Pafnuty Lvovich Chebyshev (1821 - 1894)

Chebyshev was born in Okatovo in western Russia, and was one of nine children. He was prevented from taking part in many typical childhood activities because he had one leg longer than the other, which caused him to limp.

The family moved to Moscow when Chebyshev was eleven years old, and just five years later went to study mathematical sciences at the Moscow University. He got his first degree in 1841 and went on to study for his Master’s degree. It is clear that Chebyshev was interested in international recognition from the very start of his career - his very first paper was on multiple integrals and was also written in French!

Chebyshev has many mathematical results that are attached to his name. In the field of probability, he derived a fundamental inequality about any distribution. It was the foundation for much later work by Statisticians. However, he is mainly known for his work in Number Theory, and particularly for some incredible work with prime numbers.

He became assistant professor of mathematics at the University of St. Petersburg in 1847, and over the next six years published some of his most famous papers on number theory.

In 1849 Chebyshev submitted, for his doctorate, perhaps his most important book Teoria sravneny (‘Theory of Congruences’), which made him widely known in the mathematical world and was used as a textbook in Russian universities for many years, for which he was awarded a prize from the Academy of Sciences.

Chebyshev was promoted to extraordinary professor at St Petersburg in 1850, and travelled extensively to France, London and Germany.

During these trips he took the opportunity to investigate his other areas of interest, namely various types of steam engines and their mechanics.

His mathematical writings covered topics such as the construction of geographic maps, the calculation of geometric volumes and the construction of calculating machines.

In mechanics he studied 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 many papers on his mechanical inventions and some of these models and drawings were exhibited at the Conservatoire National des Arts et Métiers in Paris.

In 1893 a number of his mechanical inventions, including his special bicycle for women, were exhibited at the World’s Exposition in Chicago, which was a celebration of the 400th anniversary of Christopher Columbus’ discovery of America.

He pioneered the St. Petersburg mathematical school and was renowned for his work on the theory of prime numbers and on the approximation of functions.

Chebyshev’s mathematics

Two years after Chebshev’s death, an important breakthrough was to be made on a long outstanding problem about primes - how they are distributed.

This is called the Prime Number Theorem, and it concerns the number of primes that do not exceed a given number. Simply stated it is that the number of primes that do not exceed n, \lambda(n) is given by,

\lambda(n)\approx{n\over\log n} here \approx means ‘approximately’.

Gauss, and many others, had explored millions of prime numbers and thought that they were distributed in such a way.

In order to understand this approximation, think of it like this: the probability of any whole number being prime is inversely related to the number of digits needed to express it in a particular number base - the exponential base, e. But no one could prove it. Chebyshev came very close. His work includes: