In this episode, we explore the question of computational limits using the Turing Machine Argument . Here, we will learn how mathematicians have approached the problem of characterizing the computational limits of computing machines by using many examples. We are interested in useful mathematics which can help  solve real-world problems. If the assumptions and conclusions of the mathematical model makes contact with reality, then mathematics can be an amazingly powerful tool which can then play a crucial role in the development and evaluation of complex systems such as artificially intelligent machines.