In 1847, Pafnuty 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 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 got large, then that limit is 1. He was unable to prove the existence of the limit however. The proof of this result was only completed two years after Chebyshev's death independently by Hadamard and de la Vallée Poussin.

In his work on integrals, he generalized the beta function. 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.