Here's what is meant by operators and methods.Attempting to keep the questions as simple and open ended as possible, since the question is more about the conceptual nature of operators and methods NOT how a language has decided to implement them. Proof of Concept: This example in Ruby is more of a proof of concept than anything else. EXAMPLE: In Ruby, 1+2 is equivalent to 1.+(2), meaning the object 1 implements a method called + with object 2 as the method's argument.
Are operators just special methods?
computer science;syntax
Some languages (SML of NJ comes to mind) allow you to declare functions as infix. In this case a function and an operator are pretty much identical, differing only in notation. I can neither recall nor google up the source, but I've read an essay claiming that Combinatory Logic has, as its (philosophical) roots, the desire to make operators the foundation of mathematics.I think you'll probably get a lot of bad arguments both for and against the idea of operators being identical to functions.  The arguments will feel similar to arguments about what's an object?, except that mathmatically, function and operator really are identical, while object doesn't have a good mathematical foundation.