(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 Friedrich Gauss and Janos Bolyai, both of whom discovered this type of non-Euclidean Geometry independently and shortly after Lobachevsky did, had nothing but praises for the Russian genius. These extolments were well-deserved: given the magnitude of his geometric revolution. Previously, mathematicians sought to deduce Euclid’s Fifth Postulate from other axioms (or postulates). But Lobachevsky approached the problem differently: by devising a kind of geometry which rendered that fifth postulate invalid. 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 Academy of Sciences to reject it. Needless to say that this rejected “stone” is now one of the “cornerstones” of non-Euclidean Geometry. Like many mathematicians of his era, Nikolai Lobachevsky researched physics and astronomy early in his career. He made inroads in Algebraic Equations and Functional Analysis; and even came-up with the definition of a Function before Peter Dirichlet did. His doctoral advisor was Johann Christian Bartels: the same professor who nurtured Carl Gauss. His own notable students include Nikolai Brashman, who later founded the Moscow Mathematical Society. Among his many publications are: Geometrical Investigations on the Theory of Parallels, Pangeometry, and his flagship: Geometriya. The asteroid, 1858 Lobachevskij, is dedicated to his honor.


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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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