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On the nature of the Theory of Computation (ToC)

[This paper is a (self contained) chapter in a new book on computational complexity theory, called Mathematics and Computation, available at https://www.math.ias.edu/avi/book]. I attempt to give here a panoramic view of the Theory of Computation, that demonstrates its place as a revolutionary, disruptive science, and as a central, independent intellectual discipline. I discuss many aspects of the field, mainly academic but also cultural and social. The paper details of the rapid expansion of interactions ToC has with all sciences, mathematics and philosophy. I try to articulate how these connections naturally emanate from the intrinsic investigation of the notion of computation itself, and from the methodology of the field. These interactions follow the other, fundamental role that ToC played, and continues to play in the amazing developments of computer technology. I discuss some of the main intellectual goals and challenges of the field, which, together with the ubiquity of computation across human inquiry makes its study and understanding in the future at least as exciting and important