So the thing I'll do is just try and find numbers, that are generated by a program, for no actual reason? What's the point of it?
It's not "
for no actual reason". There is a very important reason for this effort. It is called "proof of work" and it ensures that transactions are not removed/modified after they are complete. The effort of the miners is a service to the entire network. To encourage people to participate in this effort the protocol is designed to reward those who choose to be miners. Every time a new block is added to the blockchain, a reward is created that assigns a predetermined amount of BTC to the miner.
There is no one behind that?
There is a protocol behind it. An agreed to set of rules that are unable to be changed unless a significant number of participants all agree to the change.
No big man making profit from me?
No.
If that's the case how can BTCs actually have any value?
The value is in the usability. People desire to have them for their usability, since you have them and someone else wants them, they are willing to pay for them. Therefore the desire translates to a value.
If you are mining gold out of the ground, who is the "big man making a profit from you". You dig up some gold. Other people want the gold for its usability. They give you something that you value (maybe USD ?) in exchange for the gold that you dug up.
Note: mining BTC does require certain resources (electricity, computer equipment, etc). So the providers of those resources are certainly making a profit off of you.