On the probability of mutual simplicity of two randomly chosen natural numbers (Chebyshev's problem and its history)

The talk attempts to demonstrate the rich history of one truly remarkable problem situated at the confluence of probability theory and theory of numbers ‒ finding the probability of co-primality of two randomly selected natural numbers. The goal of the talk is to reveal the genesis of the problem and understand the role of mathematicians of the past (Dirichlet, Kronecker, Chebyshev, Cesaro, Sylvester, Erdős, and others) in solving this problem and using it as a background for advancing mathematical ideas. The talk also describes different approaches to the solution of the problem, reviews its various generalizations, examines similar problems, and offer diverse further perspectives.