Lobachevsky came to the conclusion that at least part of Euclidean geometry could be revised.

After much consideration Lobachevsky modified one of the postulates of Euclid.

As a result he got the geometry, which was hard to imagine in the usual representation; so Lobachevsky called his geometry “imaginary.” At the conclusion of other scientists, it is the Lobachevsky geometry that is the most correct description of the real world.

According to the Lobachevsky geometry through one point can pass several lines that are parallel to another line:

Lobachevsky Geometry

Great German mathematician Gauss admired the works of Lobachevsky … in their personal correspondence, but he never found the courage to make any public statements about them. Although, reportedly, Gauss even started learning Russian to be able to read all of the Lobachevsky works in the original language.

Triumph of Lobachevsky Geometry

After just 10 years after the death of the scientist, serious works on geometry of Lobachevskybegan to appear. In 1868, Beltami proposed a description of the pseudo-sphere, in 1871 Klein offered the first complete model of the Lobachevsky plane (Klein model), and then there was a model by Poincare. The models confirmed the consistency of the Lobachevsky geometry.

Lobachevsky geometry was also used by Albert Einstein in creating his General theory of relativity.

“Imperishable glory of Lobachevsky is that solved a challenge for us, which remained unsolved for two thousand years”.

Sophus Lie

Lobachevsky Award

It is awarded every three years (with interruptions) for outstanding achievements in the field of geometry.

Achievements of Lobachevsky are not limited by creating Lobachevsky geometry: he gave the refinement of the concept of the function (later it was repeated by Dirichlet), he gave the distinction of continuity of the function and its differentiability, he conducted a number of studies of trigonometric series, he developed a method for the numerical solution of equations (it was later repeated by Graeffe) and he carried out many other studies.


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