Nikolai Ivanovich Lobachevsky
“The Copernicus of Geometry”

Part I – An Intro to the Life & Time of Nikolai Lobachevsky Nikolai Lobachevsky was born and lived in Russia from 1792 until 1856. During this historic time in Russia, one era of rulers ended and another began. In 1796, 7 decades of women rulers came to an end. Catherine the Great died in 1796 after thirty-four years as Empress of Russia. The throne then falls to her son Paul I, whose reign is cut short when he is murdered in his bed in 1801. After Paul’s demise, his son, Alexander I ascends the throne.[4] Alexander I was going to have his work cut out for him. Due to the Russians lack of trust in Western ideas at the end of the 18th century, advances in science and math in Russia where practically non-existent. In fact, the “modern” Saint Petersburg Academy was nearly abandoned. At this low point, the school had only 14 full-time staff members. Upon becoming Tsar, Alexander was determined to reform the suffering education system. He knew that advances in the areas of math & science would help to improve the strength of the military as well as make an impact on the economy of his nation. Just in the first three years after inheriting the throne, Alexander reopened the Dorpat University and opened 3 new universities, including Vilna in 1802, Kazan in 1804, and Karkov in 1804. With the opening of these new institutions, he still faced one major challenge: Who was going to teach the students all this math and science? As hesitant as Russia was, foreign instructors were hired to fill this role. The issue with this was that these foreigners didn’t speak Russian! This hurdle was ultimately overcome and in fact, these outsiders were able to reopen communication with the West so students received the education they needed and deserved. Unfortunately, this productive balance was short lived. During this time, the series of Russo-Turkish wars continued. One of these war periods between Russia and Turkey, has just ended in the year that Lobachevsky was born. In 1806, another Russo-Turkish War begins and lasts until 1812. This war officially ended on June 11, 1812 with the approval of the Treaty of Bucharest. Alexander I and his army had a mere 13 days of peace before Napoleon launched his invasion of Russia. Those 13 days of rest were invaluable to the Russian Army because after less than 6 months, they defeated the French forces. This retreat of Napoleon and his men ultimately led to Napoleon’s exile to the island of Elba. [3] The invasion of Napoleon in 1812 was a major setback to this new and improved education system. “The first decade of Alexander’s reign marked the last time in the nineteenth century that the Russian government regarded higher education as an unqualified good.” [2, 592] Two major upsets came after the invasion. First, the Russian’s distrust of Westerners was renewed exponentially. Additionally, there was a renewed faith in God for saving Mother Russia from France. This uprising led to a hatred of the university system because it was based on a mostly German foundation. Why is all of this information so relevant to us? One of the most influential mathematicians in history was a Russian university student during this time of unrest in the educational system.

Part II – Who was Nikolai Lobachevsky? Nikolai Ivanovich Lobachevsky was born on December 1, 1792, as one of three brothers, to Ivan Maksimovich and Praskovia Alexandrova Lobachevsky. Tragedy struck early in the young Nikolai’s life when his father passed away when he was just 7 years old. Finding it nearly impossible to support 3 young sons, his mother packed up the family and moved them to the city of Kazan in Western Russia near the edge of Siberia. Through government sponsorship, Nikolai and his brothers were able to attend Kazan Gymnasium for their primary education. Nikolai finished there in 1807 and entered Kazan University as a free student with the intention of becoming a medical doctor. As I mentioned before, during the education reform under the watchful eye of Alexander I, Kazan University had just been founded in 1804 and its doors were opened in 1805, just in time for Nikolai to enroll there 2 years later. Unbeknownst to him at the time, Nikolai Lobachevsky would spend the next 40 years of his life at Kazan University as a student, teacher, and administrator. [5] Nikolai never became a medical doctor. His primary studies changed from medicine to a broader study of advanced math and science. A highly intelligent and dedicated student, Nikolai received his Master’s Degree in Physics and Mathematics in 1811. [1] I suppose that Nikolai knew early on that his calling was to be an educator. Less than a year after graduating, Nikolai began his career by teaching geometry to government officials, who were required to earn a college degree in order to be promoted. It didn’t take the Kazan University officials long to see they had someone special in Nikolai and he received an appointment as an assistant professor in 1814. As an assistant professor, he taught all across the fields of math and science including courses in number theory, algebra, trigonometry, calculus, plane & spherical geometry, physics, and astronomy [2]. At the young age of only 23, Nikolai was given an extraordinary professorship in 1816. Nikolai, being the leading mathematician, received the title of Dean of the Physico-Mathematical College at Kazan in 1820. One more bump up in 1822, brought Nikolai the honor of becoming Full Professor of Pure Mathematics. Lobachevsky’s career at the university included more than just educating the young minds of that time. He became Head Librarian in 1825 and, in 1827, he became top dog at the university. For the next 19 years, Nikolai Lobachevsky was Kazan University Rector. As rector, Nikolai went above and beyond in his loyalty to the school and those benefitted by it. Through his “upright and independent character”, he overcame the fallout period from 1819-1826 that was brought on by the Russian people’s reaction to Napoleon’s invasion [9]. Under Lobachevsky’s direction, the university actually blossomed despite the negativity surrounding the educational system. New buildings were constructed including “a library, an astronomical observatory, new medical facilities,” and new laboratories for studies in physics, chemistry, and anatomy [9]. Lobachevsky’s educational philosophy was confirmed during a speech he gave just after his promotion to rector of the university. In “On the Most Important Subjects of Education”, he clearly “outlined the ideal of the harmonious development of the personality, emphasized the social significance of upbringing and education, and discussed the role of the sciences and the scientist's duty to his country and people” [9]. He didn’t just promote the study of the sciences. He wanted all students, including those scholars of art and the humanities, to feel welcome there. Lobachevsky saved the university, not just from the negative beliefs of the general Russian population, but also from two natural disasters. In 1830, with an impenetrable quarantine set in place under the watchful eye of Nikolai, a cholera epidemic that swept through the university was thwarted. Through his brave and bold personal actions, Nikolai again saved the university from destruction when a fire threatened to destroy Kazan in 1842. Lobachevsky’s accomplishments at Kazan did not go unnoticed by the government. Not only was he an extremely dedicated administrator, he continued educating students by personally teaching on topics such as mechanics and differential equations. In 1837, the government acknowledged his work and raised him to hereditary nobility. Unfortunately, the same government that had praised him is believed to have been behind Lobachevsky’s forced resignation as Kazan University Rector in 1847 [7]. Before they ousted him, the government wasn’t the only one with things to say about Nikolai. As a young man, he was described as “a stubborn, relentless young man, very ambitious.” As an instructor, one of his students once said this: “In the Auditorium, Professor Lobachevsky was able to be profound or enthusiastic, depending on the subject” [6]. On how Lobachevsky was key in saving the university from disintegrating during some harsh times, Vinberg says it was due to his “upright and independent character” [9]. Outside the university, Nikolai Lobachevsky did have a personal life. In 1832, at age 40, Nikolai married Lady Varvara Alexejevna Moisieva. In the Encyclopedia of World Biography, an unflattering depiction of Nikolai’s wife is presented. It describes her as “a young woman from a wealthy family who was educated, quick-witted, and unattractive.” Some accounts say that there were 11 Lobachevsky children while others mention only seven. After reading several references to his children, it probably wouldn’t be too far-fetched to say that there were 11 children conceived with only 7 of them surviving for a significant period of time. This conclusion seems reasonable after reading that most of the children were frail and prone to illness. [8] In one article, it is stated that, sadly, “Tragedy dogged Lobachevsky’s life. His contemporaries described him as hardworking and suffering, rarely relaxing or displaying humor” [8]. This appears to be an accurate description, even more so towards the end of his life. Once the constant demands of his job as rector no longer fueled his fire, and after the death of his beloved son, due to tuberculosis, it seems that Lobachevsky became increasingly depressed. It wasn’t long before this depression impacted his health. His eyesight, because of cataracts, deteriorated along with his general health during the last few years of his life. Nikolai Lobachevsky died on February 24, 1856, at the age of 63, in the city of Kazan. [10] Part III – What did Lobachevsky contribute to the field of Mathematics? When Lobachevsky was just a mere student at Kazan University, one of his mathematics instructors was a German man named Martin Bartels. As it would happen, Bartels was a close friend of Johann Carl Gauss (another great mathematician). Being an inspiring teacher in his own right, Bartels soon had Lobachevsky fascinated with math. It has been rumored that as Nikolai was becoming more and more absorbed in math that he received advice from Gauss through letters to and from Bartels. As Lobachevsky’s career at Kazan was advancing, his research was also advancing. His research was primarily focused on geometry and more directly on the work of Euclid (ca. 300 BC). Euclid’s studies on geometry led to his publication of 13 “elements”. Eventually, Lobachevsky’s number one focus of Euclid’s geometry would be Euclid’s Parallel Postulate. While many other mathematicians had attempted to prove Euclid’s postulate and thereby make it a true theorem, Lobachevsky determined that the postulate was impossible to prove. In one of his earliest works (more details about this work will be discussed later), Lobachevsky made this statement regarding Euclid’s postulate; “no rigorous proof of the truth of this had ever been discovered.” That’s right, in more than 2000 years, not one person had been able to find proof! Lobachevsky had much of his work published during his career. The official birth of non-Eucidean, or Lobachevskian, geometry came in 1829 after an article by Lobachevsky titled “On the Principles of Geometry” was published. This article describes a geometry that is in direct conflict with Euclid’s parallel postulate. Other published works of Lobachevsky include “”New Foundations (Elements) of Geometry” was published in the newly founded scientific journal of Kazan University over the course of 3 years and in three different languages from 1835 to 1838. This contained Lobachevsky’s complete theory of parallels including his basis for the Lobachevskian Parallel Postulate [1]. Also published in 1835, was Nikolai’s “imaginary geometry”. The following year his work on the applications of this “imaginary geometry” to certain integrals was put into print. While Lobachevsky’s work centered primarily on geometry, he made significant contributions to other areas of mathematics. In algebra, he developed the Lobachevsky-Graffe method for computing the roots of a polynomial, and published his study, “On the Convergence of Trigonometrical Series” in 1834 [8]. Part V – My Final Thoughts on Lobachevsky and His Work I believe that the full contributions to math made by Lobachevsky have yet to be fully appreciated. Near the end of his life, Lobachevsky completed his magnum opus, a book called PanGeometry. This treatise was dictated by Nikolai and published in two different languages in 1855. It did not, however, receive the praise worthy of it, mainly due to the fact that it wasn’t written and published in Nikolai’s “own hand” and was considered by some to be incomplete. [2]. It only took 53 years following the death of its author for PanGeometry to be published in its complete and original form. I suppose that I have always held a childish belief in the false notion that “Mother Russia” was a just a big bully and an eternal enemy of the rest of the world. While the former Soviet Union caused much of the world to be made to fear it, I came to the grown-up conclusion that all Russian’s aren’t my natural born enemies. While parts of Lobachevsky’s life did indeed seem tragic, he made the best out of what he had. He turned a struggling university into a beautiful educational institution. He made significant advances in the fields of geometry and algebra among other things. When guests were invited to his family home, they were treated like royalty and lavished by his generous giving. He was a respected member of the educational system and of the community. In a final note on the great mathematician, Nikolai Ivanovich Lobachevsky, I give you a quote from our text book. “When the effects of his work were compared to Copernicus’s heliocentric system, William Kingdon Clifford said, ‘What Vesalius was to Galen, what Copernicus was to Ptolemy, that was Lobachevsky to Euclid.’” My personal compliment to Lobachevsky hangs just this computer on my desk. He was once quoted as saying, “There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world.” [2]

Works Cited
[1] Boyer, Carl B., and Uta C. Merzbach. A History of Mathematics. New York: Wiley, 1991. 520+. Print.
[2] Burton, David M. The History of Mathematics: An Introduction. New York: McGraw-Hill, 2011. 569+. Print.
[3]"Emperors & Empresses of Russia Alexander I." Www.royalrussia.org. N.p., n.d. Web. 23 Sept. 2012. <http://www.angelfire.com/pa/ImperialRussian/royalty/russia/tsar15.html>.
[4] "HISTORY OF RUSSIA." HISTORY OF RUSSIA. N.p., n.d. Web. 09 Sept. 2012. <http://www.historyworld.net/wrldhis/plaintexthistories.asp?paragraphid=ixd>.
[5] "Lobachevsky, Nikolai Ivanovich (1792 - 1856)." Hutchinson Dictionary Of Scientific Biography (2005): 1. Science Reference Center. Web. 9 Sept. 2012.
[6] Lobachevsky, Nikolai. "Preface to Lobachevsky's 1886 Biography." Trans. Athanase Papadopoulos. Pangeometry. N.p.: European Mathematical Society, n.d. N. pag. Print.
[7] "Lobachevsky, Nikolaiivanovich." Complete Dictionary of Scientific Biography. Www.encyclopedia.com, 2009. Web. 23 Sept. 2012. <http://www.encyclopedia.com/doc/1G2-2830902647.html#>.
[8] "Nikolai Ivanovich Lobachevskii." Encyclopedia of World Biography. 2004. Encyclopedia.com. 9 Sep. 2012 .
[9] "Nikolai Ivanovich Lobachevsky." Lobachevsky Biography. N.p., n.d. Web. 05 Sept. 2012. <http://www-history.mcs.st-andrews.ac.uk/Biographies/Lobachevsky.html>.
[10] "Nikolay Ivanovich Lobachevsky (Russian Mathematician)." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web. 09 Sept. 2012. <http://www.britannica.com/EBchecked/topic/345382/Nikolay-Ivanovich-Lobachevsky>.
[11] Perminov, V. YA. "The Philosophical and Methodological Thought of N. I. Lobachevsky." Philosophia Mathematica 5.1 (1997): 3-20. Academic Search Complete. Web. 23 Sept. 2012.