The Intention of This Paper Is to Study the Recent Trends In Present-Day Mathematics and Role of Mathematics In Other Disciplines. the Paper Is In Five Parts. Section One Is Introduction. Section Two Is Dealing With Trends of Application Areas of Mathematics at the Wake of the Twentieth Century, Section Three Looks at the Changes In Mathematics Application As a Result of the Modern Approach to Mathematics and Discoveries In Other Fields, Section Four Addresses The Current Thinking of Collaborative and Inter Discipline Mathematics and the Section Five Gives some Examples Of Application Areas Where Mathematics Is Emerging As a Vital Component With Great Opportunities For Inter Discipline Research.