However, at the university, Lobachevsky was unable to attend Kartashevsky's lectures, as the latter was removed from his position in December 1806 by the director I.F. Yakovkin for having shown a spirit of disobedience and dissent. The mathematics courses were then taught by M.F. Bartels, who arrived in Kazan in 1808.

Lobachevsky's successes as a student, competing in his studies with I.P. Simonov, who later became a well-known astronomer and participant in a circumnavigation, consistently drew the approval of M.F. Bartels and other professors.

On August 3, 1811, Lobachevsky was established as a master. His supervisor, Professor M.F. Bartels, was a qualified mathematician and experienced teacher, but he did not engage in creative work. Under his supervision, Lobachevsky studied classical works on mathematics and mechanics: Gauss's "Theory of Numbers" (Disquisitiones Arithmeticae) and the first volumes of Laplace's "Celestial Mechanics". Having presented two scientific studies on mechanics and algebra ("The Theory of Elliptic Motion of Celestial Bodies" (1812) and "On the Solvability of the Algebraic Equation xn - 1 = 0" (1813)), he was promoted to adjunct professor (docent) ahead of schedule in 1814.

From the following year, he began independent teaching, gradually expanding the range of courses he offered and already contemplating a restructuring of the foundations of mathematics. Another year later, he received the title of professor extraordinarius.

However, a very challenging atmosphere for work soon developed at the university. In order to combat revolutionary sentiments and "free-thinking," the government of Alexander I adopted an increasingly reactionary policy, seeking ideological support in religion and mystico-Christian teachings. Universities were the first to undergo scrutiny.

In March 1819, a member of the Main Board of Schools, M. L. Magnitsky, was appointed to inspect Kazan University and he used his appointment for careerist purposes. In his report, he concluded that the university "causes public harm through the half-education of its students..." and therefore "should be destroyed in the form of its public demolition" as a cautionary example for other governments.

However, the university was not destroyed. Alexander I decided to reform it. Magnitsky became the Curator of the Kazan educational district and began an energetic "renewal of the university." His activities began with the dismissal of nine professors. Close surveillance of the content of lectures and student notes was established, and a strict barracks regime was introduced for students.

Seven years of this church-police system brought severe trials to Lobachevsky, but did not break his indomitable spirit. He managed to withstand this oppression through his extensive and diverse pedagogical, administrative, and research activities. He taught mathematics in all courses instead of Bartels, who had moved to Dorpat (Tartu); he filled in for Professor K. Bronner, who did not return to Kazan after his leave; he taught physics courses and managed the physics laboratory; he replaced astronomer I. P. Simonov, who went on a round-the-world voyage, and took charge of astronomy and geodesy, overseeing the observatory. For several years, he served as the dean of the physical-mathematical department. He dedicated colossal effort to organizing the library and expanding its physical and mathematical section. Simultaneously, he became one of the most active members, and later the chairman, of the construction committee responsible for building the university's main building. Finally, despite the thousands of ongoing tasks and responsibilities, Lobachevsky continued his intense creative work. He authored two textbooks for gymnasiums: "Geometry" (1823) and "Algebra" (1825). "Geometry" received negative feedback from academician N. I. Fuss, who did not appreciate the changes Lobachevsky made to traditional presentations and condemned the introduction of the metric system of measurements, as it originated in revolutionary France. "Algebra" also remained unpublished due to internal delays at the university.

Soon, conflicts began with the Curator. According to Magnitsky, Lobachevsky displayed audacity and violations of instructions. Magnitsky decided to impose special supervision over his actions.

Lobachevsky's discovery was made through a principled critical revision of the most fundamental geometric concepts accepted since the time of Euclid (3rd century BC). This requirement for absolute rigor and clarity in foundational principles, along with a keen focus on the questions of the foundations of science and a deep analysis of initial concepts, characterizes Lobachevsky's work overall. His chosen direction of research enabled him not only to surpass the contemporary level of science in geometry but also in several other areas of mathematics: for instance, he clarified the concept of a function, later attributed to Dirichlet; he distinguished clearly between the continuity of a function and its differentiability; he conducted profound research on trigonometric series that was decades ahead of his time; and he developed a method for numerically solving equations that unjustly received the name of the Greffe method later on, despite both Lobachevsky and the Belgian mathematician Dandelin having developed it much earlier.

Lobachevsky's report coincided with Magnitsky's downfall. A special audit uncovered a number of abuses, and the obscurantist Curator was removed and exiled.

Lobachevsky achieved a significant improvement in the level of scientific and teaching work across all faculties. He oversaw the construction of a whole complex of auxiliary university buildings: the library, astronomical and magnetic observatories, an anatomical theatre, a physics cabinet, and a chemistry laboratory. He attempted to establish a "Society of Sciences" at the university but was denied permission for this. He replaced the mixed-content journal "Kazan Bulletin" with a strict scientific journal he organized, "Proceedings of Kazan University," the first issue of which was published in 1834 and began with a preface by Lobachevsky outlining the goals of the scientific publication. For 8 years, he continued to manage the library alongside his role as rector. He himself taught several specialized courses for students. He wrote guidance for mathematics teachers and worked on improving teaching methods in schools and gymnasiums. He participated in a trip to Penza in 1842 to observe a solar eclipse. He skillfully protected university staff and students during the cholera epidemic in 1830 by isolating the university territory and conducting thorough disinfection. He organized the rescue of astronomical instruments and the removal of books from the burning library during the massive fire in Kazan in 1842, managing to save almost all university buildings from the flames. Finally, he organized public lectures on scientific topics for the population and opened free access to the library and museums of the university.

In 1834, a mocking anonymous review of this work appeared in the reactionary journal of F. Bulgarin, "Syn Otchizny (Son of the Fatherland)". The reviewer wrote, "How could one think that Mr. Lobachevsky, an ordinary professor of mathematics, wrote a book with any serious intent that would bring honor even to the last schoolteacher? If not erudition, then at least common sense should be possessed by every teacher, yet this quality is often lacking in the new geometry," said the unknown reviewer, hiding behind the initials S.S.

Faced with misunderstanding and even mockery, Lobachevsky did not cease his research. After his 1829-1830 work "On the Foundations of Geometry," he published in the "Proceedings" the following papers:

1835: "Imaginary Geometry"
1836: "Application of Imaginary Geometry to Some Integrals".

From 1835 to 1838, he published his most extensive work, "New Foundations of Geometry with Complete Theory of Parallels". Finally, in 1840, "Geometric Research on the Theory of Parallels" was published in German, providing a clear and concise exposition of his main ideas.

This courageous struggle for scientific truth sharply distinguishes Lobachevsky from his contemporaries who were also approaching the discovery of non-Euclidean geometry.

The remarkable Hungarian mathematician Janos Bolyai published his study "Appendix" three years after Lobachevsky, which was an addentum to his father's book. In this work, he approached the same results as Lobachevsky from a somewhat different angle. However, encountering a lack of approval and support, he ceased his efforts. The outstanding German mathematician Gauss, as revealed in his posthumously published correspondence, received some of the initial equations of the new geometry but, in an effort to protect his peace and perhaps uncertain of the correctness and objective significance of these results, prohibited his correspondents from expressing any opinions about his views. Although he admired Lobachevsky's geometric work in private correspondence with friends, he never spoke about it publicly.

Lobachevsky received no positive feedback for his work, except for a single statement by Professor of Mechanics at Kazan University, P.I. Kotelnikov, who, in his inaugural address in 1842, noted that Lobachevsky's amazing work, the construction of a new geometry based on the assumption that the sum of the angles of a triangle is less than two right angles, would sooner or later find its admirers.

Lobachevsky's many years of fruitful work could not receive a positive assessment from the government of Nicholas I. In 1846, Lobachevsky was effectively removed from his work at the university. Outwardly, he received a promotion – he was appointed Assistant of the Curator (however, he was not assigned a salary for this work), but at the same time he lost his chair and rectorship.

It should be noted that less than a year before that, he had been approved as rector of the university for the sixth time for another four years. At the same time, he had managed the Kazan Educational District for over a year, replacing M.N. Musin-Pushkin, who had been transferred to St. Petersburg. Pointing to these service duties, shortly before the unexpected order from the Ministry, Lobachevsky recommended A.F. Popov, a teacher at the Kazan Gymnasium who had defended his doctoral dissertation, to replace him in the mathematics department. He considered it necessary to encourage a young, talented scientist and found it unfair to occupy the chair under such circumstances. But, having lost his professor chair and rectorship and being in the position of Assistant of the Curator, Lobachevsky lost the opportunity not only to manage the university but also to effectively participate in the university's life in general.

The forced removal from the activity to which he dedicated his life, the deterioration of his financial situation, and then a family misfortune (in 1852 his eldest son died) devastatingly affected his health; he aged considerably and began to go blind. But even deprived of sight, Lobachevsky did not cease to attend exams, ceremonial meetings, scientific disputes, and did not stop his scientific work.

The lack of understanding of the significance of his new geometry, the cruel ingratitude of his contemporaries, material adversity, family misfortune, and finally, blindness did not break his courageous spirit. A year before his death, he completed his last work, "Pangeometry", dictating it to his students.

On February 24 (O.S. February 12), 1856, the life of the great scientist, entirely dedicated to Russian science and Kazan University, ended.