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Pafnuty Lvovich Chebyshev

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Born: 16 May 1821 in Okatovo, Russia

Died: 8 Dec 1894 in St Petersburg, Russia

See a Russian article
from the Brokhaus & Efron Dictionary
In 1847 Chebyshev was appointed to the University of St Petersburg.
He became a foreign associate of the Institut de France in 1874 and also
of the Royal Society.

His work on prime numbers included the determination of the number of
primes not exceeding a given number. He wrote an important book *Teoria
sravneny* on the theory of congruences in 1849.

In 1845 Bertrand conjectured that there was always at least one prime
between n and 2n for n > 3. Chebyshev proved Bertrand's conjecture in 1850.
Chebyshev also came close to proving the prime number theorem, proving
that if

(\pi(n)log n)/n

had a limit as n->\infty then that limit is 1. He was unable to prove,
however, that this limit exists. The proof of this result was only completed
two years after Chebyshev's death by Hadamard and (independently) de la
Vallée Poussin.
In his work on integrals he generalised the beta function and examined
integrals of the form

\int x^{p}(1-x)^{q}
dx.

Chebyshev was also interested in mechanics and studied the problems involved
in converting rotary motion into rectilinear motion by mechanical coupling.
The Chebyshev parallel motion is three linked bars approximating rectilinear
motion.
He wrote about many subjects, including probability theory, quadratic
forms, orthogonal functions, the theory of integrals, the construction
of maps, and the calculation of geometric volumes.

About Chebyshev's attitude towards applications, see an interesting
remark by Clive J. Grant and a quotation
by Chebyshev.

Academician (1859), Fellow of Berlin Academy (1871), Bologna Academy
(1873), Paris Academy (1874), the Royal Society (1877), Swedish Academy
(1893).

**List of References**

Article by: *J.J. O'Connor and E.F. Robertson*

Source: MacTutor History of Mathematics archive