Lobachevsky, Nikolai Ivanovich

LOBACHEVSKY, NIKOLAI IVANOVICH

(1792–1856), mathematician; creator of the first non-Euclidean geometry.

Nikolai Lobachevsky was born in Nizhny Novgorod to the family of a minor government official. In 1809 he enrolled in Kazan University, selecting mathematics as his major field. From Martin Bartels and Franz Bronner, German immigrant professors, he learned the fundamentals of trigonometry, analytical geometry, celestial mechanics, differential calculus, the history of mathematics, and astronomy. Bronner also introduced him to the current controversies in the philosophy of science.

In 1811 Lobachevsky was granted a magisterial degree, and three years later he was appointed instructor in mathematics at Kazan University. His first teaching assignment was trigonometry and number theory as advanced by Carl Friedrich Gauss. In 1816 he was promoted to the rank of associate professor. In 1823 he published a gymnasium textbook in geometry and, in 1824, a textbook in algebra.

Lobachevsky's strong interest in geometry was first manifested in 1817 when, in one of his teaching courses, he dwelt in detail on his effort to adduce proofs for Euclid's fifth (parallel) postulate. In 1826, at a faculty meeting, he presented a paper that showed that he had abandoned the idea of searching for proofs for the fifth postulate; in contrast to Euclid's claim, he stated that more than one parallel could be drawn through a point out-side a line. On the basis of his postulate, Lobachevsky constructed a new geometry including, in some opinions, Euclid's creation as a special case. Although the text of Lobachevsky's report was not preserved, it can be safely assumed that its contents were repeated in his "Elements of Geometry," published in the Kazan Herald in 1829–1830. In the meantime, Lobachevsky was elected the rector of the university, a position he held until 1846.

In order to inform Western scientists about his new ideas, in 1837 Lobachevsky published an article in French ("Geometrie imaginaire") and in 1840 a small book in German (Geometrische Untersuchungen zur Theorie der Parallellinien ). His article "Pangeometry" appeared in Russian in 1855 and in French in 1856, the year of his death. At no time did Lobachevsky try to invalidate Euclid's geometry; he only wanted to show that there was room and necessity for more than one geometry. After becoming familiar with the new geometry, Carl Friedrich Gauss was instrumental in Lobachevsky's election as an honorary member of the Gottingen Scientific Society.

After the mid-nineteenth century, Lobachevsky's revolutionary ideas in geometry began to attract serious attention in the West. Eugenio Beltrami in Italy, Henri Poincare in France, and Felix Klein in Germany contributed to the integration of non-Euclidean geometry into the mainstream of modern mathematics. The English mathematician William Kingdon Clifford attributed Copernican significance to Lobachevsky's ideas.

On the initiative of Alexander Vasiliev, professor of mathematics, in 1893 Kazan University celebrated the centennial of Lobechevsky's birth. On this occasion, Vasiliev presented a lengthy paper explaining not only the scientific and philosophical messages of the first non-Euclidean geometry but also their growing acceptance in the West. At this time, Kazan University established the Lobachevsky Prize, to be given annually to a selected mathematician whose work was related to the Lobachevsky legacy. Among the early recipients of the prize were Sophus Lie and Henri Poincaré.

In 1926 Kazan University celebrated the centennial of Lobachevsky's non-Euclidean geometry. All speakers placed emphasis on Lobachevsky's influence on modern scientific thought. Alexander Kotelnikov advanced important arguments in favor of close relations of Lobachevsky's geometrical propositions to Einstein's general theory of relativity. Lobachevsky also received credit for a major contribution to modern axiomatics and for proving that entire sciences could be created by logical deductions from assumed propositions.

See also: academy of sciences

bibliography

Kagan, V. N. (1952). N. I. Lobachevsky and His Contributions to Science. Moscow: Foreign Languages Publishing House.

Vucinich, Alexander. (1962). "Nikolai Ivanovich Lobachevskii: The Man Behind the First Non-Euclidean Geometry." ISIS 53:465–481

Alexander Vucinich