Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a
Russian
Russian(s) refers to anything related to Russia, including:
*Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries
*Rossiyane (), Russian language term for all citizens and peo ...
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 ...
and considered to be the founding father of Russian mathematics.
Chebyshev is known for his fundamental contributions to the fields of
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 ...
,
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
,
mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...
, and
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
. A number of important mathematical concepts are named after him, including the
Chebyshev inequality
In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from th ...
(which can be used to prove the
weak law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials shou ...
), the
Bertrand–Chebyshev theorem,
Chebyshev polynomial
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions:
The Chebyshe ...
s,
Chebyshev linkage
In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion.
It was invented by the 19th-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechanism ...
, and
Chebyshev bias
In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4''k'' + 3 than of the form 4''k'' + 1, up to the same limit. This phenomenon was first observed by Russian mathematic ...
.
Transcription
The surname Chebyshev has been transliterated in several different ways, like Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov, Chebyshov (according to native Russian speakers, this one provides the closest pronunciation in English to the correct pronunciation in old Russian), and Chebychev, a mixture between English and French transliterations considered erroneous. It is one of the most well known data-retrieval nightmares of the entire mathematical literature. Currently, the English transliteration ''Chebyshev'' has gained widespread acceptance, except by the French, who prefer ''Tchebychev.'' The correct
transliteration
Transliteration is a type of conversion of a text from one writing system, script to another that involves swapping Letter (alphabet), letters (thus ''wikt:trans-#Prefix, trans-'' + ''wikt:littera#Latin, liter-'') in predictable ways, such as ...
according to
ISO 9
ISO 9 is an international standard establishing a system for the transliteration into Latin characters of Cyrillic characters constituting the alphabets of many Slavic and non-Slavic languages.
Published on February 23, 1995 by the International ...
is ''Čebyšëv''. The
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
adopted the transcription ''Chebyshev'' in its
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science.
The AMS also pu ...
.
His first name comes from the
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
Paphnutius (Παφνούτιος), which in turn takes its origin in the
Coptic
Coptic may refer to:
Afro-Asia
* Copts, an ethnoreligious group mainly in the area of modern Egypt but also in Sudan and Libya
* Coptic language, a Northern Afro-Asiatic language spoken in Egypt until at least the 17th century
* Coptic alphabet ...
Paphnuty (Ⲡⲁⲫⲛⲟⲩϯ), meaning "that who belongs to God" or simply "the man of God".
Biography
Early years
One of nine children,
[Biography in MacTutor Archive]
/ref> Chebyshev was born in the village of Okatovo in the district of Borovsk
Borovsk (russian: Бо́ровск) is a town and the administrative center of Borovsky District of Kaluga Oblast, Russia, located on the Protva River just south from the oblast's border with Moscow Oblast. Population: 12,000 (1969).
History
...
, province of Kaluga
Kaluga Oblast (russian: Калу́жская о́бласть, translit=Kaluzhskaya oblast) is a federal subject of Russia (an oblast). Its administrative center is the city of Kaluga. The 2021 Russian Census found a population of 1,069,904.
Ge ...
. His father, Lev Pavlovich, was a Russian nobleman and wealthy landowner. Pafnuty Lvovich was first educated at home by his mother Agrafena Ivanovna Pozniakova (in reading and writing) and by his cousin Avdotya Kvintillianovna Sukhareva (in French and 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 ...
). Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis."
Trendelenburg's gait affected Chebyshev's adolescence and development. From childhood, he limped and walked with a stick and so his parents abandoned the idea of his becoming an officer in the family tradition. His disability prevented his playing many children's games and he devoted himself instead to mathematics.
In 1832, the family moved 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 ...
, mainly to attend to the education of their eldest sons (Pafnuty and Pavel, who would become lawyers). Education continued at home and his parents engaged teachers of excellent reputation, including (for mathematics and physics) P.N. Pogorelski, held to be one of the best teachers in Moscow and who had taught (for example) the writer Ivan Sergeevich Turgenev.
University studies
In summer 1837, Chebyshev passed the registration examinations and, in September of that year, began his mathematical studies at the second philosophical department of Moscow University. His teachers included N.D. Brashman, N.E. Zernov and D.M. Perevoshchikov of whom it seems clear that Brashman had the greatest influence on Chebyshev. Brashman instructed him in practical mechanics and probably showed him the work of French engineer J.V. Poncelet.
In 1841 Chebyshev was awarded the silver medal for his work "calculation of the roots of equations" which he had finished in 1838. In this, Chebyshev derived an approximating algorithm for the solution of algebraic equations of ''nth'' degree based on Newton's method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...
. In the same year, he finished his studies as "most outstanding candidate".
In 1841, Chebyshev's financial situation changed drastically. There was famine in Russia, and his parents were forced to leave Moscow. Although they could no longer support their son, he decided to continue his mathematical studies and prepared for the master examinations, which lasted six months. Chebyshev passed the final examination in October 1843 and, in 1846, defended his master thesis "An Essay on the Elementary Analysis of the Theory of Probability." His biographer Prudnikov suggests that Chebyshev was directed to this subject after learning of recently published books on probability theory or on the revenue of the Russian insurance industry.
Adult years
In 1847, Chebyshev promoted his thesis pro venia legendi
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
"On integration with the help of logarithms" at St Petersburg University and thus obtained the right to teach there as a lecturer. At that time some of Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
's works were rediscovered by P. N. Fuss and were being edited by V. Ya. Bunyakovsky, who encouraged Chebyshev to study them. This would come to influence Chebyshev's work. In 1848, he submitted his work ''The Theory of Congruences'' for a doctorate, which he defended in May 1849.[ He was elected an ]extraordinary professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia.
Overview
Appointment grades
* (Pay grade: ''W3'' or ''W2'')
* (''W3'')
* (''W2'')
* (''W2'', ...
at St Petersburg University in 1850, ordinary professor in 1860 and, after 25 years of lectureship, he became merited professor in 1872. In 1882 he left the university and devoted his life to research.
During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo
Tsarskoye Selo ( rus, Ца́рское Село́, p=ˈtsarskəɪ sʲɪˈlo, a=Ru_Tsarskoye_Selo.ogg, "Tsar's Village") was the town containing a former residence of the Russian imperial family and visiting nobility, located south from the cen ...
(now Pushkin), a southern suburb of St Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
.
His scientific achievements were the reason for his election as junior academician
An academician is a full member of an artistic, literary, engineering, or scientific academy. In many countries, it is an honorific title used to denote a full member of an academy that has a strong influence on national scientific life. In syst ...
(adjunkt) in 1856. Later, he became an extraordinary (1856) and in 1858 an ordinary member of the Imperial Academy of Sciences
The Russian Academy of Sciences (RAS; russian: Росси́йская акаде́мия нау́к (РАН) ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across t ...
. In the same year he became an honorary member of 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 ...
. He accepted other honorary appointments and was decorated several times. In 1856, Chebyshev became a member of the scientific committee of the ministry of national education. In 1859, he became an ordinary member of the ordnance department of the academy with the adoption of the headship of the commission for mathematical questions according to ordnance and experiments related to ballistics. The Paris academy
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...
elected him corresponding member in 1860 and full foreign member in 1874. In 1893, he was elected honorable member of the St. Petersburg Mathematical Society
The Saint Petersburg Mathematical Society (russian: Санкт-Петербургское математическое общество) is a mathematical society run by Saint Petersburg mathematicians.
Historical notes
The St. Petersburg Mathe ...
, which had been founded three years earlier.
Chebyshev died in St Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
on 26 November 1894.
Mathematical contributions
Chebyshev is known for his work in the fields of 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 ...
, statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...
, and number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
. The Chebyshev inequality
In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from th ...
states that if is a random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
with standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
''σ'' > 0, then the probability that the outcome of is no less than away from its mean is no more than :
:
The Chebyshev inequality is used to prove the weak law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials shou ...
.
The Bertrand–Chebyshev theorem (1845, 1852) states that for any , there exists a prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
such that . This is a consequence of the Chebyshev inequalities for the number of prime numbers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
less than , which state that is of the order of . A more precise form is given by the celebrated prime number theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying ...
: the ''quotient'' of the two expressions approaches 1.0 as tends to infinity.
Chebyshev is also known for the Chebyshev polynomial
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions:
The Chebyshe ...
s and the Chebyshev bias
In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4''k'' + 3 than of the form 4''k'' + 1, up to the same limit. This phenomenon was first observed by Russian mathematic ...
– the difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4).
Chebyshev was the first person to think systematically in terms of random variables
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
and their moments and expectations.
Legacy
Chebyshev is considered to be a founding father of 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 ...
n mathematics.[ Among his well-known students were the mathematicians ]Dmitry Grave
Dmitry Aleksandrovich Grave (russian: Дми́трий Алекса́ндрович Гра́ве; September 6, 1863 – December 19, 1939) was an Imperial Russian and Soviet mathematician.
Naum Akhiezer, Nikolai Chebotaryov, Mikhail Kravchuk, ...
, Aleksandr Korkin
Aleksandr Nikolayevich Korkin (russian: Александр Николаевич Коркин; – ) was a Russian mathematician. He made contribution to the development of partial differential equations, and was second only to Chebyshev among the ...
, Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (russian: Алекса́ндр Миха́йлович Ляпуно́в, ; – 3 November 1918) was a Russian mathematician, mechanician and physicist. His surname is variously romanized as Ljapunov, Liapunov, Liapo ...
, and Andrei Markov. According to the Mathematics Genealogy Project
The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. By 31 December 2021, it contained information on 274,575 mathematical scientists who contributed to research-level mathematics. For a ty ...
, Chebyshev has 13,709 mathematical "descendants" as of January 2020.
The lunar crater ''Chebyshev
Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a Russian mathematician and considered to be the founding father of Russian mathematics.
Chebyshe ...
'' and the asteroid 2010 Chebyshev were named to honor his major achievements in the mathematical realm.
Publications
*
*
*
See also
* List of things named after Pafnuty Chebyshev
References
External links
*
Mechanisms by Chebyshev
– short 3d films – embodiment of Tchebishev's inventions
*
*
*
an
(all in Russian
Russian(s) refers to anything related to Russia, including:
*Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries
*Rossiyane (), Russian language term for all citizens and peo ...
).
Biography
in French.
* ''Œuvres de P.L. Tchebychef'
Vol. I
Vol. II
(in French)
{{DEFAULTSORT:Chebyshev, Pafnuty Lvovich
1821 births
1894 deaths
People from Kaluga Oblast
People from Borovsky Uyezd
Russian people of Tatar descent
19th-century mathematicians from the Russian Empire
Probability theorists
Inventors from the Russian Empire
Number theorists
Numerical analysts
Ballistics experts
Statisticians from the Russian Empire
Moscow State University alumni
Full members of the Saint Petersburg Academy of Sciences
Members of the French Academy of Sciences
Demidov Prize laureates
Foreign Members of the Royal Society