This Paper Makes an Attempt to Study a Role of Mathematics As the Current Thinking of Collaborative Approach to Inter-Disciplinary Trends Towards Enriched Society In the 21St Century. It Begins With Trends of Applications of the 20Th Century Bridging the Line of Inter-Disciplinary Research. It Tries to Address the Changes In Mathematics Applications As a Result of the Modern Approach to Mathematics and Discoveries In Other Fields Such As Computer, Socio-Economic, Medical Science, Biological Science, Industries, Business, Environmental Sciences, Etc. the Paper Also Highlights What Are the Hindrances In Bridging the Integrated Knowledge Towards Enriched Society Suggesting Fuzzy Mathematics As a New Area Where Mathematics Is Emerging As Vital Trends With Greater Opportunities For Inter Disciplinary Research.