Bolyai …

• János Bolyai lived in Hungary (now Romania) from 1802 to 1860.
• His father Farkas Bolyai asked Gauss if his son could study mathematics with him - but Gauss said no.
• He mastered Calculus by the age of 13 and wrote over 20,000 pages of mathematics in his life.
• Instead, he took a 7 year college curriculum in 4 years, played a violin at concert level, and learned 9 languages includung Chinese and Tibetan.
• He followed in his father's footsteps trying to replace Euclid's 5th Postulate about Parallel Lines. He stopped this effort in 1820, however, because he had a fresh new idea.
• He began a totally new Geomtery of his own, called Hyperbolic Geometry. Instead of the same Euclicean Geometry people had studied for over 2,000 years, Bolyai said he had, "... created a new, another world out of nothing..." .