces. Limitsequences of points, the gap between them and the angle between the vectors defined the Hilbert space - similar to the Euclidean one.

## On putting things in order in the exact sciences

In 1898-1899, David Hilbert published a book on the foundations of geometry, which immediately became a bestseller. In it, he gave a complete system of axioms of Euclidean geometry, systematized them into groups, trying to determine the limiting values of each of them.

Such luck led Hilbert to the idea that in every mathematical field you can apply a clear system of irreplaceable axioms and definitions. As a key example, the mathematician chose the general set theory, and in it - the well-known Cantor continuum hypothesis. David Hilbert succeeded in proving the unprovability of this conjecture. However, in 1931, the young Austrian Kurt Godel proved that postulates like the continuum hypothesis, which Hilbert considered one of the mandatory axioms of set theory, can be found in any system of axioms. This statement indicates that the development of science does not stand still and will never stop, although each time it will be necessary to invent new axioms and definitions - something that the human brain is fully adapted to. Hilbert knew this from his own experience, so he sincerely rejoiced at Gödel's amazing discovery.

## Hilbert's Mathematical Problems

At the age of 38, at the Mathematical Congress in Paris, which brought together the whole color of science of that time, Hilbert made a report "Mathematical Problems", at which he proposed 23important topics. Hilbert considered the key tasks of mathematics of that time to be actively developing areas of science (set theory, algebraic geometry, functional analysis, mathematical logic, number theory), in each of which he singled out the most important problems that, by the end of the 20th century, had either been solved or had been proved. undecidability.

## The most important problem for mathematics

One day, young students asked Hilbert what he thought was the most important problem in mathematics, to which the aging scientist replied: “Catch a fly on the far side of the moon!” According to Hilbert, such a problem was not of particular interest, but what prospects could open up if it was solved! How many important discoveries and inventions of powerful methods would this entail!

The correctness of Hilbert's words was confirmed by life: it is worth remembering that the invention of computers occurred for instantaneous calculation of the hydrogen bomb. Discoveries such as the landing of the first man on the moon, the weather forecast for the whole planet, the launch of an artificial satellite of the Earth became a kind of by-product of the decision. Unfortunately, Gilbert did not have the opportunity to witness such significant events.

In the last years of his life, the professor impotently watched the disintegration of the mathematical school in Göttingen, which took place under the rule of the Nazis. David Hilbert, a mathematician who made a huge contribution to science, died on February 14, 1943 from the consequences of a broken arm. The cause of death was the physical immobility of the mathematician.