Janos Bolyai

Janos Bolyai was born in his grandparents’ home in Kolozsvar, Hungary (now Cluj, Romania) on December 15, 1802. Janos was the son on Farkas Bolyai and Zsuzsanna Benko. Being a teacher of mathematics, physics, and chemistry at the Calvinist College, Farkas Bolyai always had the expectations that his son would be a mathematician himself. Even though is was obvious from early on that Janos was extremely talented and bright, education was not of utmost importance during his early years. Farkas believed that great academic things could only come from an individual with a sound, healthy body, and so in the early years most attention was paid to Janos’ physical development.

Growing up in a poor household, despite his father’s strong work ethic, Janos did not have many education opportunities. Until the age of nine, he was taught all the usual school subjects by the best students from the Marosvasarhely College students. The only subject that they did not teach him was mathematics, which he learned from his father. At the age of nine, Janos was finally able to attend school. Within only a few years he had mastered calculus and other forms of math. He progressed very quickly in school taking senior level classes well before his years.

After Janos Bolyai’s graduation from Marosvasarhely College in June of 1817, he was not sure of where he would go to pursue his mathematical education. He had been rejected by Carl Friedrich Gauss to be his pupil, neither of the universities in the area offered a quality mathematics program, and his father could not afford to send him to any school abroad. With no other option left, Janos decided to enroll at the Academy of Engineering at Vienna to study military engineering. Janos excelled in all areas of mathematics that he studied and completed the seven year course in four years. After completing his course work, Janos entered the military as a sublieutenant of the army engineering corps. He spent 11 years in the military service.

During his military service, Janos Bolyai continued to pursue his passion for understanding and discovering mathematics. Like his father, Farkas, Janos began studying the parallel axioms and tried to find a replacement for Euclid’s Fifth Postulate. Within a couple of years, Janos had given up on this path when he realized that “Out of nothing I have created a strange new universe.” This new universe was what we now call non-Euclidean “hyperbolic” geometry.

In 1932, after pressure from his father, Janos published his work on non-Euclidean geometry as a twenty-six page appendix to Farkas’ two-volume semi-philosophical work on elementary mathematics. The publication contained his own definitions of ‘parallel’ and showed that if the Fifth Postulate held in one region of space it held throughout, and vice versa. The three geometries he expressed are today called, Euclidean, hyperbolic, and absolute. For the most part he dealt with absolute geometry in the appendix.

When the Appendix was published, by June of 1831, Janos Bolyai did not receive the recognition nor acclaim he deserved for his discovery of non-Euclidean geometry. In fact, Gauss wrote to Farkas,

To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupies my mind for the past thirty or thirty-five years.

These remarks greatly depressed Janos, and he lived the rest of his life as a very different and difficult individual. Throughout the rest of his life he continued to study and develop mathematical theories including a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Janos had come to write more than 20,000 pages of manuscript, but after his first awful experience decided not to publish anything further.

Janos Bolyai lived most of his adult life isolated from the rest of the world, thinking that he had made no significant contributions to the mathematical world. When he died on January 27, 1860 in Marosvasarhely, Hungary (now Tirgu-Mures, Romania), Janos Bolyai was not a famous mathematician. It was not until after his death that other foreign mathematicians became interested in his work. After several years of studying his Appendix, the world began to realize that Janos Bolyai was an illustrious Hungarian mathematician who was one of the creators of non-Euclidean geometry, the other creator being Nicolai Lobachevsky. In 1891, the Janos Bolyai Mathematics Society was established, and in 1903 the Hungarian Academy of Sciences established the Bolyai Prize to be awarded every five years the mathematician whose work in the previous 25 years had given most to the progress of mathematics. Like many other famous individuals the life and work of Janos Bolyai was not appreciated and accepted until his death, but all that he accomplished was a major breakthrough for mathematics today.

Further Links about Janos Bolyai:

http://www.conferences.hu/Bolyai/

http://library.thinkquest.org/22584/temh3019.htm

Books about Janos Bolyai:

Janos Bolyai, Euclid, and the Nature of Space