Nikolai Lobachevsky
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Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.
William Kingdon Clifford William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his ...
called Lobachevsky the "
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formula ...
of Geometry" due to the revolutionary character of his work.


Biography

Nikolai Lobachevsky was born either in or near the city of Nizhny Novgorod in the
Russian Empire The Russian Empire was an empire and the final period of the List of Russian monarchs, Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended th ...
(now in
Nizhny Novgorod Oblast Nizhny Novgorod Oblast (russian: link=no, Нижегородская область, ''Nizhegorodskaya oblast''), is a federal subject of Russia (an oblast). Its administrative center is the city of Nizhny Novgorod. It has a population of 3,31 ...
,
Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eigh ...
) in 1792 to parents of Russian and Polish origin – Ivan Maksimovich Lobachevsky and Praskovia Alexandrovna Lobachevskaya.Victor J. Katz. ''A history of mathematics: Introduction''. Addison-Wesley. 2009. p. 842. Stephen Hawking. ''God Created the Integers: The Mathematical Breakthroughs that Changed History''. Running Press. 2007. pp. 697–703. He was one of three children. When he was seven, his father, a clerk in a land-surveying office, died, and Nikolai moved with his mother to Kazan. Nikolai Lobachevsky attended
Kazan Gymnasium Kazan Gymnasium was a gymnasium of Kazan, Tatarstan, Russia. It is notable for its alumnus, Nikolai Ivanovich Lobachevsky, who graduated from the school in 1807. Other notable alumni include Ivan Shishkin, a Russian landscape artist, and Gavri ...
from 1802, graduating in 1807, and then received a scholarship to Kazan University, which had been founded just three years earlier in 1804. At Kazan University, Lobachevsky was influenced by professor Johann Christian Martin Bartels, a former teacher and friend of the German mathematician
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refe ...
(1777-1855). Lobachevsky received a Master of Science in physics and mathematics in 1811. In 1814 he became a lecturer at Kazan University, in 1816 he was promoted to associate professor. In 1822, at the age of 30, he became a full
professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professor ...
, teaching mathematics, physics, and astronomy. He served in many administrative positions and became the
rector Rector (Latin for the member of a vessel's crew who steers) may refer to: Style or title *Rector (ecclesiastical), a cleric who functions as an administrative leader in some Christian denominations *Rector (academia), a senior official in an edu ...
of Kazan University 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 in Arskoe Cemetery, Kazan. In 1811, in his student days, Lobachevsky was accused by a vengeful supervisor of atheism ( ru , признаки безбожия , translation = signs of godlessness ).


Career

Lobachevsky's main achievement is the development (independently from
János Bolyai János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consist ...
) of a non-Euclidean geometry, also referred to as Lobachevskian geometry. Before him, mathematicians were trying to deduce Euclid's
fifth postulate In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: ''If a line segment ...
from other
axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy o ...
s. Euclid's fifth is a rule in Euclidean geometry which states (in John 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 a
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
in which the fifth postulate was not true. This idea was first reported on February 23 (Feb. 11, O.S.), 1826 to the session of the department of physics and mathematics, and this research was printed as ''On the Origin of Geometry'' (''О началах геометрии'') in 1829–1830 (Kazan University Course Notes). In 1829 Lobachevsky wrote a paper about his ideas called "A Concise Outline of the Foundations of Geometry" that was published by the ''Kazan 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 as hyperbolic geometry. Lobachevsky replaced Playfair's axiom with the statement that for any given point there exists ''more 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 the angle of parallelism which depends on the distance the point is off the given line. In hyperbolic geometry the sum of angles in a hyperbolic triangle must be less than 180 degrees. Non-Euclidean geometry stimulated the development of differential 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. Lobachevsky's magnum opus ''Geometriya'' 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 of ''New Foundations of Geometry'' (1835–1838). He also wrote ''Geometrical Investigations on the Theory of Parallels'' (1840) and ''Pangeometry'' (1855). Another of Lobachevsky's achievements was developing a method for the
approximation An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix '' ...
of the roots of algebraic equations. This method is now known as the Dandelin–Gräffe method, named after two other mathematicians who discovered it independently. In Russia, it is called the Lobachevsky method. Lobachevsky gave the definition of a function as a correspondence between two sets of real numbers ( Peter Gustav Lejeune Dirichlet gave the same definition independently soon after Lobachevsky).


Impact

E. T. Bell Eric Temple Bell (7 February 1883 – 21 December 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Tain ...
wrote about Lobachevsky's influence on the following development of mathematics in his 1937 book '' Men of Mathematics'':
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.


Honors

* 1858 Lobachevskij, an asteroid discovered in 1972, was named in his honour. * The lunar crater Lobachevsky was named in his honor. * Lobachevsky Prize, a
mathematics award This list of mathematics awards is an index to articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the wor ...
by the Kazan State University. * The
Lobachevsky University The National Research State University of Nizhny Novgorod named after N.I. Lobachevsky, UNN (Russian: Нижегородский национа́льный иссле́довательский госуда́рственный университ ...
was named in his honor.


In popular culture

* Lobachevsky is the subject of songwriter/mathematician Tom Lehrer's humorous song " Lobachevsky" from his 1953 '' Songs 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 Research is "creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness t ...
". According to Lehrer, the song is "not intended as a slur on obachevsky'scharacter" and the name was chosen "solely for prosodic reasons".Liner notes, "The Tom Lehrer Collection", ''Shout!'' Factory, 2010 * In Poul Anderson's 1969
fantasy Fantasy is a genre of speculative fiction involving magical elements, typically set in a fictional universe and sometimes inspired by mythology and folklore. Its roots are in oral traditions, which then became fantasy literature and drama ...
novella "Operation Changeling" – which was later expanded into the novel '' Operation Chaos'' (1971) – a group of sorcerers navigate a non-Euclidean universe with the assistance of the ghosts of Lobachevsky and Bolyai. The story also contains the line, "Nikolai Ivanovich Lobachevsky is his name," possibly a nod to the Tom Lehrer song. *
Roger Zelazny Roger Joseph Zelazny (May 13, 1937 – June 14, 1995) was an American poet and writer of fantasy and science fiction short stories and novels, best known for '' The Chronicles of Amber''. He won the Nebula Award three times (out of 14 nom ...
's science fiction novel '' Doorways in the Sand'' contains a poem dedicated to Lobachevsky. * Morris Panych's Governor General's Award-winning play, '' Girl in the Goldfish Bowl'', references Lobachevsky repeatedly as the focus of Owen's geometry obsession. * Vladimir Nabokov mentions Lobachevsky in his Lectures on Russian Literature.


Works

* Kagan V. F. (ed.): ''N. I. Lobachevsky – Complete Collected Works'', Vol. I–IV (Russian), Moscow–Leningrad (GITTL), (1946–51). ** Vol. I: ''Geometrical Researches on the Theory of Parallels'' (1840); ''On the Origin of Geometry'' (1829–30). ** Vol. II: ''New Principles of Geometry with Complete Theory of Parallels'' (1835–38). ** Vol. III: ''Imaginary Geometry'' (1835); ''Application of imaginary geometry to certain integrals'' (1836); ''Pangeometry'' (1856). ** Vol. IV: ''Works on Other Subjects''. ;English translations: *
Geometrical Researches on the Theory of Parallels
'.
G. B. Halsted George Bruce Halsted (November 25, 1853 – March 16, 1922), usually cited as G. B. Halsted, was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and ...
(tr.). 1891. Reprinted in Roberto Bonola: ''Non-Euclidean Geometry: A Critical and Historical Study of its Development''. 1912. Dover reprint 1955. : Also in: Seth Braver ''Lobachevski illuminated'', MAA 2011. *
Pangeometry
'. translated by Henry P. Manning: in
D. E. Smith David Eugene Smith (January 21, 1860 – July 29, 1944) was an American mathematician, educator, and editor. Education and career David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cort ...
''A Source Book in Mathematics''. McGraw Hill 1929. Dover reprint, pp. 360–374. *
New Principles of Geometry with Complete Theory of Parallels
'. G. B. Halsted (tr.). 1897. * Nikolai I. Lobachevsky, ''Pangeometry'', translator and editor: A. Papadopoulos, Heritage of European Mathematics Series, Vol. 4, European Mathematical Society. 2010.


See also

* 1858 Lobachevskij *
Gauss–Bolyai–Lobachevsky space In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...
* Hyperbolic geometry * Hyperboloid structure * Non-Euclidean geometry *
Lobachevsky (crater) Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, k ...
*
Lobachevsky function In mathematics, the Clausen function, introduced by , is a transcendental, special function of a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other forms. It is intimately ...
*
Lobachevsky Medal The Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky. History The Lobachevsky Prize was establish ...
*
Lobachevsky University The National Research State University of Nizhny Novgorod named after N.I. Lobachevsky, UNN (Russian: Нижегородский национа́льный иссле́довательский госуда́рственный университ ...
* Upper half-plane


References


External links

* *
Website dedicated to Lobachevsky

Nikolaj Ivanovič Lobačevskij - Œuvres complètes, tome 2
– Gallica-Math
Lobachevsky State University of Nizhny Novgorod
{{DEFAULTSORT:Lobachevsky, Nikolai Ivanovich 1792 births 1856 deaths 19th-century mathematicians from the Russian Empire Mathematicians from Kazan Geometers Russian atheists Russian people of Polish descent Burials at Arskoe Cemetery Kazan Federal University faculty