János Bolyai (
December 15,
1802 –
January 27,
1860) was a
Hungarian mathematician, known for his work in
non-Euclidean geometry.Bolyai was born in
Kolozsvár,
Transylvania (today
Cluj-Napoca,
Romania), the son of a well-known mathematician,
Farkas Bolyai. By the age of 13, he had mastered
calculus and other forms of
analytical mechanics, receiving instruction from his father. He studied at the Royal Engineering College in
Vienna from
1818 to
1822. He became so obsessed with
Euclid's
parallel postulate that his father wrote to him: "For God's sake, I beseech you, give it up. Fear it no less than sensual passions because it too may take all your time and deprive you of your health, peace of mind and happiness in life". János, however, persisted in his quest and eventually came to the conclusion that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on its negation. He wrote to his father: "Out of nothing I have created a strange new universe". Between
1820 and
1823 he prepared a treatise on a complete system of
non-Euclidean geometry. Bolyai's work was published in
1832 as an appendix to a mathematics textbook by his father.
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