Chebyshev is largely remembered for his investigations in number
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-> infinity then that
limit is 1. He was unable to prove, however, that
lim ( pi (n)log n)/n as n-> infinity
exists. The proof of this result was only completed two years after
Chebyshev's death by Hadamard and (independently) de la Vallée
In his work on integrals he generalised the beta function and examined
integrals of the form
integral 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.
Biographies of mathematicians are from the
Mathematics archive at the University of St. Andrews, and are
used with permission.