Farkas Bolyai (1775-1856), was born in Bolya, near Nagyenyed (Hungary) on 9 February 1775. His family had a long historical past; some members were remembered as fighters against the Turks, other active participants in Transylvanian politics; however, they became impoverished. And so his father, Gáspár Bolyai, owned only a small estate in Bolya, and his mother, Kristina Pávai Vajua, had also inherited a small farm in Marosvásárhely. Until he was 6 years old, Farkas was taught by his father, somehow a scholar, and then entered the famous Calvinist school in Nagyenyed.
His exceptional talent, which first manifested itself in language learning and numerical calculation, was matched by his application to study and quickly distinguished him from his colleagues. At the age of 12, he went to the estate of Baron Kemény and became tutor of little Simon Kemény, 4 years younger than him; A cultured family helped him in his development and young Simon became his close friend. In 1970, they were both studying at the Kologsvár Calvinist School. A philosophy teacher tried to entice him into religious fanaticism, strongly warning him not to engage in mathematics. On the other hand, the math teacher worked diligently and enthusiastically with Farkas; but his professional knowledge was light and shallow, hardly able to counteract the influence of the philosophy teacher. For a few weeks Farkas also tried his acting career, but in the fall of 1795 he decided, together with Simon, to travel abroad on a study tour which turned out to be a turning point in his career.
The trip due to unforeseen and somewhat long illness was postponed and they could not leave for Jena until the following spring. The few months that Farkas had been ill in Jena were of crucial importance to his future because it was then that he began to devote himself to mathematics systematically and entirely. The illness had prevented him from excessive reading but had not inhibited him from thinking about the axioms of mathematics in his long and lonely walks. The next stay of the two friends went to Gottingen, where they arrived in September 1796. Both enrolled at the University which provided them with an opportunity to study within the framework of established education.
F. Bolyai's specialization in mathematics was determined by the years at Gottingen; He made many friends and made scientific contacts with many people, including Seyffer (1762-1822), Kastner (1719-1800). Carl Friedrich Gauss was also attending this university, and F. Bolyai was particularly impressed by the friendly talks and discussions with him. Then a mathematical system began to take shape in his thinking, and it must have been those conversations that drove later to deal with Euclid's 5th postulate. But Gauss and F. Bolyai went their separate ways; while the 1st received recognition of his work from the outset and financial independence and ideal conditions to continue, the 2nd experienced financial distress. Mr Bolyai remained a year in Gottingen, in a very precarious situation, almost surviving charity, but he always remembered this period with great affection, as he had the opportunity to absorb knowledge and exchange opinions with people who understood and appreciated his ideas; later that year, one of his defending professor sent him enough money to pay his debts and he could return to his home in Marosvásárhely on foot in 1799. He then took a seat in the new Department of Mathematics. Physics and Chemistry, in college; but at low pay, it forced him to look for other sources of income. Almost completely isolated at his Marosvásárhely retreat, however, he tried to develop his mathematical system; In 1832/33, he published "TENTAMEN", the result of much meditation by a scientist who could not rely on anything but a couple of books; It contains a great deal of material in various fields of mathematics, with diverse mathematical knowledge accumulated from the beginning to the last century.