# The two Bolyais

The University was named after two famous scholars: Farkas and János Bolyai.

# Farkas Bolyai (1775-1856)

He was an important mathematician of his age. He was born in Bolya and went to school to the old and renowned Reformat College in Aiud/Nagyenyed from age six. He already excelled with his unusual linguistic and arithmetic skills. At age 17 or 18 he was already fluently speaking, writing and reading in seven languages. He continued his studies in the Reformat College in Kolozsvár/Cluj, and after that went to a study trip abroad for a longer period of time during which he met and became friends with Gauss in Göttinga. After returning to Transylvania, he began to teach first in Kolozsvár/Cluj and then in Marosvásárhely/Targu Mures. In 1804 he became professor of mathematics, physics and chemistry at the Reformat College in Marosváráshely/Targu Mures. In addition he also wrote dramas, poetry and a variety of studies. His most significant work in mathematics, Tentamen was published in 1832 which is both a collection of his scientific papers and a handbook. The appendix to Tentamen contained, in fact, Appendix, a paper of his son, János Bolyai.

# János Bolyai (1802-1860)

He was born in Kolozsvár/Cluj. He is one of the creators of the non-Euclidean geometry. This theory, which revolutionized geometry, was developed at the beginning of the 19th century by three mathematicians working separately: Bolyai, Lobacevski and Gauss. Bolyai summarized his results in wiring first in 1823. The so-called parallelism axiom in the Euclidean geometry states that given a plane containing a line and a point, there is one and only one line which passes trough the given external point and is not intersecting the given line. János Bolyai began to work on this problem in 1820, and in 1823 he wrote to his father that “Starting from nothing, I have created a whole new world.” János Bolyai, like Lobacevski or Gauss, independently from him, replaced this axiom with its negation: given a plane with a line l and a point P, there are several lines passing point P that are not intersecting with line l. During their studies, they revealed that this replacement is not conducive to contradiction. And thus, with this modified system of axioms, a new geometry was born.

*Authentic graphic, no pictures have survived of János Bolyai.*.