I was trying Math m = new Math(); and later found that Math constructor is private and it does not have any other constructors as well. I understand that all the methods in Math are static but i was just trying my SCJP knowledge. Here is the code of class Math taken from Sun Java 1.5
In real world if requirement is to write a Utility class that has only static methods then is the above behavior of making the constructor private done just to avoid instantiation of the class inorder to save memory? Or is there any other significance behind this?
Making the constructor private is a common trick for utility classes that contain only static methods and that should not be instantiated or subclassed.
Note that making the constructor private also makes it impossible to make a subclass, because the constructor of the subclass needs to be able to access the constructor of the superclass, and it can't if the constructor of the superclass is private.
I wouldn't say this is just "to save memory". Utility classes such as Math are not supposed to be instantiated. Calling static methods via an instance reference is bad style. Making it impossible to instantiate a class prevents users from using that bad style.
Making the class abstract still allows someone to extend the class and then instantiate that subclass. A private constructor prevents instantiation of both the class itself and any subclasses.
But note that Math is also declared to be final, to prevent it from being subclassed at all. Unfortunately, you can't declare a class as both final and abstract at the same time, so it still needs to define the private constructor to prevent instantiation.