Prominent Russians: Nikolai Lobachevsky

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Early years and the love of math

Lobachevsky was the second of three boys born into the family of a land surveyor in the city of Nizhny Novgorod on the Volga River. When he was only eight, his father died, leaving his widow and three sons with virtually no means of survival. In her effort to escape poverty, Lobachevsky’s mother moved further east, to the city of Kazan, closer to her family. Here in Kazan, she was able to put her sons in a special gymnasium, which prepared students to enter the Moscow University. It was partially sponsored by the government, and she managed to enroll the boys into the program for free.

All three boys were bright and liked to study, but Nikolai soon discovered a particular gift for mathematics. His math teacher, who at the time was one of the best in the gymnasium, singled out Nikolai and paid him extra attention in class.

The University of Kazan - from studying to teaching

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In 1805, a new university was founded in Kazan – it needed new students, and the gymnasium was full of potential academicians. The university offered new students free scholarships – it couldn’t have come at a better time for the Lobachevskys, who were still struggling to make ends meet. In February 1807, at the age of 14, Lobachevsky enrolled in the university. The young man was thrilled by the new opportunities and decided to focus on natural sciences in preparation to study medicine.

The university had very few qualified professors at the beginning. The school’s council saw no better solution than to hire them from Europe. Besides their brilliant knowledge and pedagogical talents, the foreign professors brought their bold, free thinking as well as high moral standards – they opened the “windows to Europe” to the students; their ideas were a breath of fresh air in remote Kazan.

One of the most popular and reputable professors at the university was Martin Bartels, a mathematician from Germany. Before coming to Russia he taught at the University of Brunswick. He was known for having tutored the child prodigy Carl Gauss, who became one of the greatest mathematicians of all time. Lobachevsky was completely taken by Bartel’s lectures, and threw himself into mathematics without any reserves. Bartels also noticed the talented young man; he tutored Lobachevsky four extra hours a week at home, and had Nikolai helped him with students who had difficulties in class. Bartels efforts paid off in full – Lobachevsky adored him as a professor and became an excellent mathematician – he no longer solved only the problems his teacher gave him, but tried to make his own discoveries.

Despite Lobachevsky’s academic success, he somehow managed to get in the bad books with the University Council. His records describe him as “stubborn,” “arrogant,” “rebellious” and even “blasphemous.” He was on the verge of being expelled from the university and to serve in the army, but was rescued by his professors, who spoke up in his defense.

Lobachevsky was allowed to continue his studies – apparently the risk of losing his scholarship was enough motivation for him to change his behavior. He devoted himself fully to his studies and kept out of trouble. In 1811, Lobachevsky earned a Master’s degree in Mathematics and Physics. Furthermore he was allowed to continue his studies at the university to become a professor.

In 1816, Lobachevsky became a lecturer, which marked the beginning of his 30-year career at the Kazan University. Professor Bartels, who by then had been teaching in Russia for 12 years, passed all of his responsibilities onto his best student and left Russia. With time, other foreign professors left as well and soon Lobachevsky took on the whole Physics and Mathematics Faculty. He embraced the challenge - the University had become his life by then and Lobachevsky was involved in its every aspect – he lectured in mathematics, astronomy and physics, he was the Chief University Librarian, practically building it from scratch and he was a member of the University Council, which oversaw construction on the campus premises. The University of Kazan was on its way to becoming a top academic institution of the Russian Empire.

The time of change

However, very soon, this vigorous activity was interrupted. In 1819, Mikhail Magnitsky, who was favored by Emperor Alexander I, had been appointed curator of the Kazan Academic District and came to inspect the University. His report was shocking – he accused the staff of wasting the government’s money and eliminating the religious aspect of education, and suggested demolishing the very building that housed the university. This drastic measure was supported neither by the Emperor nor by the District Education Council. Instead they suggested that the university be restructured, with Magnitsky overseeing the changes.

The essence of the reformation, according to Magnitsky, came down to two things - eliminating free thinking and bringing in religious education. The university lost its independence and soon resembled a monastery rather than an educational institution. Magnitsky fired 11 professors and anyone who didn’t agree with his line of thinking. As for the students, their lives were made even more miserable – according to the new ideology “the essence of learning was in submission.” They were incarcerated in “submission rooms” for the smallest violation of the rules and their rations reduced to bread and water.

Lobachevsky, who had become a professor in 1822, was appalled by the changes at his alma mater. The man who got in trouble for his free mindedness as a student was now in trouble as a professor - his vocal criticism of the new rules put him on the brink of being fired. In his report to the university rector, Magnitsky wrote: “Not a year goes by without Professor Lobachevsky willfully trying to violate our instructions… He should be closely watched.”

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There is little doubt that Lobachevsky would have lost his job, had it not been for the death of Emperor Alexander I of typhoid fever at the end of 1825. In the spring of the following year the new Emperor Nicholas I sent an independent inspection committee to the university. Upon their arrival, the inspectors witnessed the total deterioration of the school and an enormous embezzlement of government funds – Magnitsky was fired and his property was confiscated to make up for his theft.

Lobachevsky the Rector - years of university revival

In 1927, 35-year-old Lobachevsky was elected Rector of the Kazan University. He brought a much-longed-for revival – he reorganized the staff, built new laboratories and observatories, launched the printing of a local newspaper, Kazansky Vestnik (The Kazan Messenger), and even gave special lectures for Kazan residents, who weren’t students. Soon the University of Kazan became a major educational and research hub for the entire Volga Region. He showed his ability in handling the most extreme situations - during the time of Lobachevsky’s terms two disasters hit the University - a cholera epidemic in 1830 and a big fire in 1842. He was able to keep the damage to a minimum and even received a special message of thanks from Emperor Nicholas I. Lobachevsky was so popular, he was reelected rector six consecutive times until 1846.

Discovery of non-Euclidean geometry

As successful as he was as the Kazan University Rector, Lobachevsky earned his world fame and place in history as the Copernicus of Geometry. Throughout his lifetime he continuously worked on a problem, which had puzzled the minds of scholars for nearly two thousand years – the Fifth postulate of Euclid, stating that for any given line and point not on the line, there is one parallel line through the point not intersecting the line. Lobachevsky had set it apart from the other axioms and found a way to disprove it. In 1826 he presented his findings in a report (A Concise Outline of the Foundations of Geometry) to the Department of Physical-Mathematical Sciences at the Kazan University. If it was deemed correct by the mathematicians of the Faculty he wanted it to be published in the Kazan Messenger. His findings, however, turned out to be far ahead of contemporary scientific thought and his report was neglected and didn’t appear in print until a few years later.

At the time no one had any idea that Lobachevsky’s work contained one of the greatest discoveries, disproving Euclid’s Fifth postulate, also known as the Parallel Postulate. Lobachevsky’s geometry, which was called non-Euclidean geometry, stated there is more than one line that can be extended through any given point parallel to another line of which that point is not part. Its tremendous value was in providing a mathematical basis for the theory of relativity, which was yet to be discovered by Albert Einstein.

Lobachevsky tried to print his works in a scientific journal in St. Petersburg, but was rejected by the St. Petersburg Academy of Sciences. In his attempt to gain international recognition, he also published in French Géométrie imaginaire (Imaginary Geometry), and German Geometrische Untersuchungen zur Theorie der Parellellinien (Geometric Investigations of the Theory of Parallel Links). The latter publication attracted the attention of German mathematician Carl Gauss, who had also independently discovered non-Euclidean geometry, but shared his discoveries with very few people.

Both Lobachevsky and Gauss had been taught by the same professor, the two had similar views on geometry and perhaps that’s what led them to the same kind of conclusions – they began a correspondence. Gauss supported Lobachevsky, but unfortunately he never published his views and only mentioned them in letters to his friends. One such letter was published in 1865, after both Gauss and Lobachevsky had already died. This drew wide attention to non-Euclidean geometry in Europe and spread the fame of Lobachevsky.

Besides making the greatest discovery of his life, Lobachevsky also wrote works on algebra, mathematical analysis, the calculus of probabilities, mechanics, physics and astronomy. Though much of Lobachevsky’s work was dismissed in his lifetime, he was given a hereditary title of nobility in 1837. Perhaps this honor was bestowed on him in part for his efforts during the cholera epidemic of 1830.

Interestingly enough, three years after Lobachevsky made his discovery, the Hungarian mathematician Janos Bolyai also disproved Euclid’s Fifth postulate on his own. At some point, the fact that Gauss and Bolyai had made the same discoveries as Lobachevsky formed opinions, accusing Lobachevsky of plagiarism. However, those claims were proved groundless. A century later, in the 1950s, the rumors were picked up by Tom Lehrer, a mathematician and humorist, who wrote a song about Lobachevsky. In the song Lehrer sarcastically credited Lobachevsky with teaching him the secret of success as a mathematician – plagiarism. The funny little song however, didn’t have anything to do with Lobachevsky’s alleged misdemeanor. Most likely it was the fact that Lobachevsky rhymed with Stanislavsky, and Lehrer was trying to parody the American comedian Danny Kaye’s song about Stanislavsky.

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Family life

When Lobachevsky reached his forties, he finally decided he should have some time for himself. He married a woman much younger than himself, the daughter of a rich landowner, Varvara Moiseeva. Her father gave them a little village with peasants as a dowry. That, combined with Lobachevsky’s rector’s salary, provided sufficient income to support the family. Perhaps the age difference had something to do with it, but Lobachevsky’s marriage wasn’t as successful as his career.

Lobachevsky had seven children (according to some sources that number is as actually as high as fifteen). He was a very good father, investing a lot of time and effort into his children. He also spent his own money on modernizing the rector’s residence, a big three-storey house where he received many guests with lavish hospitality. All this left Lobachevsky virtually no means to fall back on after retirement.

In 1946, Lobachevsky’s last term as rector came to an end. Officially the reason he was made to leave was his poor health, however, some say politics affected the decision. The only consolation Lobachevsky had was lecturing for free, yet the respect of students wasn’t enough to pay the bills. At the same time his eldest son, a university student, who bore a stunning resemblance to young Lobachevsky and his father’s hope and pride, died unexpectedly. This was a tremendous blow to Lobachevsky, who had already lost one son. A few years later his wife’s brother gambled away his family’s money, which forced Lobachevsky to sell the family property to cover his brother-in-law’s debts. This was a great stress for the grief-stricken Lobachevsky; his health deteriorated further and he began to lose his eyesight.

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The last decade of his life was a mere shadow of the years past. Deprived of any motivation, Lobachevsky was withering away, virtually becoming blind. His very last work Pangeometry was published thanks to a student who had written it down to Lobachevsky’s dictation.

The impact of Lobachevsky's work

Lobachevsky died blind and poor at the age of 63. He never lived to see the major work of his life recognized by his contemporaries, and thought it was unappreciated and forgotten. It was a shame he never knew what kind of an impact it would have on the world a few decades later, how it would overturn the concepts of the time and serve as a foundation for mathematical thinking of future generations.

Perhaps no one has described his achievements better than William Clifford, an English mathematician and philosopher: "What Vesalius was to Galen, what Copernicus was to Ptolemy, that was what Lobachevsky was to Euclid. There is, indeed, a somewhat instructive parallel between the last two cases. Copernicus and Lobachevsky were both of Slavic origin. Each of them has brought about a revolution in scientific ideas so great that it can only be compared with that wrought by the other. And the reason of the transcendent importance of these two changes is that they are changes in the conception of the Cosmos."

Written by Olga Prodan, RT