NIKOLAI LOBACHEVSKY

(1792 – 1856)

PERSONAL HISTORY:

Nikolai Lobachevsky was born in Russia to a poor family. His father was a clerk in a surveyor’s office. His father died when he was seven and his mother moved the family to Kazan, a town located on the western border of Siberia.

Nikolai attended Kazan University:

In 1811, he received a master’s degree in both mathematics and physics.

In 1814, he became a lecturer at the University.

In 1822, he became a full professor.

He taught courses in mechanics, physics, mathematics and hydrodynamics. He even lectured to the public at large on physics.

In addition to his teaching duties, Nikolai was a rector of the university. This presented him with a heavy administrative load. He was in charge of the construction of new university buildings, recruitment of both students and teachers, and curriculum. He had an observatory built and even introduced a center for Oriental Studies. Unfortunately, this heavy work load would eventually take its toll on Nikolai’s health.

In 1832, he married a much younger woman who bore him seven children.

In 1846 he was dismissed from Kazan University despite twenty years of outstanding service as a teacher and rector.

Toward the end of his life, Nikolai suffered from an unspecified illness that led to blindness. He died in 1856 without the fame that would later be accorded his work.

LOBACHEVSKY’S ACHIEVEMENTS

Nikolai’s main accomplishment was the development (independently from Janos Bolyai and Gauss) of non-Euclidean geometry. It is speculated that his fascination with Euclid’s fifth postulate came from a course taught by Bartels and the book, Montucla, which discussed the postulate. Euclid’s fifth postulate states that given a line and a point not on the line, a unique line can be drawn through the point parallel to the given line. Nikolai developed a geometry in which the uniqueness part of Euclid’s Fifth Postulate is false. Hyperbolic geometry, sometimes referred to as Lobachevskian geometry, [2] assumes there are at least two lines parallel to a given line through a given point. Euclidean geometry, according to Lobachevsky, was a special case of this more general geometry.

Nikolai was the first to publish on this new non-Euclidean geometry. His research was first published in the Bulletin of Kazan University, but was rejected for publication by the St Petersburg Academy of Science.

In 1823, he completed his major work, Geometriya, but it was not published in its original form until 1909

In 1837 he published an article, “Geometrie Imaginaire”.

In 1840 he published, “Geometry on the Theory of Parallelism” (translated)

In other areas of mathematics, Lobachevsky developed a method for the approximation of the roots of algebraic equations. This method of solutions is today known as the Dandelin-Graffe method; only in Russia is it named after Lobachevsky. All three men developed it independently of one another.

He also defined a function as the correspondence between two sets of real numbers.

His name is also seen in the Gauss-Bolyai-Lobachevsky space.

ISSUES

Some historians have speculated that Martin Bartels, a professor of Mathematics at Kazan University and teacher of Lobachevsky, may have provided Nikolai with hints on hyperbolic geometry. Bartels was a friend of Gauss and the two corresponded regularly. Gauss himself discovered non-Euclidean Geometry, but feared to publish it, choosing instead only to talk about it with his closest friends – Bartels one of them.

LOBACHEVSKY AND POPULAR CULTURE

Lobachevsky has also been immortalized in popular culture and has a crater on the moon named for him.

[1] In the 1950’s, humorist, satirist and mathematician Tom Lehrer wrote a song in which Lobachesvky teaches him the secret of success as a mathematician: plagerism.

[2] In the novella “Operation Changeling”, a group of sorcerers navigate a non-Euclidean universe with the assistance of the ghosts of Lobachevsky and Bolyai.