Chebyshev is known for his fundamental contributions to the fields of probability, statistics, mechanics, and number theory.

The surname Chebyshev has been transliterated in several different ways, like Tchebichef, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, Tschebyscheff, Čebyčev, Čebyšev, Chebysheff, Chebychov, Chebyshov (according to native Russian speakers, this one provides the closest pronunciation in English to the correct pronunciation in old Russian), and Chebychev, a mixture between English and French transliterations considered erroneous.

Currently, the English transliteration Chebyshev has gained widespread acceptance, except by the French, who prefer Tchebychev.

One of nine children,[5] Chebyshev was born in the village of Okatovo in the district of Borovsk, province of Kaluga.

Pafnuty Lvovich was first educated at home by his mother Agrafena Ivanovna Pozniakova (in reading and writing) and by his cousin Avdotya Kvintillianovna Sukhareva (in French and arithmetic).

Chebyshev mentioned that his music teacher also played an important role in his education, for she "raised his mind to exactness and analysis".

From childhood, he limped and walked with a stick and so his parents abandoned the idea of his becoming an officer in the family tradition.

[citation needed] In 1832, the family moved to Moscow, mainly to attend to the education of their eldest sons (Pafnuty and Pavel, who would become lawyers).

Education continued at home and his parents engaged teachers of excellent reputation, including (for mathematics and physics) the senior Moscow University teacher Platon Pogorelsky [ru], who had taught, among others, the future writer Ivan Turgenev.

[citation needed] In summer 1837, Chebyshev passed the registration examinations and, in September of that year, began his mathematical studies at the second philosophical department of Moscow University.

Brashman instructed him in practical mechanics and probably showed him the work of French engineer J.V.

In this, Chebyshev derived an approximating algorithm for the solution of algebraic equations of nth degree based on Newton's method.

[citation needed] Although they could no longer support their son, he decided to continue his mathematical studies and prepared for the master examinations, which lasted six months.

Chebyshev passed the final examination in October 1843 and, in 1846, defended his master thesis "An Essay on the Elementary Analysis of the Theory of Probability."

His biographer Prudnikov suggests that Chebyshev was directed to this subject after learning of recently published books on probability theory or on the revenue of the Russian insurance industry.

[citation needed] In 1847, Chebyshev promoted his thesis pro venia legendi "On integration with the help of logarithms" at St Petersburg University and thus obtained the right to teach there as a lecturer.

At that time some of Leonhard Euler's works were rediscovered by P. N. Fuss and were being edited by Viktor Bunyakovsky, who encouraged Chebyshev to study them.

[citation needed] During his lectureship at the university (1852–1858), Chebyshev also taught practical mechanics at the Alexander Lyceum in Tsarskoe Selo (now Pushkin), a southern suburb of St Petersburg.

: Fifty years later, in 1896, the celebrated prime number theorem was proved, independently, by Jacques Hadamard[7] and Charles Jean de la Vallée Poussin:[8] using ideas introduced by Bernhard Riemann.