Algorithms are the computational content of proofs.

For having a clear influence on methodologies for the creation of efficient and reliable software, and for helping to found the following important subfields of computer science: the theory of parsing, the semantics of programming languages, automatic program verification, automatic program synthesis, and analysis of algorithms.
robert w floydAs the size of software systems increases, the algorithms and data structures of the computation no longer constitute the major design problems. When systems are constructed from many components, the organization of the overall system the software architecture presents a new set of design problems. This level of design has been addressed in a number of ways including informal diagrams and descriptive terms, module interconnection languages, templates and frameworks for systems that serve the needs of specific domains, and formal models of component integration mechanisms.
If I ask another professor what he teaches in the introductory programming course, whether he answers proudly "Pascal" or diffidently "FORTRAN," I know that he is teaching a grammar, a set of semantic rules, and some finished algorithms, leaving the students to discover, on their own, some process of design.
Mathematics my foot! algorithms are mathematics too, and often more interesting and definitely more useful.
doron zeilbergeralgorithms existed for at least five thousand years, but people did not know that they were algorithmizing. Then came Turing (and Post and Church and Markov and others) and formalized the notion.
doron zeilberger