Now, I have a pretty simple question to ask , How does Bitcoin benefit from giving us money for solving math problems? Another question is that why does it want us to do it? & is there a bigger purpose behind it???
"Bitcoin" is not a company. Bitcoin is an open-source project and a lot of people are working on it. And an open-source project does not need to get rich. The intention of a big part of that community is more like "changing something".
How does Bitcoin benefit from giving us money for solving math problems?
You did probably not understand that "solving the sha256-algorithm (that's what solving math problems means)" secures the network by preventing double-spends.