Bolyai, Janos

Category: Genius

The following has been extracted from Wikipedia and the biography of the University of Saint Andrews.

János Bolyai (15 December 1802 – 27 January 1860) was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.

Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.

... when he was four he could distinguish certain geometrical figures, knew about the sine function, and could identify the best known constellations. By the time he was five [he] had learnt, practically by himself, to read. He was well above the average at learning languages and music. At the age of seven he took up playing the violin and made such good progress that he was soon playing difficult concert pieces.

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: "I created a new, different world out of nothing.”

Portrait by Márkos Ferenc

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.

Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order". In 1848 Bolyai discovered that Lobachevsky had published a similar piece of work in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained only hyperbolic geometry. Bolyai and Lobachevsky did not know each other or each other's works.

In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died. These can now be found in the Bolyai–Teleki library in Târgu Mureş, where Bolyai died.

Bolyai was also a genius in other areas.  He was an accomplished polyglot speaking nine foreign languages, including Chinese and Tibetan. And he could play the violin well enough to perform in Vienna.

No original portrait of Bolyai survives. An unauthentic picture appears in some encyclopedias and on a Hungarian postage stamp.  The one I have included is that used by Wikipedia.

References

Observations

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• Bolyai, Janos - Geometrical Examinations and Theorem 35