Short answers, pulled from the story.
Pafnuty Lvovich Chebyshev was born in the village of Okatovo within the district of Borovsk and the province of Kaluga. He suffered from Trendelenburg's gait which caused him to limp and walk with a stick throughout his youth.
Pafnuty Chebyshev defended his master thesis An Essay on the Elementary Analysis of the Theory of Probability in 1846 after passing his final examination in October 1843. He had previously passed registration examinations at Moscow University in summer 1837.
The Chebyshev inequality states that if x is a random variable with standard deviation sigma greater than zero then the probability that the outcome of x is k or more away from its mean is at most one over k squared. This statement provides bounds on probabilities without requiring knowledge of the exact distribution of values.
The Bertrand Chebyshev theorem from 1845 and 1852 states that for any integer n greater than one there exists a prime number p such that n is less than p and p is less than two times n minus two. This result follows from Chebyshev inequalities for the number pi of prime numbers less than x.
Pafnuty Chebyshev presented a paper on garment cutting to the French Association for the Advancement of the Sciences in 1878. His research included the development of the Chebyshev linkage which was designed to convert rotational motion into approximate straight-line movement.