János Bolyai (1802-1860) is the greatest Hungarian mathematician who after recognizing the impossibility to prove Euclid's fifth (the so called parallel) postulate from Euclid's others, developed the absolute geometry (maybe the first non-Euclidian geometry) that is independent of the fifth postulate. He was only 21 years old when in 1823 he reported his finding to his father, Farkas Bolyai: "I ... [Show full abstract] have created a new, different world out of nothing." His discovery was published in 1832 as an appendix to his father's book Tentamen, so generally reffered to as Appendix. For more than hundred years his mathematical activity was identified with the Appendix, but he was not only a geometer. He also developed in the unpublished Responsio a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Although he never published more than the 26-page Appendix, mainly because he was unable to gain recognition for his work, he left more than 14000 pages of manuscript of mathematical work when he died. Recently these have been thoroughly researched by Elemér Kiss with surprising success: mathematical gems have been found, mainly results in number theory and algebra which were new in Bolyai's time.