Nicolai Lobachevsky was born in Russia. At seven he lost his father. Despite financial difficulties, he attended Kazan University, where he contacted professors from Germany, including Bartels, who had taught Gauss. This is due to his preference for the German and geometric currents, unlike his contemporary and also Russian rival Ostrogradsky, who followed French ideas and Cauchy's analysis. At 21, Lobachevskv became a professor at Kazan University where he was later appointed rector, a post he held until the end of his life.
In 1823, in an exposition, he said from Euclid's parallel postulate simply that no rigorous proof of its validity was ever discovered "and in 1826 presented some theorems about the new theory he advocated. In 1829 he published an article" On the Principles of Geometry. "which marks the birth of non-Euclidean geometry, being completely convinced that Euclid's fifth postulate cannot be proved on the basis of the other four.
He built this new geometry fully grounded in the hypothesis, contrary to Euclid's, that "From a point C out of a line AB one can draw more than one line on the plane that does not find AB," it seemed so contradictory to common sense that Lobachevsky himself called it "Imaginary Geometry." For this result they called him "Copernicus of Geometry", revolutionizing the subject and showing that Euclidean geometry was not the absolute truth assumed until then, and making it necessary to make a complete review of the fundamental concepts of mathematics.
In 1838 he published "New Foundations of Geometry" in Russian; In 1840 he published "Geometric Invertigations on the theory of para" in German and finally in 1855 he published his book "Pangeometry" in French and Russian. Lobachevsky never enjoyed a prominent position in society and was an enthusiastic advocate of popular liberal causes. In 1842 he was elected to the Gottingen Scientific Society, but his discoveries were only recognized very slowly and this was his greatest chagrin. The great mathematicians of the time, such as Gauss, taking note of his new theory, praised but lacked the courage to publish comment on it for fear of being ridiculed.