Nikolay I. Lobachevsky was born in 1792 in Nizhniy Novgorod. When the boy was nine years old his family moved to Kazan. There Nikolay entered a grammar school and began to study at public expense.
In 1807 at the age of 14 years Nikolay Lobachevsky became a student of the Kazan University, which had been founded two years earlier. Among the famous mathematicians, who had been teaching there at that time, there was professor Martin F. Bartels (Johann Martin Christian), a close acquaintance of Gauss. The university professors distinguished two students: 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 knowledgeable in mathematical sciences, Lobachevsky excels him, especially in subtle points". The dean of the University was sure that Lobachevsky was doomed to become a celebrity n future.
Lobachevsky’s career was evolving very swiftly and successfully. He was approved as an adjunct (assistant professor) in 1814 following the recommendation of Bartels, and in two years, at the age of 23, he was elected an extraordinary professor (corresponds to an associate professor). In 1822 Lobachevsky became an ordinary professor of the university.
The list of disciplines, he lectured on during the first 10-12 years of his pedagogical activity, covers 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, etc). One can see, that the young professor lectured not only on different fields of Mathematics, but also on Physics and Astronomy. He was a very diligent lecturer.
Once the instruction, approved by the Emperor Alexander I, was received by the Kazan University and it ran in the following wording: "A professor of the Theoretical and Experimental Physics must mention all the way through his lectures the God’s wisdom and a limited nature of our feelings and means for perceiving the miracles surrounding us". It is hard to believe, 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. In his lectures he used to tell students about the attempts to prove, that one can draw only one parallel straight line through the point located outside the straight line. Many famous mathematicians investigated the problem of the fifth postulate. However there had always been a lot of ambitious ignorant persons, who used to take up the problem for the only reason of its simple wording. Lobachevsky considered the task to be of special importance. He wrote, that "the problem of parallel lines was a difficult one, which hadn’t been solved yet; but it included beyond any doubt sensational truths so important for science, that they could not be overlooked".
Initially Lobachevsky approached the problem as many other mathematicians had done, i.e. he was looking for by reductio ad absurdum. In this way he deduced a lot of statements and some of them, putting it mildly, were rather strange, but he never succeeded in finding the contradiction he was looking for. In 1823 he came to the conclusion that the fifth postulate could not be proved and one could speak of a new geometry. What was even more important, Lobachevsky understood that the concept of 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 discovery of the new geometry and suggested it to a few university professors. He never received any response from his colleagues, and the work was lost soon.
In 1829 the "Kazansky Vestnik" magazine published Lobachevsky’s article, devoted to the non-Euclidean geometry. The famous academician M. V. Otrogradsky wrote in his review of the Lobachevsky’s work, that "the author seems to have set up his mind on writing in such a way, that nobody would understand him. He has achieved his objective: the greater part of the book remains as unknown for me, as if I have never set my eyes on it".
A genius is always well in advance of its time. The works proving that Lobachevsky’s geometry is as legitimate as the Euclidean one, and the discovery of it is an important step towards better understanding of the surrounding world, were published 30-40 years later. But in the 1820-ies Lobachevsky found himself in a very difficult situation. He was not understood and was even disapproved 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 had enough endurance to get through this trial with credit. The first large article was followed by new articles on the same subject. That was his major distinguishing feature from Gauss: another discoverer 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 the conclusion of non-Euclidean geometry legitimacy, but he had not published his results at all.
However Gauss made a great contribution to the only lifetime recognition of Lobachevsky. Nikolay I. Lobachevsky was elected a corresponding member of the Gettingen Scientific Society (Academy of Sciences) in 1842. The resolution and the diploma were signed by Gauss himself.
It is worth noting Lobachevsky’s response to Gauss: “I apologize, that I have been hesitating to answer for a long time; it has been due to the disastrous fire in the city; it has impaired my health… and burdened me with a lot of special official duties”. The scientist was informed about his nomination 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 combined really his mathematical talent and unusual passionate attitude to science with the elevated understanding of social duty.
At the age of 25-30 years Lobachevsky already headed the observatory and was dean of the mathematics faculty. For many years he was director of the university library. Understanding quite well the importance of the library for education, Lobachevsky used to go to St. Petersburg to select and buy books himself. As a chairman of the construction committee he directed the construction of new university buildings.
In 1827 Lobachevsky was elected 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 competently devoted himself to different activities: lecturing and scientific work, finances and construction. The periods of cholera epidemic of 1835 and the fire of 1842 mentioned above were the most difficult time for him.
In 1846 the authorities dismissed Lobachevsky from the rector’s position. His elder son died in January 1852. The family faced serious financial difficulties. Not long before his death, Nikolay Lobachevsky became blind. Being very weak and blind he dictated to his students his last work “Pangeomentry” (a Greek prefix "pan" means "all", "universal") timed to the 50-th jubilee of the Kazan University. Lobachevsky died in 1856.
In 1828 on the occasion of the first year of his rector’s activity Lobachevsky presented a speech titled "The Most Important Subjects of Education", which became quite famous later on. In particularly, he said: "The examples teach us better, than interpretations and books". The life of Nikolay Ivanovich Lobachevsky is a remarkable example of devotion to motherland and science.