Bolyai, Janos (1802-1860), a Hungarian mathematician, was one of the founders of the theory of non-Euclidean geometry. The system of logical rules established by the Greek mathematician Euclid in about 300 B.C. had been accepted as the only geometry for more than 2,000 years. Bolyai proved that other systems were possible.
Bolyai was born on Dec. 15, 1802, in Kolozsvar, Hungary (now Cluj-Napoca, Romania). From an early age, he received instruction from his father, Farkas Bolyai, also known as Wolfgang Bolyai, a distinguished mathematician. Janos studied at the Royal Engineering College in Vienna, Austria, from 1818 to 1822. He served in the army engineering corps from 1822 to 1833.
Farkas Bolyai had been examining the work of Euclid, in particular a statement known as Euclid’s fifth axiom or the parallel postulate. This postulate says that, given a straight line and a point not on that line, only one straight line can be drawn through the point, parallel to the given line. Farkas Bolyai attempted to prove that the parallel postulate was a logical consequence of Euclid’s other axioms. Janos Bolyai continued his father’s work but came to the conclusion that no such proof was possible. In 1820, he began to develop a system of geometry that did not include Euclid’s parallel postulate. He completed the work in 1823, but it was only published in 1832 as an appendix to a book by his father. Bolyai discovered that two other mathematicians, Carl Friedrich Gauss and Nikolai Ivanovich Lobachevsky, had independently been working on the same subject. Lobachevsky’s article “On the Principles of Geometry” was published in 1829. Bolyai’s work received little recognition, and non-Euclidean geometry did not gain importance until middle to late 1800’s. He died on Jan. 27, 1860.
See also Euclid ; Geometry (Rise of non-Euclidean geometry) ; Mathematics ( Geometry ).
