# Pafnuty Chebyshev

File:Pafnutiy-chebyshev.jpg
Pafnuty Lvovich Chebyshev

Pafnuty Lvovich Chebyshev (Пафну́тий Льво́вич Чебышёв) (May 16 1821 - December 9 1894) was a Russian mathematician. His name is also transliterated as Chebyshov, Tchebycheff or Tschebyscheff (obsolete French and German transcriptions).

One of nine children, he was born in central Russian village Okatovo near Borovsk, to Agrafena Ivanova Pozniakova and Lev Pavlovich Chebyshev. His father fought as an officer against Napoleon's invading army.

He was originally home-schooled by his mother and his cousin Avdotia Kvintillianova Soukhareva. He learned French early in life, which later helped him communicate with other mathematicians. A stunted leg prevented him from playing with other children, leading him to concentrate on studying instead.

Later he studied at Moscow University obtaining his degree in 1841.

He was a student of Nikolai Brashman. His own most illustrious student was Andrei Markov, although Alexandr Liapunov is also famous for the method that bears his name.

Chebyshev is known for his work in the field of probability and statistics. Chebyshev's inequality says that the probability that the outcome of a random variable is no less than a standard deviations away from its mean is no more than 1/a2:

${\displaystyle P(|X-{\mathbf {E} }(X)|\geq a\,\operatorname {sdev} (X))\leq {\frac {1}{a^{2}}}}$

Chebyshev's inequality is used to prove the weak law of large numbers and the Bertrand-Chebyshev theorem (1845|1850) that the number of prime numbers less than ${\displaystyle n}$ is ${\displaystyle p(n)=n/\log(n)+o(n)}$.