Early Bitcoin client versions allowed users to use their CPUs to mine. The advent of GPU mining made CPU mining financially unwise as the hashrate of the network grew to such a degree that the amount of bitcoins produced by CPU mining became lower than the cost of power to operate a CPU. The option was therefore removed from the core Bitcoin client's user interface.
What bitcoin miners actually do could be better described as competitive bookkeeping. Miners build and maintain a gigantic public ledger containing a record of every bitcoin transaction in history. Every time somebody wants to send bitcoins to somebody else, the transfer has to be validated by miners: They check the ledger to make sure the sender isn’t transferring money she doesn’t have. If the transfer checks out, miners add it to the ledger. Finally, to protect that ledger from getting hacked, miners seal it behind layers and layers of computational work—too much for a would-be fraudster to possibly complete.
Paint mixing is a good way to think about the one-way nature of hash functions, but it doesn’t capture their unpredictability. If you substitute light pink paint for regular pink paint in the example above, the result is still going to be pretty much the same purple, just a little lighter. But with hashes, a slight variation in the input results in a completely different output:
Nakamoto is estimated to have mined one million bitcoins before disappearing in 2010, when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation. Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin.