Farkas Bolyai (; 9 February 1775 – 20 November 1856; also known as Wolfgang Bolyai in Germany) was a
Hungarian 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 ...
, mainly known for his work in
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 ...
.
Biography
Bolyai was born in Bolya, a village near
Hermannstadt
Sibiu ( , , german: link=no, Hermannstadt , la, Cibinium, Transylvanian Saxon: ''Härmeschtat'', hu, Nagyszeben ) is a city in Romania, in the historical region of Transylvania. Located some north-west of Bucharest, the city straddles the Ci ...
,
Grand Principality of Transylvania
Grand may refer to:
People with the name
* Grand (surname)
* Grand L. Bush (born 1955), American actor
* Grand Mixer DXT, American turntablist
* Grand Puba (born 1966), American rapper
Places
* Grand, Oklahoma
* Grand, Vosges, village and co ...
(now
Buia,
Sibiu County
Sibiu County () is a county ( ro, județ) of Romania, in the historical region of Transylvania. Its county seat ( ro, reședință de județ) is the namesake town of Sibiu (german: Hermannstadt).
Name
In Hungarian, it is known as ''Szeben ...
,
Romania
Romania ( ; ro, România ) is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern, and Southeast Europe, Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, S ...
). His father was Gáspár Bolyai and his mother Krisztina Vajna. Farkas was taught at home by his father until the age of six when he was sent to the
Calvinist
Calvinism (also called the Reformed Tradition, Reformed Protestantism, Reformed Christianity, or simply Reformed) is a major branch of Protestantism that follows the theological tradition and forms of Christian practice set down by John Ca ...
school in
Nagyszeben
Sibiu ( , , german: link=no, Hermannstadt , la, Cibinium, Transylvanian Saxon: ''Härmeschtat'', hu, Nagyszeben ) is a city in Romania, in the historical region of Transylvania. Located some north-west of Bucharest, the city straddles the Ci ...
. His teachers recognized his talents in arithmetics and in learning languages. He learned
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
,
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
,
Romanian
Romanian may refer to:
*anything of, from, or related to the country and nation of Romania
**Romanians, an ethnic group
**Romanian language, a Romance language
*** Romanian dialects, variants of the Romanian language
** Romanian cuisine, tradition ...
,
Hebrew
Hebrew (; ; ) is a Northwest Semitic language of the Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, the Jews and Samaritans. It was largely preserved ...
and later also
French,
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
and
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
. He easily multiplied, divided 13- or 14-digit numbers in his head, and was able to draw square and cubic roots from them. At the age of 12 he left school and was appointed as a tutor to the eight-year-old son of the
count
Count (feminine: countess) is a historical title of nobility in certain European countries, varying in relative status, generally of middling rank in the hierarchy of nobility. Pine, L. G. ''Titles: How the King Became His Majesty''. New York: ...
Kemény. This meant that Bolyai was now treated as a member of one of the leading families in the country, and he became not only a tutor but a real friend to the count's son. In 1790 Bolyai and his pupil both entered the Calvinist College in Kolozsvár (today
Cluj-Napoca
; hu, kincses város)
, official_name=Cluj-Napoca
, native_name=
, image_skyline=
, subdivision_type1 = Counties of Romania, County
, subdivision_name1 = Cluj County
, subdivision_type2 = Subdivisions of Romania, Status
, subdivision_name2 ...
) where they spent five years.
The professor of philosophy at the College in Kolozsvár tried to turn Bolyai against mathematics and towards religious philosophy. Bolyai, however, decided to go abroad with Simon Kemény on an educational trip in 1796 and began to study mathematics systematically at
German
German(s) may refer to:
* Germany (of or related to)
** Germania (historical use)
* Germans, citizens of Germany, people of German ancestry, or native speakers of the German language
** For citizens of Germany, see also German nationality law
**Ge ...
universities first at
Jena
Jena () is a German city and the second largest city in Thuringia. Together with the nearby cities of Erfurt and Weimar, it forms the central metropolitan area of Thuringia with approximately 500,000 inhabitants, while the city itself has a popu ...
and then at
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
. In these times Bolyai became a close friend of
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 ...
.
He returned home to Kolozsvár in 1799. It was there he met and married Zsuzsanna Benkő and where their son
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 ...
– later an even more famous mathematician than his father – was born in 1802. Soon thereafter he accepted a teaching position for mathematics and sciences at the Calvinist College in Marosvásárhely (today
Târgu-Mureş), where he spent the rest of his life.
Mathematical work
Bolyai's main interests were the foundations of
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 ...
and the
parallel axiom.
His main work, ''Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi'' (''An Attempt to Introduce Studious Youths to the Elements of Pure Mathematics''; 1832),
Online version
/ref> was an attempt at a rigorous and systematic foundation of geometry, arithmetic, algebra and analysis. In this work, he gave iterative
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
procedures to solve equations which he then proved convergent by showing them to be monotonically increasing and bounded above. His study of the convergence
Convergence may refer to:
Arts and media Literature
*''Convergence'' (book series), edited by Ruth Nanda Anshen
*Convergence (comics), "Convergence" (comics), two separate story lines published by DC Comics:
**A four-part crossover storyline that ...
of series includes a test equivalent to Raabe's test, which he discovered independently and at about the same time as Raabe. Other important ideas in the work include a general definition of a function and a definition of an equality between two plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* ''Planes' ...
figures if they can both be divided into a finite equal number of pairwise congruent
Congruence may refer to:
Mathematics
* Congruence (geometry), being the same size and shape
* Congruence or congruence relation, in abstract algebra, an equivalence relation on an algebraic structure that is compatible with the structure
* In mod ...
pieces.
He first dissuaded his son from the study of 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 ...
, but by 1832 he became enthusiastic enough to persuade his son to publish his path-breaking thoughts. János's ideas were published an appendix to the ''Tentamen''.
Notes
References
* A. Todea, F. Maria, M. Avram, ''Oameni de știință mureșeni - Dicționar biobibliografic'', CJ Mureș Biblioteca Județeană Mureș, tipografia Mediaprint SRL, 2004
External links
*
*
*
Further references on Farkas Bolyai
*
The Bolyai Memorial Museum
{{DEFAULTSORT:Bolyai, Farkas
1775 births
1856 deaths
18th-century Hungarian mathematicians
19th-century Hungarian mathematicians
People from Sibiu County
Hungarian Calvinist and Reformed Christians
Hungarian inventors
Members of the Hungarian Academy of Sciences