Nikolai Lobachevsky was born either in or near the city ofNizhny Novgorod in theRussian Empire (now inNizhny Novgorod Oblast,Russia) in 1792 to parents of Russian andPolish origin – Ivan Maksimovich Lobachevsky and Praskovia Alexandrovna Lobachevskaya.[12][13][h] He was one of three children. When he was seven, his father, a clerk in aland-surveying office, died, and Nikolai moved with his mother toKazan. Nikolai Lobachevsky attendedKazan Gymnasium from 1802, graduating in 1807, and then received a scholarship toKazan University,[12][13] which had been founded just three years earlier in 1804.
At Kazan University, Lobachevsky was influenced by professorJohann Christian Martin Bartels, a former teacher and friend of the German mathematicianCarl Friedrich Gauss (1777–1855).[12] Lobachevsky received aMaster of Science inphysics and mathematics in 1811. In 1814, he became a lecturer at Kazan University, and in 1816, he was promoted to associate professor. In 1822, at the age of 30, he became a fullprofessor,[12][13] teaching mathematics, physics, and astronomy.[13] He served in many administrative positions and became therector of Kazan University[12] in 1827. In 1832, he married Varvara Alexeyevna Moiseyeva. They had a large number of children (eighteen according to his son's memoirs, though only seven apparently survived into adulthood). He was dismissed from the university in 1846, ostensibly due to his deteriorating health: by the early 1850s, he was nearly blind and unable to walk. He died in poverty in 1856 and was buried inArskoe Cemetery, Kazan.
In 1811, in his student days, Lobachevsky was accused by a vengeful supervisor ofatheism(Russian:признаки безбожия,lit. 'signs of godlessness').[15][16][17][18]
Lobachevsky's main achievement is the development (independently fromJános Bolyai) of anon-Euclidean geometry,[13] also referred to as Lobachevskian geometry. Before him, mathematicians were trying to deduceEuclid'sfifth postulate from otheraxioms. Euclid's fifth is a rule in Euclidean geometry which states (inJohn Playfair's reformulation) that for any given line and point not on the line, there is only one line through the point not intersecting the given line. Lobachevsky would instead develop ageometry in which the fifth postulate was not true. This idea was first reported on 23 [O.S. 1826] February to the session of the department of physics and mathematics, and this research was printed in the periodical 'Kazan University Course Notes' asOn the Origin of Geometry (О началах геометрии) between 1829 and 1830. In 1829, Lobachevsky wrote a paper about his ideas called "A Concise Outline of the Foundations of Geometry" that was published by theKazan Messenger but was rejected when it was submitted to the St. Petersburg Academy of Sciences for publication.
The non-Euclidean geometry that Lobachevsky developed is referred to ashyperbolic geometry. Lobachevsky replacedPlayfair's axiom with the statement that for any given point there existsmore than one line that can be extended through that point and run parallel to another line of which that point is not part. He developed theangle of parallelism which depends on the distance the point is off the given line. In hyperbolic geometry the sum of angles in ahyperbolic triangle must be less than 180 degrees.Non-Euclidean geometry stimulated the development ofdifferential geometry which has many applications. Hyperbolic geometry is frequently referred to as "Lobachevskian geometry" or "Bolyai–Lobachevskian geometry".
Some mathematicians and historians have wrongly claimed that Lobachevsky in his studies in non-Euclidean geometry was influenced by Gauss, which is untrue. Gauss himself appreciated Lobachevsky's published works highly, but they never had personal correspondence between them prior to the publication. Although three people—Gauss, Lobachevsky and Bolyai—can be credited with discovery of hyperbolic geometry, Gauss never published his ideas, and Lobachevsky was the first to present his views to the world mathematical community.[19]
Lobachevsky's magnum opusGeometriya was completed in 1823, but was not published in its exact original form until 1909, long after he had died. Lobachevsky was also the author ofNew Foundations of Geometry (1835–1838). He also wroteGeometrical Investigations on the Theory of Parallels (1840)[20] andPangeometry (1855).[21][i]
Another of Lobachevsky's achievements was developing a method for theapproximation of theroots ofalgebraic equations. This method is now known as theDandelin–Gräffe method, named after two other mathematicians who discovered it independently. In Russia, it is called the Lobachevsky method. Lobachevsky gave the definition of afunction as a correspondence between two sets of real numbers (Peter Gustav Lejeune Dirichlet gave the same definition independently soon after Lobachevsky).
E. T. Bell wrote about Lobachevsky's influence on the following development of mathematics in his 1937 bookMen of Mathematics:[23]
The boldness of his challenge and its successful outcome have inspired mathematicians and scientists in general to challenge other "axioms" or accepted "truths", for example the "law" of causality which, for centuries, have seemed as necessary to straight thinking as Euclid's postulate appeared until Lobachevsky discarded it. The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry, for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
Russian1 rouble coin commemorating the 200th anniversary of Lobachevsky's birth, 1992.
Stamp of 1956 marking the centenary of Lobachevsky's death
Lobachevsky is the subject of songwriter/mathematicianTom Lehrer's humorous song "Lobachevsky" from his 1953Songs by Tom Lehrer album. In the song, Lehrer portrays a Russian mathematician who sings about how Lobachevsky influenced him: "And who made me a big success / and brought me wealth and fame? / Nikolai Ivanovich Lobachevsky is his name." Lobachevsky's secret to mathematical success is given as "Plagiarize!", as long as one is always careful to "call it, please,research". According to Lehrer, the song is "not intended as a slur on [Lobachevsky's] character" and the name was chosen "solely forprosodic reasons".[24] The song was based onDanny Kaye andSylvia Fine's monologue onStanislavsky and the secret of success in the acting profession.
In the sitcom3rd Rock from the Sun, "Dick and the Single Girl" (season 2 episode 24) originally aired on May 11 1997, Sonja Umdahl (Christine Baranski),[25] a forgotten colleague who is transferring to teach at another university, gives as the reason behind her departure that Columbia is the only holder of Nikolai Lobachevsky's manuscripts.[26]
Nikolai I. Lobachevsky,Pangeometry, translator and editor: A. Papadopoulos, Heritage of European Mathematics Series, Vol. 4, European Mathematical Society. 2010, 310 p.
^This is the date given by Kagan (1957)[3] and Andronov (1956)[4] (the latter gives 1 December [O.S. 20 November] 1792).
^Older sources in Russian—e.g., Popov (1857)[5]—give 1793 rather than 1792, while theDictionary of Scientific Biography (1970) gives December 2, 1792. Further information on Lobachevsky's birthdate can be found in Papadopoulos (2010)[6] However, note that page 207 incorrectly converts 1792-11-20 to 1792-12-02 instead of 1792-12-01
^spelledMakaryev, notMakaryevo, at that time; nominative form in Russian:Макарьев.
^This is a quote from G. B. Halsted's translator's preface to his 1914 translation ofThe Theory of Parallels: "WhatVesalius was toGalen, whatCopernicus was toPtolemy that was Lobachevsky toEuclid." —W. K. Clifford
^Ivan Maksimovich Lobachevsky (Jan Łobaczewski in Polish) came from a Polish noble family of theJastrzębiec andŁada coats-of-arms, and was classified as a Pole in Russian official documents[14]
^Lobachevsky dictated two versions of that work, a first one in Russian, and a second one in French.[22]
^V. F. Kagan,N. Lobachevsky and His Contribution to Science, 1957 (first published in Russian in 1943), p. 26
^A. A. Andronov, "Где и когда родился Н.И.Лобачевский" ("Where and when was Lobachevsky born?"), 1956
^A. F. Popov, "Воспоминания о службе и трудах проф. Казанского университета Н. И. Лобачевского" ("Memoirs of the Service and Work of N. I. Lobachevsky"), 1857
^Bardi, Jason (2008).The Fifth Postulate: How Unraveling a Two Thousand Year Old Mystery Unraveled the Universe. John Wiley & Sons. p. 186.ISBN978-0-470-46736-7.His stubbornness, reported atheism, and genius supported his rise as a champion of the proletariat. To the Soviets, Lobachevsky represented not just the greatness of the common man, emerging from a humble background as he did, he also was a revolutionary of sorts.
^"The History of Science".Soviet Science. Taylor & Francis. p. 329.Though Lobachevsky appears to have invented non-Euclidean geometry without the help of the Almighty, he built a church on the instructions of the University council. It is said that he was an atheist.
^Kramer, Edna E. (1982) [1970]. "Mathematical Reasoning from Eudoxus to Lobachevsky".The Nature and Growth of Modern Mathematics (corrected reprint ed.). Princeton: Princeton University Press. pp. 56–57.ISBN9780691023724. Retrieved18 August 2022.It was [Kondyrev's] responsibility to supervise the students and to report their conduct to the principal. Kondyrev avenged himself by submitting very bad reports on Lobachevsky, even to the extent of accusing him of atheism, a charge which was not at all justified but which might have had tragic consequences for Lobachevsky.
^The 1914 English translation by George Bruce Halsted is available at"Quod.lib.umich.edu". The University of Michigan Historical Mathematics Collection. Retrieved2012-12-17.
^The 1902 German translation byHeinrich Liebmann is available at"Quod.lib.umich.edu". The University of Michigan Historical Mathematics Collection. Retrieved2012-12-17.
