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, structure, space, models, and change. History On ...
and
geometer A geometer is a mathematician whose area of study is geometry. Some notable geometers and their main fields of work, chronologically listed, are: 1000 BCE to 1 BCE * Baudhayana (fl. c. 800 BC) – Euclidean geometry, geometric algebra * ...
, known primarily for his work on
hyperbolic geometry 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 ...
, otherwise known as
Lobachevskian geometry 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'' ...
, and also for his fundamental study on
Dirichlet integrals In mathematics, there are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of the sinc function over the positive real line: : \int_0^\inf ...
, known as the
Lobachevsky integral formula In mathematics, Dirichlet integrals play an important role in distribution theory. We can see the Dirichlet integral in terms of distributions. One of those is the improper integral of the sinc function over the positive real line, : \int_0^\inf ...
. William Kingdon Clifford 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 formulated ...
of Geometry" due to the revolutionary character of his work.


Biography

Nikolai Lobachevsky was born either in or near the city of
Nizhny Novgorod Nizhny Novgorod ( ; rus, links=no, Нижний Новгород, a=Ru-Nizhny Novgorod.ogg, p=ˈnʲiʐnʲɪj ˈnovɡərət ), colloquially shortened to Nizhny, from the 13th to the 17th century Novgorod of the Lower Land, formerly known as Gork ...
in the
Russian Empire The Russian Empire was an empire and the final period of the 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 the Great Northern War. ...
(now in
Nizhny Novgorod Oblast Nizhny Novgorod Oblast (russian: link=no, Нижегородская область, ''Nizhegorodskaya oblast''), is a federal subjects of Russia, federal subject of Russia (an oblast). Its administrative center is the types of inhabited localiti ...
,
Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
) 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 Kazan ( ; rus, Казань, p=kɐˈzanʲ; tt-Cyrl, Казан, ''Qazan'', IPA: ɑzan is the capital and largest city of the Republic of Tatarstan in Russia. The city lies at the confluence of the Volga and the Kazanka rivers, covering a ...
. Nikolai Lobachevsky attended Kazan Gymnasium from 1802, graduating in 1807, and then received a scholarship to
Kazan University Kazan (Volga region) Federal University (russian: Казанский (Приволжский) федеральный университет, tt-Cyrl, Казан (Идел буе) федераль университеты) is a public research uni ...
, which had been founded just three years earlier in 1804. At Kazan University, Lobachevsky was influenced by professor
Johann Christian Martin Bartels Johann Christian Martin Bartels (12 August 1769 – ) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan. Biography Bartels was born in Brunswick, i ...
, 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 refer ...
(1777-1855). Lobachevsky received a
Master of Science A Master of Science ( la, Magisterii Scientiae; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to ...
in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
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 Academy, academic rank at university, universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who pr ...
, 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 Arskoe Cemetery is the central necropolis in Kazan, and is located in the city's Vakhitovsky City District, to the northeast of Kazan's centre in Tatarstan, Russia. The cemetery church was built in 1796, and was the only church in Kazan to rema ...
, Kazan. In 1811, in his student days, Lobachevsky was accused by a vengeful supervisor of
atheism Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no d ...
( 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 consisten ...
) of a
non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
, also referred to as Lobachevskian geometry. Before him, mathematicians were trying to deduce
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
's fifth postulate 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 or f ...
s. Euclid's fifth is a rule in Euclidean geometry which states (in
John Playfair John Playfair FRSE, FRS (10 March 1748 – 20 July 1819) was a Church of Scotland minister, remembered as a scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh. He is best known for his book ''Illu ...
'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 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 ...
. Lobachevsky replaced
Playfair's axiom In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): ''In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the ...
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 In hyperbolic geometry, the angle of parallelism \Pi(a) , is the angle at the non-right angle vertex of a right hyperbolic triangle having two asymptotic parallel sides. The angle depends on the segment length ''a'' between the right angle an ...
which depends on the distance the point is off the given line. In hyperbolic geometry the sum of angles in a
hyperbolic triangle In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called ''sides'' or ''edges'' and three points called ''angles'' or ''vertices''. Just as in the Euclidean case, three po ...
must be less than 180 degrees.
Non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
stimulated the development of
differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
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 equality (mathematics), equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very ...
of the
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...
s of
algebraic equation In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation'' ...
s. This method is now known as the
Dandelin–Gräffe method In mathematics, Graeffe's method or Dandelin–Lobachesky–Graeffe method is an algorithm for finding all of the roots of a polynomial. It was developed independently by Germinal Pierre Dandelin in 1826 and Lobachevsky in 1834. In 1837 K ...
, named after two other mathematicians who discovered it independently. In Russia, it is called the Lobachevsky method. Lobachevsky gave the definition of a
function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...
as a correspondence between two sets of real numbers (
Peter Gustav Lejeune Dirichlet Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and ...
gave the same definition independently soon after Lobachevsky).


Impact

E. T. Bell wrote about Lobachevsky's influence on the following development of mathematics in his 1937 book ''
Men of Mathematics ''Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré'' is a book on the history of mathematics published in 1937 by Scottish-born American mathematician and science fiction writer E. T. Bell (1883 ...
'':
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 1858 Lobachevskij (Minor planet provisional designation, ''prov. designation'': ) is a rare-type background asteroid from the central region of the asteroid belt, approximately 13 kilometers in diameter. It was discovered on 18 August 1972, by So ...
, an asteroid discovered in 1972, was named in his honour. * The lunar crater
Lobachevsky Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, kn ...
was named in his honor. *
Lobachevsky Prize 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 established ...
, a mathematics award by the
Kazan State University Kazan (Volga region) Federal University (russian: Казанский (Приволжский) федеральный университет, tt-Cyrl, Казан (Идел буе) федераль университеты) is a public research uni ...
. * The Lobachevsky University was named in his honor.


In popular culture

* Lobachevsky is the subject of songwriter/mathematician
Tom Lehrer Thomas Andrew Lehrer (; born April 9, 1928) is an American former musician, singer-songwriter, satirist, and mathematician, having lectured on mathematics and musical theater. He is best known for the pithy and humorous songs that he recorded in ...
's humorous song "
Lobachevsky Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, kn ...
" from his 1953 ''
Songs by Tom Lehrer ''Songs by Tom Lehrer'' is the debut album of musical satirist Tom Lehrer, released in 1953 on his own label, Lehrer Records. In 2004 it was included into the National Recording Registry. Production and release history ''Songs by Tom Lehrer'' was ...
'' 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 Plagiarism is the fraudulent representation of another person's language, thoughts, ideas, or expressions as one's own original work.From the 1995 '' Random House Compact Unabridged Dictionary'': use or close imitation of the language and thought ...
!"'', as long as one is always careful to "call it, please,
research Research is "creativity, 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 att ...
". According to Lehrer, the song is "not intended as a slur on obachevsky'scharacter" and the name was chosen "solely for
prosodic In linguistics, prosody () is concerned with elements of speech that are not individual phonetic segments (vowels and consonants) but are properties of syllables and larger units of speech, including linguistic functions such as intonation, st ...
reasons".Liner notes, "The Tom Lehrer Collection", ''Shout!'' Factory, 2010 * In
Poul Anderson Poul William Anderson (November 25, 1926 – July 31, 2001) was an American fantasy and science fiction author who was active from the 1940s until the 21st century. Anderson wrote also historical novels. His awards include seven Hugo Awards and ...
's 1969
fantasy Fantasy is a genre of speculative fiction involving Magic (supernatural), 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 ...
novella "Operation Changeling" – which was later expanded into the novel ''
Operation Chaos Operation CHAOS or Operation MHCHAOS was a Central Intelligence Agency domestic espionage project targeting the American people from 1967 to 1974, established by President Lyndon B. Johnson and expanded under President Richard Nixon, whose mission ...
'' (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 nomin ...
's science fiction novel ''
Doorways in the Sand ''Doorways in the Sand'' is a science fiction novel by American writer Roger Zelazny. Featuring both detective fiction and comic elements, it was originally published in serial form in the magazine ''Analog Science Fiction and Science Fact''; ...
'' contains a poem dedicated to Lobachevsky. *
Morris Panych Morris Stephen Panych (born 30 June 1952) is a Canadian playwright, director and actor. Early life Panych was born in Calgary, Alberta and grew up in Edmonton, Alberta. He studied at Northern Alberta Institute of Technology, and the Univers ...
's
Governor General's Award The Governor General's Awards are a collection of annual List of awards presented by the Governor General of Canada, awards presented by the Governor General of Canada, recognizing distinction in numerous academic, artistic, and social fields. Th ...
-winning play, ''
Girl in the Goldfish Bowl ''Girl in the Goldfish Bowl'' is a 2003 Governor General's Award-winning play by Canadian playwright Morris Panych. Set in Steveston, British Columbia in 1962, it tells the story of a young girl named Iris who believes that the world has been ...
'', references Lobachevsky repeatedly as the focus of Owen's geometry obsession. *
Vladimir Nabokov Vladimir Vladimirovich Nabokov (russian: link=no, Владимир Владимирович Набоков ; 2 July 1977), also known by the pen name Vladimir Sirin (), was a Russian-American novelist, poet, translator, and entomologist. Bo ...
mentions Lobachevsky in his
Lectures on Russian Literature A lecture (from Latin ''lēctūra'' “reading” ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical inform ...
.


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 (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 ''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 1858 Lobachevskij (Minor planet provisional designation, ''prov. designation'': ) is a rare-type background asteroid from the central region of the asteroid belt, approximately 13 kilometers in diameter. It was discovered on 18 August 1972, by So ...
*
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 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 ...
*
Hyperboloid structure Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the gro ...
*
Non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
* Lobachevsky (crater) * Lobachevsky function *
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 established ...
* Lobachevsky University *
Upper half-plane In mathematics, the upper half-plane, \,\mathcal\,, is the set of points in the Cartesian plane with > 0. Complex plane Mathematicians sometimes identify the Cartesian plane with the complex plane, and then the upper half-plane corresponds to ...


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