So where are the transactions stored? Nodes?
I was studying the mining rigs and noticed there aren't any hard drives on them.
So the mining is just computing the mathematical algorithms, and fills up nodes.
So where are the nodes stored?
Generally, full nodes are run by solo-miners, mining pools, and merchants, but a node can be run by anybody that has enough resources and wants to. There is no need to gain permission from any entity first. Just install the software and run it.
Mining consists of 2 pieces...
The first piece is verifying the transactions and blocks that are received as well as building new blocks (you need a full node to do this). The second piece is the "proof-of-work", which involves calculating a HUGE number of SHA256 hashes to search for a nonce that will result in a low enough hash value (you need ASIC hardware to do this).
A solo-miner handles both of these pieces themselves.
Miners that mine in a mining pool are actually only performing the "proof-of-work" portion. They rely on the pool to run the node and handle the verification for them. Since they are simply calculating SHA256 hashes as fast as possible on 80 bytes of data that is supplied to them from the pool, they don't need a hard drive.