Map Comparison Fails in Function Const

[JaySoyer]

So I'm very confused on why I'm getting an error here. I've dumbed down my code for simplicity and removed irrelevant code. Hopefully it doesn't take away the issue.

class Foo
{
    public:
        bool IsNull() const;

    private:
        std::map<int, int*> test;
}

bool Foo::IsNull() const
{
    if (test[0] == 0)
        return true;
    else
        return false;
} 

I'm getting a "passing...discards qualifiers" error on my if statement and not sure why because I'm not changing anything. I know removing const or making test mutable fixes the issue. I've been taught to always make a function const if it doesn't change anything, in which case, have I finally come across an acceptable time to use mutable?