Nikolay I. Lobachevsky was born in 1792 in Nizhniy Novgorod. When he was nine years old, the family moved to Kazan. There Nikolay entered gymnasia and began to study at public expense.

In 1807 the 14-year-old Nikolay Lobachevsky became a student of the Kazan University, which had been founded two years earlier. Among famous mathematicians, who had been teaching there at that time, was professor Martin F. Bartels (Johann Martin Christian), the acquaintance of Gauss. The university lecturers distinguished two students of the year, Ivan Simonov, who became a professor of Kazan University later on, and Nikolay Lobachevsky.  The dean’s report, dated 1812, runs as follows: “Although Simonov is keen on mathematical sciences, Lobachevsky excelled him, especially in delicate questions”. The dean of the University was sure that Lobachevsky wouldn’t be unknown in future.

Lobachevsky’s career was swift and successful. In 1814, recommended by Bartels, he was confirmed as an adjunct (assistant professor) and in two years, at the age of 23, was elected an extraordinary professor (associate professor). In 1822 Lobachevsky became an ordinary professor of the university.

The list of disciplines, he lectured during the first 10-12 years of his pedagogical activity, enumerates more than a dozen subjects. It includes Gauss Theory of Numbers, Plane and Spherical Trigonometry, Analytical and Descriptive Geometry, Astronomy, Differential and Integral Calculus (Physics, Statics and Dynamics and so on). One can see, that the young professor lectured not only on different spheres of Mathematics, but also on Physics and Astronomy. He was a very diligent lecturer.

The instruction, approved by the Emperor Alexander I, which was received by Kazan University, ran as follows, that “A professor of Theoretical and Experimental Physics must mention the God’s wisdom and limited nature of our feelings and means for knowing the miracles surrounding us all the time, during the whole course”. It could be hardly possible, that Lobachevsky, who lectured on “Theoretical and Practical Physics” at that time followed this instruction. By that moment (since 1817) he had been already working on one of the most difficult problems, the proof for the fifth Euclid postulate on parallel straight lines. During his lectures he told students about the attempts to prove, that one can draw only one parallel straight line beyond the straight line. Many famous mathematicians studied the problem of the fifth postulate. But there had always been a lot of ambitious ignorant people, who took up the problem only for the reason of its simple wording. Lobachevsky considered the task to be of special importance. He wrote, that the problem of parallel lines is a difficult one, which hasn’t been solved yet; but including sensation truths and  being so important for science, it can no be avoided, beyond any doubt”.

At first Lobachevsky behaved as many other mathematicians, namely seeking for the rule of contraries. Thus, he deduced a lot of statements, some of them were, kindly speaking, rather strange, but the contradiction, being sought for, wasn’t found. In 1823 he came to conclusion that the fifth postulate can not be proved and one could speak of new geometry. More over, Lobachevsky understood that this “imaginary” geometry couldn’t be disproved by our experience in principle despite its unusual content.

In February 1826 Lobachevsky wrote the first work on the new geometry and suggested it to a few university professors. His colleagues didn’t response, and soon the work was lost.

In 1829 the “Kazansky Vestnik” magazine published Lobachevsky’s article, devoted to the non-Euclidean geometry. A famous academician M. V. Otrogradsky wrote in his review to Lobachevsky’s work, that “the author seems to have a goal of writing in such way, that one can’t understand him. He achieved his object. The major part of the book remains as unknown for me, as if I had never seen it”.

Genius always goes ahead of its time. The works, which prove that Lobachevsky’s geometry is as rightful as the non-Euclidean one, and the discovery of it is an important step towards the understanding of the surrounding world, came to light in 30-40 years. But in the 1820th Lobachevsky found himself in a very difficult situation. He was not understood and even blamed by the best mathematicians of that time; colleagues mocked him, writing offensive reviews to his work. It was a severe trial for the scientist’s character. Lobachevsky stood the test with credit. New articles on the same subject followed the first work. That was the way he differed from Gauss, the other founder of the non-Euclidean geometry. The “king of mathematicians” had been working on the theory of parallel lines for about 30 years and came to conclusion of non-Euclidean geometry rightfulness, but hadn’t published his results.  

However Gauss made a great contribution to the only lifetime recognition of Lobachevsky. In 1842 Nikolay I. Lobachevsky was elected a correspondence member Göttingen Scientific Society (Academy of Sciences). The resolution and the diploma were signed by Gauss himself.

One should pay attention to Lobachevsky’s response to Gauss: “I’m sorry, that I have been hesitating to answer for a long time; ill-fated fire of the city is responsible for that; it ruined my health… and burdened me with a lot of special official duties”. The scientist is informed about his being elected as a member of the most authoritative scientific society, and he had no time to write an answer because of the fire in the city. The letter reveals another side of Lobachevsky’s personality. He really combined mathematical talent and unusual passion for science with high idea of social duty.

At the age of 25-30 Lobachevsky headed the observatory and was the dean of mathematics faculty. For many years he was the director of the university library. Understanding quite well, how important the library is for education, Lobachevsky used to go to Petersburg to choose and buy books himself. As the chairman of the construction committee he directed the construction of new university buildings.

In 1827 Lobachevsky was elected the rector of the Kazan University. Later on he was re-elected six times, heading the university for twenty years. As the rector he energetically and with competence devoted himself to different activities: lecturing and scientific work, finances and construction. The period of cholera epidemic of 1835 and the fire of 1842 mentioned above was the most difficult time for him.

In 1846 the government dismissed Lobachevsky from the rector’s post. In January 1852 his elder son died. The family faced serious financial difficulties. Not long before his death, Nikolay Lobachevsky became blind. Being very weak, he dictated his last work “Pangeomentry” (the Greek prefix “pan” means “all”, “universal”), timed to the 50th jubilee of the Kazan University, he dictated to his students. Lobachevsky died in 1856.

In 1828 on occasion of the first year of his rector’s activity Lobachevsky made a speech titled “The Most Important Subjects of Education”, which became well-known later on. In particularly, he said: “The examples teach us better, than explanations and books”. The life of Nikolay Ivanovich Lobachevsky is a remarkable example of devotion to motherland and science.