Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (
N.S.The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
); November 20, 1792 – February 12, 1856 (
O.S.The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
)) was a
RussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n
mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and geometer, renowned primarily for his pioneering works on
hyperbolic geometryIn mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
, otherwise known as Lobachevskian geometry.
William Kingdon CliffordWilliam Kingdon Clifford FRS 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 honour, with interesting applications in contemporary mathematical physics...
called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work.
Life
Lobachevsky was born in
Nizhny NovgorodNizhny Novgorod , colloquially shortened to Nizhny, is, with the population of 1,250,615, the fifth largest city in Russia, ranking after Moscow, St. Petersburg, Novosibirsk, and Yekaterinburg...
,
RussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
in 1792. His parents were Ivan Maksimovich Lobachevsky, a clerk in a
landsurveyingSee Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...
office, and Praskovia Alexandrovna Lobachevskaya. In 1800, his father died, and his mother moved to
KazanKazan is the capital and largest city of the Republic of Tatarstan, Russia. With a population of 1,143,546 , it is the eighth most populous city in Russia. Kazan lies at the confluence of the Volga and Kazanka Rivers in European Russia. In April 2009, the Russian Patent Office granted Kazan the...
. In Kazan, Lobachevsky attended
Kazan GymnasiumKazan 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....
, graduating in 1807 and then
Kazan University, which was founded just three years earlier in 1804.
At Kazan University, Lobachevsky was influenced by professor
Johann Christian Martin BartelsJohann Christian Martin Bartels 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 :...
(1769–1833), a former teacher and friend of German mathematician
Carl Friedrich GaussJohann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
. Lobachevsky received a
Master's degreeA master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...
in
physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and mathematics in 1811. In 1814, he became a lecturer at Kazan University, and, in 1822, he became a full
professorA professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
, teaching mathematics, physics, and astronomy. He served in many administrative positions and became the
rectorThe word rector has a number of different meanings; it is widely used to refer to an academic, religious or political administrator...
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, while 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.
Career
Lobachevsky's main achievement is the development (independently from
János BolyaiJános Bolyai was a Hungarian mathematician, known for his work in non-Euclidean geometry.Bolyai was born in the Transylvanian town of Kolozsvár , then part of the Habsburg Empire , the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.-Life:By the age of 13, he had mastered...
) of a
non-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
, also referred to as Lobachevskian geometry. Before him, mathematicians were trying to deduce
EuclidEuclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
's fifth postulate from other
axiomIn traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s. Euclid's fifth is a rule in Euclidean geometry which states (in
John PlayfairJohn Playfair FRSE, FRS was a Scottish scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh. He is perhaps best known for his book Illustrations of the Huttonian Theory of the Earth , which summarized the work of James Hutton...
's reformulation) that for any given line and point not on the line, there is one parallel line through the point not intersecting the line. Lobachevsky would instead develop a
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
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 in the UMA
(Вестник Казанского университета) in 1829–1830. Lobachevsky wrote a paper about it 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 geometryIn mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
. Lobachevsky replaced Euclid's parallel postulate with the one stating that there is more than one line that can be extended through any given point parallel to another line of which that point is not part; a famous consequence is that the sum of angles in a triangle must be less than 180 degrees.
Non-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
is now in common use in many areas of mathematics and physics, such as
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
; and hyperbolic geometry is now often referred to as "Lobachevskian geometry" or "Bolyai-Lobachevskian geometry".
Some mathematicians and historians have wrongfully claimed that Lobachevsky in his studies in non-Euclidean geometry was influenced by Gauss, which is untrue - Gauss himself appreciated Lobachevsky's published works very highly, but they never had personal correspondence between them prior to the publication. In fact out of the three people that can be credited with discovery of hyperbolic geometry - Gauss, Lobachevsky and Bolyai, Lobachevsky rightfully deserves having his name attached to it, since Gauss never published his ideas and out of the latter two Lobachevsky was the first who duly presented 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
approximationAn approximation is a representation of something that is not exact, but still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.Approximations may be used because...
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
functionIn mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
as a correspondence between two sets of real numbers (
DirichletJohann Peter Gustav Lejeune Dirichlet was a German mathematician with deep contributions to number theory , as well as to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a...
gave the same definition independently soon after Lobachevsky).
Impact
E.T.BellEric Temple Bell , was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life...
in his book
Men of MathematicsMen of Mathematics is a book on the history of mathematics written in 1937 by the mathematician E.T. Bell. After a brief chapter on three ancient mathematicians, the remainder of the book is devoted to the lives of about forty mathematicians who worked in the seventeenth, eighteenth and nineteenth...
wrote about Lobachevsky's influence on the following development 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 till Lobatchewsky discarded it.
The full impact of the Lobatchewskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobatchewsky 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.
Works
- Kagan V.F.(ed.): N.I.Lobachevsky - Complete Collected Works, Vols I-IV (Russian), Moscow-Leningrad (GITTL) 1946-51
- Vol.I Geometrical investigations on the theory of parallel lines; On the foundations of geometry (1829-30).
- Vol.II New foundations of geometry with a 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 investigations on the theory of parallel lines. Halstead G.N.(tr) 1891. Reprinted in Bonola: NonEuclidean Geometry 1912, Dover reprint 1955.
- Pangeometry. D.E. Smith: Source Book of Mathematics. McGraw Hill. Dover reprint
- Nikolai I. Lobachevsky, Pangeometry, Translator and Editor: A. Papadopoulos, Heritage of European Mathematics Series, Vol. 4, European Mathematical Society, 2010.
In popular culture
- Lobachevsky is the subject of songwriter/mathematician Tom Lehrer
Thomas Andrew "Tom" Lehrer is an American singer-songwriter, satirist, pianist, mathematician and polymath. He has lectured on mathematics and musical theater...
's humorous song "Lobachevsky" from his Songs by Tom Lehrer-Production and release history:Songs by Tom Lehrer was recorded in a single one hour session on January 22, 1953 at the TransRadio studio in Boston for the total studio cost of $15. The first pressing was an issue of 400 copies, produced at Lehrer's own expense in the 10" LP record format. Records...
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 "researchResearch can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
". According to Lehrer, the song is "not intended as a slur on [Lobachevsky's] character" and the name was chosen "solely for prosodic reasons".
- In Poul Anderson
Poul William Anderson was an American science fiction author who began his career during one of the Golden Ages of the genre and continued to write and remain popular into the 21st century. Anderson also authored several works of fantasy, historical novels, and a prodigious number of short stories...
's 1969 fantasyFantasy is a genre of fiction that commonly uses magic and other supernatural phenomena as a primary element of plot, theme, or setting. Many works within the genre take place in imaginary worlds where magic is common...
novella "Operation Changeling" – which was later expanded into the fix-upA fix-up is a novel created from short stories that may or may not have been initially related or previously published. The stories may be edited for consistency, and sometimes new connecting material—such as a frame story—is written for the new novel. The term was coined by the science fiction...
novel Operation Chaos (1971) – a group of sorcerers navigate a non-Euclidean universe with the assistance of the ghosts of Lobachevsky and Bolyai.
- Roger Zelazny
Roger Joseph Zelazny was an American writer of fantasy and science fiction short stories and novels, best known for his The Chronicles of Amber series...
's science fiction novel Doorways in the SandDoorways in the Sand is a Nebula- and Hugo-nominated science fiction novel with mystery and comic elements by Roger Zelazny. It was originally published in serial form in the magazine Analog Science Fiction and Science Fact; the hardcover edition was first published in 1976 and the paperback in...
contains a poem dedicated to Lobachevsky.
- 1858 Lobachevsk
1858 Lobachevsk is a Main-belt asteroid that was discovered August 18, 1972, by L. V. Zhuravleva. The asteroid was named in honor of mathematician Nikolai Lobachevsky...
, an asteroid discovered in 1972, was named in his honour.
See also
- Hyperbolic geometry
In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...
- Hyperboloid structure
Hyperboloid structures are architectural structures designed with hyperboloid geometry. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, but hyperboloid geometry is also often used for decorative...
- Gauss-Bolyai-Lobachevsky space
- Upper half-plane
- Lobachevsky function
- Lobachevsky (crater)
- 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:...
- Lobachevsky University
- 1858 Lobachevsk
1858 Lobachevsk is a Main-belt asteroid that was discovered August 18, 1972, by L. V. Zhuravleva. The asteroid was named in honor of mathematician Nikolai Lobachevsky...
External links