TLDR: Anonymous functions are like secret agents in programming. They are functions that don't have a name and can be used in different ways. They are often used as arguments in other functions or to create new functions. They have been around since the 1930s and are commonly used in many programming languages.

Anonymous functions, also known as function literals, lambda abstractions, or lambda expressions, are a type of function in computer programming that don't have a name. They are often used as arguments in higher-order functions or to create new functions. Higher-order functions are functions that can take other functions as arguments or return functions as results.

The use of anonymous functions can make code more concise and readable, especially when the function is only used once or a limited number of times. They are commonly used in functional programming languages and other languages that support first-class functions, where functions can be treated as values.

Anonymous functions have been around since the 1930s when they were introduced by Alonzo Church in his work on lambda calculus. Lambda calculus is a mathematical system that deals with anonymous functions. Since then, anonymous functions have been a feature of many programming languages, starting with Lisp in 1958.

Anonymous functions can be used in various ways. One common use is for sorting elements in a non-standard way. Instead of creating a named function for the sorting logic, an anonymous function can be used to define the sorting criteria. For example, in Python, you can sort a list of strings by their length using an anonymous function.

Another use of anonymous functions is in closures and currying. Closures are functions that are evaluated in an environment that contains bound variables. They are often used to create functions that remember the values of variables from their enclosing scope. Currying is the process of transforming a function that takes multiple arguments into a sequence of functions, each taking a single argument.

Anonymous functions are also commonly used in higher-order functions like map, filter, and fold. Map applies a function to each element of a list, filter returns a new list containing only the elements that satisfy a condition, and fold combines all elements of a list into a single value.

In summary, anonymous functions are a powerful tool in programming that allow for more flexible and concise code. They can be used in various ways, such as sorting, closures, currying, and higher-order functions. They have been around for a long time and are supported by many programming languages.