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He co-authored a complete edition of Euler's 99 number theory papers, in a two-volume set published in 1849. In 1850, Chebyshev proved Bertrand's conjecture that there is always at least one prime between n and 2n, for n > 3. Chebyshev also made progress on proving the Prime Number Theorem.

He co-authored a complete edition of Euler's 99 number theory papers, in a two-volume set published in 1849. In 1850, Chebyshev proved Bertrand's conjecture that there is always at least one prime between n and 2n, for n > 3. Chebyshev also made progress on proving the Prime Number Theorem.

Subsequently, Chebyshev made his greatest contribution by advancing the understanding of orthogonal polynomials, and "Chebyshev polynomials" are named after him.  This generalized the work of Legendre and Laplace

Subsequently, Chebyshev made his greatest contribution by advancing the understanding of orthogonal polynomials, and "Chebyshev polynomials" are named after him.  This generalized the work of Legendre and Laplace.

In probability, Chebyshev was the first to clarify the concepts of "random quantity" and its "expectation (mean) value."  

In probability, Chebyshev was the first to clarify the concepts of "random quantity" and its "expectation (mean) value."