Mathematician:Pafnuty Lvovich Chebyshev

Mathematician

Russian mathematician whose work was mainly in the fields of probability, statistics and number theory.

He is best known for proving Bertrand's Postulate in $1850$. It has since been known as the Bertrand-Chebyshev Theorem.

Nationality

Russian

History

• Born: May 16, 1821, Okatovo, Borovsk, Kaluga, Russia
• Died: December 8, 1894, St Petersburg, Russia

Theorems and Definitions

• Chebyshev Approximation
• Chebyshev Bias
• Chebyshev Cube Root
• Chebyshev Distance
• Chebyshev's Equation
• Chebyshev Filter

• Chebyshev Functions:
  • First Chebyshev Function
  • Second Chebyshev Function

• Chebyshev Linkage
• Chebyshev Net
• Chebyshev Node
• Chebyshev Polynomials:
  • Chebyshev Polynomials of the First Kind
  • Chebyshev Polynomials of the Second Kind

• Chebyshev Rational Function

• Chebyshev-Sylvester Constant (with James Joseph Sylvester)

• Chebyshev's Sum Inequality (also known as Chebyshev's Inequality)
• Chebyshev's Theorem

• Chebyshev-Grübler-Kutzbach Criterion
• Chebyshev-Markov-Stieltjes Inequalities (with Andrey Andreyevich Markov and Thomas Joannes Stieltjes)

• Bertrand-Chebyshev Theorem (with Joseph Louis François Bertrand)
• Bienaymé-Chebyshev Inequality (with Irénée-Jules Bienaymé) (also known as Chebyshev's Inequality)
• Gauss-Chebyshev Rule (with Carl Friedrich Gauss), also known as the Gaussian Integration Rule
• Roberts-Chebyshev Theorem (with Samuel Roberts)

Results named for Pafnuty Lvovich Chebyshev can be found here.

Definitions of concepts named for Pafnuty Lvovich Chebyshev can be found here.

Publications

• 1847: On integration by means of logarithms
• 1867: On mean values
• 1887: On two theorems concerning probability

Notable Quotes

To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls.

Critical View

He was the only man ever able to cope with the refractory character and erratic flow of prime numbers and confine the stream of their progression within algebraic limits, building up, if I may say so, banks on either side which that stream, devious and irregular as are its windings, can never overflow.

-- James Joseph Sylvester

Also known as

His name in Russian is presented as Пафну́тий Льво́вич Чебышёв.

His name can be seen transliterated into Latin script as Chebychev, Chebysev, Chebyshov, Tchebyshev, Tchebitchev, Tchebycheff or Tschebyscheff, according to the target language.

Some sources even use Čebyšev, but modern usage discourages the unnecessary use of diacritics.

Some sources render his middle name Livovich, but that may be a mistake.

Sources

• John J. O'Connor and Edmund F. Robertson: "Pafnuty Lvovich Chebyshev": MacTutor History of Mathematics archive

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.31$: Chebyshev ($\text {1821}$ – $\text {1894}$)
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Chebyshev (or Chebychev, Chebysev, Chebycheff, Tchebychev, etc.), Pafnuty Lvovich (1821-94)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Chebyshev
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Tchebyshev, Pafnuty Livovich (1821-94)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Chebyshev
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Tchebyshev, Pafnuty Livovich (1821-94)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Chebyshev, Pafnuty Lvovich (1821-94)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Tchebyshev