Pafnuty Chebyshev

Pafnuty Lvovich Chebyshev (Пафнутий Львович Чебышёв) (May 16 1821 – December 9 1894) was a Russian mathematician. His name is also transliterated as Chebyshov, Tchebycheff or Tschebyscheff (obsolete German transcription).

He was born in western Russian city Okatovo, in the family of Agrafena Ivanova Pozniakova and Lev Pavlovich Chebyshev with 9 children. His father fought as an officer against Napoleon's invading army.

His was originally home-schooled by his mother and his cousin Avdotia Kvintillianova Soukhareva. He learned French early in life that helped him in the future to communicate with other mathematicians. From childhood he had one leg longer than another that prevented him from playing with other kids and allowed to concentrate on studying.

Later he joined Moscow University.

He was a student of Nikolai Brashman. His own most illustrious student was Andrei Markov.

He 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:

<math>P(|X – {\mathbf E}(X)| \ge a\,\operatorname{sdev}(X)) \le \frac {1}{a^2} <math>

Chebyshev's inequality is used to prove the weak law of large numbers and the Bertrand-Chebyshev theorem (1845|1850) that number of primes less than n is <math>p(n)=n/log(n)+o(n)<math>.

See also

• Bienaymé-Chebyshev inequality – (1853|1866)
• Chebyshev distance
• Chebyshev filter, in electronics and signal processing, a family of electronic filters
• Chebyshev polynomials
• Chebyshev's sum inequality

External link

• MacTutor biography