Explore the foundational concepts of theoretical computer science in this lecture from CMU's "Great Ideas in Theoretical Computer Science" course. Delve into Turing's legacy, examining the concept of problems as mappings of instances to solutions and the limitations of this approach. Investigate interpreters and the invention of Turing Machine programming languages. Learn the official definition and visual representation of Turing Machines, and discover essential TM subroutines and tricks. Gain insights from Professor Ryan O'Donnell's expertise in this comprehensive exploration of computational theory.