I have no idea what you just said or why solving complicated maths equations generates value. Who is benefiting from the solved equations?
there are some somewhat shady "exchanges" where you can trade them for real currency.
they are also a god send for criminals, as it's a completely untraceable method of paying for things.
There are are finite number of Bitcoins. They are hidden in encrypted blocks - anyone can buy an unencryption machine and start mining blocks. They get a certain number of Bitcoins for every block they uncover, unlocking the extra Bitcoins.
The reward they get reduces eventually as the more they uncover the more the value of individual Bitcoins decreases.