Farkas Bolyai | |
|---|---|
 Farkas Bolyai | |
| Born | (1775-02-09)9 February 1775 |
| Died | 20 November 1856(1856-11-20) (aged 81) |
| Alma mater | University of Jena University of Göttingen |
| Known for | Contributions to the foundations ofgeometry Wallace–Bolyai–Gerwien theorem |
| Scientific career | |
| Fields | Mathematics |
| Academic advisors | Abraham Gotthelf Kästner |
| Notable students | János Bolyai |
Farkas Bolyai (Hungarian:[ˈfɒrkɒʃˈboːjɒi]; 9 February 1775 – 20 November 1856; also known asWolfgang Bolyai in Germany) was aHungarianmathematician, mainly known for his work ingeometry.
Bolyai was born in Bólya, a village nearNagyszeben,Grand Principality of Transylvania,Kingdom of Hungary (nowBuia,Sibiu County,Romania). 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 theCalvinist school inNagyszeben. His teachers recognized his talents in arithmetics and in learning languages. He learnedLatin,Greek,Romanian,Hebrew and later alsoFrench,Italian andEnglish. He easily multiplied, divided 13- or 14-digit numbers in his head, and was able to draw square and cubic roots from them.[1] At the age of 12 he left school and was appointed as a tutor to the eight-year-old son of thecount 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 (todayCluj-Napoca) 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 atGerman universities first atJena and then atGöttingen. In these times Bolyai became a close friend ofCarl Friedrich Gauss.
He returned home to Kolozsvár in 1799. It was there he met and married Zsuzsanna Benkő and where their sonJános Bolyai – 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 (todayTârgu-Mureş), where he spent the rest of his life.
Bolyai's main interests were the foundations ofgeometry and theparallel 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),[2] was an attempt at a rigorous and systematic foundation of geometry, arithmetic, algebra and analysis. In this work, he gaveiterative procedures to solve equations which he then proved convergent by showing them to be monotonically increasing and bounded above. His study of theconvergence of series includes a test equivalent toRaabe's test, which he discovered independently and at about the same time asRaabe. Other important ideas in the work include a general definition of a function and a definition of an equality between twoplane figures if they can both be divided into a finite equal number of pairwisecongruent pieces.
He first dissuaded his son from the study ofnon-Euclidean geometry, 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 theTentamen.
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