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Pafnuty Chebyshev

Master of Approximation and Number Theory

Pafnuty Lvovich Chebyshev (1821–1894) was a towering figure of Russian mathematics, often called the “father of Russian pure mathematics.” His works covered probability, approximation theory, and number theory, and he trained an entire generation of mathematicians who advanced Russian science in the 19th century.

Contributions

• Probability — Chebyshev’s inequality laid the foundation for modern statistics, bounding the probability that a random variable deviates from its mean: \[ P(|X - \mu| \geq k\sigma) \leq \frac{1}{k^2} \]
• Number Theory — He worked on the distribution of prime numbers and proved results that anticipated the Prime Number Theorem.
• Approximation Theory — Introduced Chebyshev polynomials \(T_n(x)\), essential in minimizing approximation errors.

Legacy

Chebyshev’s school shaped Russian mathematics, producing major successors like Markov and Lyapunov. His focus on rigor, applications, and education firmly established Russia on the global mathematical map.

Facts

• Born near Moscow, Russia.
• Known as the founder of the St. Petersburg school of mathematics.
• Mentor to Markov and Lyapunov.
• Namesake of Chebyshev polynomials and inequalities.