Answer.

Historically, in some languages (like C++), programming allows for operator overloading to make user-defined data types more "natural" to work with. In Java, during the language's design phase, the decision was made not to support operator overloading to combat excessive complexity and unreadability of code.

The problem is that sometimes it would indeed be convenient to define operator behavior for your objects, for example, + for vector addition, but this is not allowed in Java at the syntax level.

The solution is to define regular methods (like add, multiply) for working with objects or to use standard approaches: overriding equals() and compareTo() methods for comparisons; or applying design patterns (like the "Builder" or "Composite" pattern).

Example code:

public class Vector {
    private int x, y;
    public Vector(int x, int y) { this.x = x; this.y = y; }

    public Vector add(Vector other) {
        return new Vector(this.x + other.x, this.y + other.y);
    }

    @Override
    public String toString() {
        return "Vector(" + x + ", " + y + ")";
    }
}

Vector v1 = new Vector(1, 2);
Vector v2 = new Vector(3, 4);
Vector sum = v1.add(v2); // "Vector(4, 6)"

Key features:

Java does not support user-defined operator overloading
The equals() and compareTo() methods are used for comparison operators, and custom methods for arithmetic operations
This approach makes the code explicitly readable and predictable

Trick Questions.

Can you "overload" the == operator in Java for your classes to compare values instead of references?

No, the == operator always compares references for object classes. To compare values of objects, you need to override equals() and use it wherever logical equivalence is important.

Can you somehow make the behavior of "a + b" for your own classes?

Only through regular methods, like a.add(b). The syntax for operator overloading, as in C++, is not supported.

Do strings (String) not behave like overloaded + operator in Java?

Actually, string concatenation using + works only for the String type and is supported at the compiler level — this is a special syntax rule.

Common Mistakes and Anti-Patterns

Expecting that the == operator will compare object values
Trying to write code like a + b for your own classes, even though such syntax is impossible
Not implementing equals() and hashCode(), leading to bugs with collections

Real-life Example

Negative case

A developer uses == to compare two points for the "Point" class and expects the comparison to give true for matching coordinates.

Pros:

The code looks simple

Cons:

Almost always gives false results if the points are created at different times or by different constructors

Positive case

A developer implements the equals() method to compare the contents of points, and uses the add() method for addition.