Nikolai Vasilievich Bugaev (russian: Никола́й Васи́льевич Буга́ев; September 14, 1837 – June 11, 1903) was a prominent

Russia Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, the father of

Andrei Bely Boris Nikolaevich Bugaev ( rus, Бори́с Никола́евич Буга́ев, p=bɐˈrʲis nʲɪkɐˈlajɪvʲɪtɕ bʊˈɡajɪf, a=Boris Nikolayevich Bugayev.ru.vorb.oga), better known by the pen name Andrei Bely or Biely ( rus, Андр� ...

Early life and education

Bugaev was born in

Georgia Georgia most commonly refers to: * Georgia (country), a country in the Caucasus region of Eurasia * Georgia (U.S. state), a state in the Southeast United States Georgia may also refer to: Places Historical states and entities * Related to the ...

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...

into a somewhat unstable family (his father was an army doctor), and at the age of ten young Nikolai was sent to

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

to find his own means of obtaining an education. He graduated in 1859 from

Moscow University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

, where he majored in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. Bugaev then studied

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

and then wrote a master's thesis in 1863 on the

convergence Convergence may refer to: Arts and media Literature *''Convergence'' (book series), edited by Ruth Nanda Anshen *Convergence (comics), "Convergence" (comics), two separate story lines published by DC Comics: **A four-part crossover storyline that ...

infinite series In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...

. This document was considered sufficiently impressive to win him a place studying under

Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...

and

Ernst Kummer Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a '' gymnasium'', the German equivalent of ...

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

. He also spent some time in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

studying under

Joseph Liouville Joseph Liouville (; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer. Life and work He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse ...

. He earned his doctoral degree in 1866.

Career

After his doctoral degree, Bugaev returned to Moscow and taught there for the remainder of his career. Some of his most influential papers offered proofs of previously unproven assertions of Liouville, but his most original work centered around the development of formal analogies between

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

and analytic operations. Bugaev was an active member and president (1891-1903) of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society wa ...

. He also wrote influential philosophical essays in which he trumpeted the virtues of

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

and decried the influence of

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

. Many feel he is largely responsible for the pronounced predilection towards "hard analysis" which is characteristic of so much of the best Russian mathematics. Through Bugaev's star student,

Dmitri Egorov Dmitri Fyodorovich Egorov (russian: Дми́трий Фёдорович Его́ров; December 22, 1869 – September 10, 1931) was a Russian and Soviet mathematician known for contributions to the areas of differential geometry and mathematic ...

, many famous Russian mathematicians, such as

Andrei Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

and

Nikolai Luzin Nikolai Nikolaevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlaɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 January 1950) was a Soviet/Ru ...

, directly "descend" from Bugaev—and thus from the Prince of Mathematicians,

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

Personal life

Bugaev was a talented

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to disti ...

player. Bugaev was a memorable "character" whose life was touched by scandal. He was not, it is said, much admired for his looks, but his wife was considered brilliant, beautiful, and rich, and the Bugaevs were socially prominent. Their mathematically, musically, and artistically talented son, ''Boris Nikolaevich Bugaev'' (14 October 1880 O.S.-8 January 1934), went on to adopt the pseudonym

, under which name he helped found the Symbolist movement. Professor Korobkin, the main character of Bely's innovative novel ''Moscow'', was inspired by Nikolai Bugaev. In view of his father's prejudices, Boris Bugaev was fascinated by probability and particularly by the notion of

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

, which is mentioned in several of his novels and poems.

References

* * *

Bibliography

External links

Bugaev's chess games
{{DEFAULTSORT:Bugaev, Nikolai Corresponding members of the Saint Petersburg Academy of Sciences Russian mathematicians 19th-century mathematicians from the Russian Empire 20th-century Russian mathematicians Russian philosophers 1837 births 1903 deaths Professorships at the Imperial Moscow University Imperial Moscow University alumni