(December 1, 1792 – February 24, 1856)

Nikolai Lobachevsky achieved fame through his groundbreaking development of Hyperbolic Geometry, which many people now referred to as Lobachevskian Geometry. William K. Clifford, who coined-up the term “Geometric Algebra”, dubbed Lobachevsky “the Copernicus of Geometry”. Carl Gauss and Janos Bolyai, both of whom rediscovered this non-Euclidean Geometry independently, had nothing but praises for the Russian genius. An impressed Gauss facilitated Lobachevsky’s election into Goettingen’s Science Academy (in 1842), and personally lauded him via mail. These extolments were well-deserved: given the magnitude of his revolution. Previously, mathematicians sought to deduce Euclid’s Fifth Postulate from other axioms/postulates. But Lobachevsky approached the problem differently: by devising a kind of geometry which invalidated that fifth postulate. He published the details in a treatise titled: A Concise Outline of the Foundations of Geometry. However, the revolutionary ideas in that publication made the arbiters of St. Petersburg Science Academy to reject it. Needless to stress that this rejected “stone” became one of the “cornerstones” of non-Euclidean Geometry. Like several of his Russian contemporaries, Lobachevsky’s career began with a master’s degree in Physics and Mathematics. He quickly made inroads in Algebraic Equations and Functional Analysis; and even came-up with the definition of Function before Peter Dirichlet did. His academic adviser (Johann Christian Bartels) was the same professor who nurtured Gauss, whereas his own notable students include Nikolai Brashman who founded Moscow’s Mathematical Society. Among his numerous publications are: Geometriya and Pangeometry. He is the eponym of both the Lobachevskiy lunar impact crater and the 1858 Lobachevskij asteroid.

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  2. Thank you for taking the time to write this interesting review. Lobachevsky is indeed “The Copernicus of Geometry”.

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