On
December 15, 1802 at 9 in the night he was born in Kolozsvár (today Cluj).
His native house at the corner of Tivoli Street and Belső Közép Street (later
Deák Ferenc Street, today Hősök Avenue / Bld. Eroilor) has been marked with a
memorial plaque since 1903.
His genealogical tree is more or less known from the 13th
century on. According to family traditions, the Bolyais were landowners of
importance between the 14th and 16th centuries. A number of them have been
remembered as brave soldiers, but not all of them had a fortunate life. One
Gáspár Bolyai was executed in captivity by the voivod of Wallachia in 1599, and
one János Bolyai spent ten years in Turkish prison in the first half of the 17th
century.
Beginning with the 17th century the family gradually
impoverished, and even the Bolyai castle fell in the hand of strangers. The
grandfather of János, Gáspár Bolyai only had a small estate near to the village
of Bolya, which was complemented by the heritage of his wife Krisztina Pávai
Vajna, another estate near to Domáld in the county of Kis-Küküllő.
His father, the mathematician, writer and educationalist Farkas
Bolyai (1775–1856), corresponding member of the Hungarian Academy of Sciences
(1832) held his inaugural speech on May 4, 184 in the Calvinist College of
Marosvásárhely (Târgu Mureş), where he taught mathematics, physics and chemistry
between 1840 and 1851. He was also concerned in playwriting, translating,
medicine, music, painting, forestry,
and
he also took up the planning and producing of energy-saving chimneys. His main
work is the mathematical Tentamen whose
first volume was published in 1832, the second in 1833. His mathematical oeuvre
focused on the attempt to demonstrate the 5th postulate of Euclid. It was later
his son János to point out that the 5th postulate could not be demonstrated from
the rest of the axioms of Euclid. The research of Farkas Bolyai is nevertheless
very important because of his recastings of the postulate. He also made
remarkable achievements in the research of the theory of sets, the convergence
of infinite series and the finite equivalences of territories. János’ mother, Zsuzsanna Benkő of Árkos (between 1778 and 1780
[?] - 1821) was the ninth, youngest son of the surgeon József Benkő and Julianna
Bachmann. In February 1805 was born Anna, the sister of János, who
died before December 18, 1807.
Between 1806–1814: János at the age of five already knew several stars, and could draw some constellations by memory. At the age of six he started to read almost by himself. One year later he began to learn to play on violin, and at the same time he started to learn German. He began his regular studies at the age of nine, but his father at this time did not send him to the College yet, but the senior students came to their home to teach him. In mathematics he was instructed by his father.
In 1814 János became an ordinary student of the Calvinist College of Marosvásárhely. He was admitted to the 4th class.
On April 10, 1816 Farkas Bolyai asked for the approval of his university friend Carl Friedrich Gauss to send János to him at the university of Göttingen. In his opinion at the universities of Pest and Vienna the level of the mathematical courses was not high enough to seriously evolve the talents of János. In his letter he characterized his son like this: “…as he reached his ninth year he could not even do addition yet. […] I started with Euclid, then he got to know Euler. By now he completely knows the first two volumes of Vega (which I use in my courses), and he is also well versed in the third and fourth volumes. He loves differential and integral calculus, and does them with an extraordinary ability and ease. […] He perceives much and quickly, and he often has highly gifted intellectual glances.” Gauss did not reply to this letter.
At the end of 1816 Farkas thought to send his son to a military officer’s career, and János also agreed with the idea.
On July 30, 1817 János passed his final exam in the Calvinist College of Marosvásárhely as the first of his year.
On August 24, 1818 he passed a successful exam of admission at the Imperial and Royal Academy of Engineering, founded in 1717. As the sixth one on the order of results, he was directly passed to the 4th class, the highest level one could reach by exam. (The academic studies embraced eight years, and thus he only had to count with four years of schooling.) His studies were supported among others by Count Miklós Kemény, the main guardian of the College of Marosvásárhely, and Count Ádám Kendeffy.
On August 24, 1818 he passed a successful exam of admission at the Imperial and Royal Academy of Engineering, founded in 1717. As the sixth one on the order of results, he was directly passed to the 4th class, the highest level one could reach by exam. (The academic studies embraced eight years, and thus he only had to count with four years of schooling.) His studies were supported among others by Count Miklós Kemény, the main guardian of the College of Marosvásárhely, and Count Ádám Kendeffy.
Before April 1820, probably in the academic year of 1819–1820 Archduke Johann – the younger brother of Emperor Franz I, and the chief director of the Academy – on an official visit took notice of the mathematical talent of the younger Bolyai, and as the supervisor of the engineering corps he did not forget about him later.
In the spring of 1820 he informed his father about his experiences concerning parallels. Farkas in a long letter warned his son against this: “…don’t go any step further, or else you’re a lost person.”
On September 18, 1821 his mother died.
On September 6, 1822 he completed the last semester of the Academy with excellent certificate, as the second best student of his year. (The order of excellence of the students was established by the professors and the students in common, and although the professors considered János as the best, the vote of the students was decisive.) The two best students, thus also János were kept at the Academy for one more year as “Ingenieur-Corps Cadets” for supplementary studies, especially important for military architects. Their subjects were: the second part of fortification, architecture, plans of fortification and architecture, German writing and French.
Around April 25, 1828 he went back to the place of his service in Arad.
From the second half of 1828 he was often ill, due to contagious malary which caused regular intermittent fever.
In October 1828 he was commanded to go from Arad to Nagyvárad (Oradea) and to complete there the survey of the fortifications by the next military year of 1829.
On the spring of 1829 he made several surveys for the renovation of the fortifications of Szeged and Nagyvárad.
From December 8, 1830 he was appointed the chief engineer of the directorship of fortification of Lemberg (Lvóv), but he occupied his post of service only six months later.
From the beginning of December 1830 until May 1831 he spent his holiday in Marosvásárhely, which was decisive in the preparation of his Appendix, as his father insisted on his putting it on paper.
Some weeks after his departure from Marosvásárhely, on July 13, 1831 his father wrote in a letter to Lajos Jakab on the space theory of János: “It is an original great work that will be appreciated everywhere; no similar work on mathematics has been written by any Hungarian author…”
During this time they decided that the work of János will be included in the first volume of the Tentamen as an Appendix. On the way to his new place of service, in Beszterce (Bistriţa) János was infected with cholera.
On May 15, 1831 he arrived to Lemberg healed, but not completely healthy, and started his service.
