**Farkas Bolyai** was a mathematics teacher, best known as the father of János Bolyai.

- When Farkas was born Nagyszeben was the military centre of Transylvania and the capital of the region.
- 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 to Simon but a close friend.
- In 1790 Bolyai and his pupil both entered the Calvinist College in Kolozsvár where they spent five years.
- The time spent in Kolozsvár was important for Bolyai's development.
- This meant that Bolyai was presented with its fundamental idea that reason was the route to understanding the universe and to improving the position of man.
- There was an increasing resentment against the Habsburgs, particularly from the workers, and Bolyai too felt support for Hungarian culture, language, and nationality.
- The professor of philosophy at the College in Kolozsvár was an impressive person, and he tried to turn Bolyai against mathematics and towards religious philosophy.
- Bolyai on the other hand had wide ranging interests, science, mathematics, and literature all interested him and in 1795 after leaving the College he spent a few weeks considering a career as an actor.
- First they reached Jena where Bolyai for the first time began to study mathematics systematically.
- After six months in Jena Bolyai and Kemény went to Göttingen.
- This was the time when one could say that Bolyai really became a mathematician.
- Bolyai taught mathematics, physics and chemistry at Marosvásárhely for the rest of his life.
- Life was not easy for Bolyai in Marosvásárhely.
- Mathematics, the subject which Farkas Bolyai loved, was relegated to something to do for relaxation.
- Through all these difficult years Bolyai was working on the Tentamen, his mathematical masterpiece published in 1832.
- All his life Bolyai was interested in the foundations of geometry and the parallel axiom.
- The Tentamen is built on Bolyai's belief that mathematics consists of arithmetic and geometry with arithmetic as the mathematics of time and geometry as the mathematics of space.
- The problem which had perplexed Bolyai most in his study of mathematics had been the independence of Euclid's Fifth postulate.
- There are other ideas in the Tentamen which show the quality of Bolyai as a mathematician.
- At first Farkas Bolyai was not enthusiastic but certainly by 1830 he had become enthusiastic for at this stage he persuaded János to write up his discoveries.
- Bolyai retired from his teaching in 1851 and after a number of strokes, died five years later.

Born 9 February 1775, Bolya (near Nagyszeben), Transylvania, Hungary (now Sibiu, Romania). Died 20 November 1856, Marosvásárhely, Transylvania, Hungary (now Târgu-Mureș, Romania).

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Geometry, Origin Romania

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive