A main method must be public, static, and return void (see JLS §12.1.4).

For example, the following method is confusing, because it is an overload of a valid main method (it has the same name and signature), but is not a valid main method:

class Test {
  static void main(String[] args) {
    System.err.println("hello world");
  }
}

$ java T.java
error: 'main' method is not declared 'public static'

TIP: If you're declaring a method that isn't intended to be used as the main method of your program, prefer to use a name other than main. It's confusing to humans and static analysis to see methods like private int main(String[] args).