Abstract : Mathematical research is mainly driven by internal questions ( internal to Mathematics). But when it is influenced by external questions, there is no liberty to change the original theme and couple of such questions which are bothering us for the last two decades will be the focus of this talk. In order to understand the context, when mathematical model is formulated to explain approximately certain physical reality, it is important to derive relevant properties mathematically. Say for example in some viscoelastic fluid flows, numerous experiments suggest that after an instantaneous cessation of the external force, the velocity of the fluid dies down with a certain rate. Translating and proving this kind of property pose a challenge in Mathematics research. Starting with a model in a layman's language, in this talk, relevant mathematical issues summarizing our efforts for the last 20-25 years will be briefly discussed. If time permits in the later part of this talk, the focus will be on the following question posed by the user community ` How do we believe the numbers crunched by the machine using an algorithm? Finally, we conclude the talk with some mathematical issues.