Nikolai Bugaev
Encyclopedia
Nikolai Vasilievich Bugaev (September 14, 1837 – June 11, 1903) was a prominent Russia
n mathematician
.
, Russian Empire
into a somewhat unstable family (his father was an army doctor), and at the age of ten young Nikolai was sent to Moscow
to find his own means of obtaining an education. He succeeded, graduating in 1859 from Moscow University, where he majored in mathematics
and physics
. He went on to study engineering
, but in 1863 wrote a Master's thesis on the convergence of infinite series. This document was sufficiently impressive to win him a place studying under Karl Weierstrass
and Ernst Kummer
in Berlin
. He also spent some time in Paris
studying under Joseph Liouville
. He earned his doctoral degree in 1866 and returned to Moscow
, where he taught 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
and analytic
operations.
Bugaev was the active member of the Moscow Mathematical Society
and the president of it (1891-1903). He also wrote influential philosophical essays in which he trumpeted the virtues of mathematical analysis
and decried the influence of geometry
and probability
. 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
, many famous Russian mathematicians, such as Andrei Kolmogorov and Nikolai Luzin
, directly "descend" from Bugaev—and thus from the Prince of Mathematicians, Carl Friedrich Gauss
.
Nikolai Bugaev was also a talented chess
player; some of his games are available at orangutan-people site.
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 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 Andrei Bely
, under which name he helped found the Symbolist movement. Professor Korobkin, the main character of Bely's innovative novel Moscow, was inspired by Nikolay Bugayev. Interestingly enough, in view of his father's prejudices, Boris Bugaev was fascinated by probability and particularly by the notion of entropy
, which is mentioned in several of his novels and poems.
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Biography
Bugaev was born in GeorgiaGeorgia (country)
Georgia is a sovereign state in the Caucasus region of Eurasia. Located at the crossroads of Western Asia and Eastern Europe, it is bounded to the west by the Black Sea, to the north by Russia, to the southwest by Turkey, to the south by Armenia, and to the southeast by Azerbaijan. The capital of...
, Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
into a somewhat unstable family (his father was an army doctor), and at the age of ten young Nikolai was sent to Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
to find his own means of obtaining an education. He succeeded, graduating in 1859 from Moscow University, where he majored in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. He went on to study engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, but in 1863 wrote a Master's thesis on the convergence of infinite series. This document was sufficiently impressive to win him a place studying under Karl Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
and Ernst Kummer
Ernst Kummer
Ernst Eduard Kummer 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 high school, where he inspired the mathematical career of Leopold Kronecker.-Life:Kummer...
in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
. He also spent some time in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
studying under Joseph Liouville
Joseph Liouville
- Life and work :Liouville graduated from the École Polytechnique in 1827. After some years as an assistant at various institutions including the Ecole Centrale Paris, he was appointed as professor at the École Polytechnique in 1838...
. He earned his doctoral degree in 1866 and returned to Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
, where he taught 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
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
and analytic
Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
operations.
Bugaev was the active member of the Moscow Mathematical Society
Moscow Mathematical Society
The Moscow Mathematical Society is a society of Moscow mathematicians aimed at the development of mathematics in Russia.The first meeting of the society was . Nikolai Brashman was the first president of MMO. Victor Vassiliev is the current president of MMO....
and the president of it (1891-1903). He also wrote influential philosophical essays in which he trumpeted the virtues of mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and decried the influence of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
. 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 Egorov
- External links :...
, many famous Russian mathematicians, such as Andrei Kolmogorov and Nikolai Luzin
Nikolai Luzin
Nikolai Nikolaevich Luzin, , was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the...
, directly "descend" from Bugaev—and thus from the Prince of Mathematicians, Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
.
Nikolai Bugaev was also a talented chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
player; some of his games are available at orangutan-people site.
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 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 Andrei Bely
Andrei Bely
Andrei Bely was the pseudonym of Boris Nikolaevich Bugaev , a Russian novelist, poet, theorist, and literary critic. His novel Petersburg was regarded by Vladimir Nabokov as one of the four greatest novels of the 20th century.-Biography:...
, under which name he helped found the Symbolist movement. Professor Korobkin, the main character of Bely's innovative novel Moscow, was inspired by Nikolay Bugayev. Interestingly enough, in view of his father's prejudices, Boris Bugaev was fascinated by probability and particularly by the notion of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, which is mentioned in several of his novels and poems.