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Functional programming is a declarative programming paradigm where programs are constructed by applying and composing functions. It emphasizes immutability, lack of side effects, and higher-order functions. In this context, "functions" are first-class citizens, meaning they can be passed as arguments to other functions, returned as values from other functions, and stored in data structures. This style of programming is well-suited for tasks that involve transforming data or computing pure mathematical functions. It has roots in lambda calculus and is a cornerstone of computer algebra systems, making it a natural fit under the "Computer Algebra" category and within the broader context of "Science" and "Mathematics".