Why is a static method considered a method?

I'm writing an explanation for some code for a course, and have been accidentally using the words method and function interchangeably. I decided to go back over and fix the wording, but ran into a hole in my understanding.

From what I understand, a subroutine is a function if it doesn't act on an instance of a class (its effect is restricted to its explicit input/output), and is a method if it operates on an instance of a class (it may carry out side effects on the instance that make it impure).

There's a good discussion here on the topic. Note that by the accepted answer's definitions, a static method should actually be a function because an instance is never implicitly passed, and it doesn't have access to any instance's members.

With this is mind though, shouldn't static methods actually be functions?

By their definition they don't act on particular instances of a class; they're only "tied" to the class because of relation. I've seen a few good looking sites that refer to static subroutines as "methods" though (Oracle, Fredosaurus, ProgrammingSimplified), so either they're all overlooking the terminology, or I'm missing something (my guess is the latter).

I'd like to make sure I am using the correct wording.
Can anybody clear this up?

Solution 1:

This quote from 8.4.3.2 may help:

A method that is declared static is called a class method.

A method that is not declared static is called an instance method [...].

• Class methods: associated with a class.
• Instance methods: associated with an instance.

Java just wants you to "think object-oriented". Also, static methods have access to a surrounding scope which may include state. In a way, the class is like an object itself.

Solution 2:

The simple answer is that when Java decided to call everything a "method", they didn't care about the distinction between a function and a method in theoretical computer science.

Solution 3:

Static methods are not exactly functions, the difference is subtle, but important.

A static method using only given input parameters is essentially a function.

But static methods may access static variables and other static functions (also using static variables) so static methods may have a state which is fundamentally different to a function which are by definition stateless. (ADDENDUM: While programmers are often not so strict with using "function" as definition, a strict function in computer science can access only input parameters). So defining this case of accessing static fields it is not valid to say that static methods are always functions.

Another difference which justifies the usage of "static method" is that you can define in C derivates global functions and global variables which can be accessed everywhere. If you cannot access the class which contain static methods, the methods are inaccessible, too. So "static methods" are limited in their scope by design in contrast to global functions.