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The Precursor of the Hyperbolic Geometry Passes Away.

On 24 February 1856, the great Russian mathematician Nikolai Lobachevsky died in Kazan, Russia, at the age of 63. This prominent Russian mathematician, among many nicknames, is known as the father of non-Euclidean geometry and as the precursor of hyperbolic geometry, which speaks volumes about his great work and immeasurable contributions to the field of mathematics. He devoted his entire life to the University of Kazan where he was an outstanding professor and researcher, even becoming the rector of the University of Kazan for at least nineteen years, of which it is important to mention that he was admitted for the first time at the precocious age of 14 years old.

Lobachevsky was one of the first mathematicians to give a critical treatment to the postulates established in Euclidean geometry, supposing that the fifth postulate of Euclidean geometry, for example, does not depend on other propositions of this geometry, thus managing to structure a new logically non-contradictory geometric system, in which the fifth postulate says: through a point that is outside the straight line can be traced not one but, at least, two parallel lines.

In terms of his philosophical positions, it can be stated with a high degree of confidence that Lobachevsky subscribed to a materialist worldview. This is evident in numerous mathematical works and in his pedagogical approach to mathematics, where he persistently sought to ascertain the tangible nature of the concepts upon which scientific inquiry is founded. As he articulated, "The fundamental data", he asserted, "will invariably be, without contention, the notions we apprehend from nature through our sensory faculties".

His two major works were: On the Principles of Geometry (1829) & New Principles of Geometry with a Complete Theory of Parallels (1835-38). He also proved several conjectures related to the tensor calculus applied to vectors in Hilbert space.

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Some of his Greatest Contributions

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Portrait Image Source

Note: All the images related to Lobachevsky Contributions are crafted by me using the text editor based on LaTeX: Beamer.

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References

Jolany, Hassan (2018). "An extension of Lobachevsky formula". Elemente der Mathematik. 73 (3): 89–94. arXiv:1004.2653. doi:10.4171/EM/358.

Hardy, G. H. (1909). The Mathematical Gazette. 5 (80): 98–103. doi:10.2307/3602798. JSTOR 3602798.

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