When your life has no connection with your Creator, then your life becomes empty with no purpose. The one who does not have Allah in his life, is nearer to be suffering from grief and madness. There is nothing in his life to give real value and meaning.
Watch the video: A talk once given by Prof. Jeffrey Lang. (He is a Professor of Mathematics at the University of Kansas).
I felt that his talk was really amazing and answered the questions that were in the minds of many people whether they are Muslims or not.
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The purpose of life :-
Additional talks (If you are interested):
The same talks as above, but with some additional points and clarity.
How he became Muslim (taking the syahadah) :-