Thanks for link, that's a very nice arcticle.
So guys, I have found answer of my 1 of my question "why theres a mathematical question to be solved to be able to valid the transaction"
It's goes like this" because long chains are always trusted for transactions, a mathematical puzzle needs to be solved ( which should take time ) so no one can create fake blocks quickly alone by himself quickly which then may outrun the legit blocks.
Correct me if I'm wrong or missing something here, I'm reading more to find out about other question's answers.