Janos Bolyai is the greatest figure of Hungarian science; many think he is the Copernicus of geometry. In his 26-page work published in 1831 and generally referred to as the Appendix, (which was published as an appendix to Vol. 1 of Tentamen, the two-volume monumental monograph of his father, Farkas Bolyai) he made a revolutionary achievement by the creation of the so-called non-Euclidean geometry. With this work Janos Bolyai broke the monopoly of Euclidean geometry and paved the way for humanity to think about space in a different fashion. Through his findings in axiomatic thinking Bolyai considerably formed the history of mathematics as a whole. The development of modern mathematics in the 19th and 20th centuries can, to a large extent, be attributed to Janos Bolyai's discovery. However, the importance of his results was recognized only after his death but even then not without resistance. In his lifetime almost no one understood his brilliant ideas, which matured in him by the time he was 21. He presented them with the revolutionary bravery of youth, having no fears for the criticism of the scientific community. Naturally, he exhibited a great degree of naivete, because he thought that great discoveries, including his, would lead to recognition and fame. But the only individual who understood Bolyai's ideas, Gauss, 'the prince of mathematicians', was unfair to Janos Bolyai when he formed his opinion of the Appendix in 1832. He wrote in his letter to Farkas Bolyai that he was unable to praise Janos's work because in so doing he would be praising himself. Gauss reasoned that Janos Bolyai's way of thinking and results coincided almost entirely with the ideas he had been developing for the last thirty-five years. After Gauss's death in 1855, no written proof of the aforementioned statement was found. Gauss behaved reprehensibly on yet another occasion. When he learned that the Russian Lobachevskii, whose election to be a foreign corresponding member of the Royal Society of Gottingen (arranged in 1842), made the same discovery as Janos Bolyai, he failed to inform Lobachevskii that there was another person who had achieved almost the same results. For many years scientists thought that although after his retirement in 1833 Janos Bolyai produced some work including an important theory on the foundation of complex numbers, the lack of recognition pushed him into a state of depression and he renounced creative mathematical research. It was Elemer Kiss, Professor at Marosvasarhely (now Targu Mures) who refuted this misconception, Having consulted Bolyai's manuscripts he found significant mathematical 'gems' in them that were new at their birth. The scientists discovered Janos Bolyai's greatness first abroad and it was recognized in Hungary later. His work became widely known on the European Continent by the turn of the 19th and 20th centuries. Also, in the Anglo-Saxon countries there were some who knew his work and were enthusiastic about it but they were fewer than those on the Continent. After World War II the world became bipolar. The Russians did not mention Janos Bolyai much but emphasized the merits of Lobachevskii. In the USA - as has been mentioned above - our scholar was less known. The year 1977 when the 200th anniversary of Gauss's birth was celebrated all over the world became a turning-point. Although Gauss had always been regarded as the primary discoverer of non-Euclidean geometry by the authors of numerous studies, this tendency became stronger, pushing even Lobachevskii into the background. Russian authors have managed to contest these opinions in the interest of Lobachevskii. We, Hungarians, have the duty to show the rest of the world where Janos Bolyai's place is in the history of mathematics and universal culture. Therefore, the relevant documents and research results should be presented to the world.
