B bábi, Tibor

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Bolyai, János (John) (Kolozsvár, now Cluj-Napoca, Romania, 15 December 1802 - Marosvásárhely, now Targu Mures, Romania, 17 January 1860) – Son of Farkas (Wolfgang) Bolyai, one of the most original mathematicians in history. His father directed his early education. His extraordinary capabilities became evident already in childhood. He studied at the Reformed College of Marosvásárhely at the age of 12, and by the age of 15 he completed his studies. In 1818, with the aid of his father’s friends, he enrolled at the Academy of Military Engineering of Vienna where, at an early stage, he showed signs of extraordinary talent in mathematics and music. In 1823 he moved first to Temesvár (now Timişoara, Romania), then to Arad. While in Arad he suffered a bout of malaria and during his transfer to Lemberg (now Lviv, Ukraine), he contracted cholera. When he reached Olmütz, he suffered a concussion and was forced into retirement due to his poor health. In Marosvásárhely, as a result of his badly impaired nervous condition, he had some unfortunate altercation with his family, and as a result, moved to the small family estate at Domald, where he occupied himself with farm work. In his solitude at Domald, besides dealing with mathematical problems, he also formulated his philosophical views. Already at an earlier stage in his life he invented the basic idea of his geometrical theory; and on 3 November 1823, in a letter to his father, he wrote: “From nothingness I created a new, different world” (“Semmiből egy új, más világot teremtettem”). He boldly rejected the Euclidean Parallel Axiom based on a new, parallel axiom, in which he first outlined the hyperbolic geometry; then he elaborated the theory. This theory is connected to the general theory of relativity. The great significance of his work was not understood or appreciated by his contemporaries. In 1832 his world-famous work was added to his father’s published work Tentamen... as an Appendix. Its title is Scientiam Spatii (The Science of Space). On 18 May 1849 he legally married Rozália Orbán; but on the return of the Habsburg power, his marriage was annulled because it was performed without the permission of the Imperial Cabinet. The collapse of the War of Independence in 1849, family problems and continual ill health was not easy on him. However, he was working on his utopian sociological Doctrine of Salvation (Üdvtan). In his mathematical study, The Science of Space (A tér tudománya), he succeeded to get as far as the realization of the inner connection between the physical gravitational field and the geometric field, as he wrote: “...the gravitational force appears to be intimately and continuously connected with the product, reality and character of space”. Tibor Toró, professor of physics (1931-2010) wrote a 1000-word essay on this single quotation, thereby proving that Bolyai, with his recognition, determined the basis for the general theory of relativity prior to Albert Einstein. The Bolyai theory of non-Euclidean geometry is closely connected with the general theory of relativity in physics. According to the newest statistics, he was one of the ten greatest mathematicians of the world. – B: 0883, 1257, T: 7456.→Bolyai, Farkas; Toró, Tibor (1).

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