Nikolai Ivanovich Lobachevsky

1792-1856

Russian Mathematician

The Russian mathematician Nikolai Lobachevsky, along with the Hungarian Janos Bolyai (1802-1860), is considered to be the founder of non-Euclidean geometry. Neither man's contribution was fully recognized until after their deaths, despite Lobachevsky's perseverance in publishing in French and German as well as Russian. Non-Euclidean geometry was later to become an essential building block for Albert Einstein's (1879-1955) theory of general relativity.

Lobachevsky was born on December 1, 1792, in Nizhny Novgorod, Russia, into very limited economic means. His father was a lowranking government official, and died when young Nikolai was only seven years old. The family then moved to Kazan, at the edge of Siberia. Lobachevsky received a public scholarship to the university in Kazan at the age of 14, intending to study medicine. Under the influence of a skilled mathematics teacher, Johann Bartels, who had taught the eminent Carl Friedrich Gauss (1777-1855), he soon switched to that field. Lobachevsky remained at Kazan for the rest of his life. He became a professor in 1816.

In 1826, Lobachevsky first announced his challenge of Euclid's fifth postulate, that one and only one line parallel to a given line can be drawn through a fixed point external to it. A successful challenge required developing a system of geometry without this postulate and which did not include any internal contradictions. Lobachevsky and Bolyai each accomplished this task independently at about the same time. However, Bolyai essentially withdrew even before becoming aware of Lobachevsky's work, when Gauss, a good friend of his father's, claimed to have had the idea decades before. Lobachevsky, probably realizing that an idea without follow-up or publication was not a valid claim of precedence, was not bothered by it. Although Gauss was acquainted with both mathematicians and knew they were working in the same field, he never introduced them. In fact, there is no evidence that Lobachevsky knew of Bolyai at all.

Lobachevsky published the first account of his non-Euclidean geometry in 1829, in the Kazan Messenger. He later wrote several more complete expositions of his work, including Geometrical Researches on the Theory of Parallels(1840), which garnered a favorable reaction from Gauss, and Pangeometrie (1855). He also worked in the areas of infinite series, integral calculus, and probability.

In addition to his mathematical research, Lobachevsky was a skilled university administrator, serving as dean of mathematics and physics, librarian, and rector as well as maintaining his professorship. The university had suffered under the reign of Tsar Alexander I. The tsar distrusted modern science and philosophy, regarding them as aberrant products of the French Revolution and a threat to orthodox religion. The result was factionalism and lowered standards in academic life, and the departure from Kazan of some of the best professors, including Lobachevsky's old teacher, Bartels.

When Tsar Nicholas I succeeded Alexander in 1826, a more tolerant period began. Lobachevsky was able to turn the university around, reestablishing it as a place of high academic standards and a collegial environment. He enforced sanitary precautions to limit the university's suffering from the cholera epidemic of 1830, rebuilt several buildings after a catastrophic 1842 fire, and improved primary and secondary education in the surrounding area. Despite all his efforts and accomplishments, in 1846 the capricious government abruptly relieved him of his university posts without explanation and despite the protests of all his colleagues. He died in 1856 in Kazan.

SHERRI CHASIN CALVO