The Math of Bitcoins

What is Bitcoin?

Bitcoin is a peer-to-peer payment system and digital currency introduced as open source software in 2009 by developer Satoshi Nakamoto. It is a cryptocurrency, so-called because it uses cryptography to control the creation and transfer of money.[5] Conventionally, the capitalized word “Bitcoin” refers to the technology and network, whereas lowercase “bitcoin” refers to the currency itself.[6] (Wikipedia)

How to mine for Bitcoins using Math?

Source: http://www.huffingtonpost.com/2013/12/02/bitcoin-basics-explained_n_4374031.html

Adding transactions to the block chain and updating a local copy of the block chain is part of a process called mining. At the same time that miners (nodes in the network) are doing the important work of processing and recording transactions, they are also competing in a race.  They are racing to “complete the current block” in order to win bitcoins.

Mining is a serious competition nowadays and it consumes large computing resources.  Although it’s possible to mine on a laptop, the math problems have become hard enough that a laptop’s CPU will likely never complete a block on its own.  The cost of the electricity needed to run the mining software would exceed the return for mining.  Macs and PC are certainly capable of computing hash functions, but are too slow compared to specialized mining hardware that is now available.

Bitcoin mining serves 2 purposes, it creates the general ledger of Bitcoin transaction and provides security.  The miners compile the transactions together into a “block” and add it to the “Bitcoin blockchain.”  If there was a central authority this would need to be done once and verified by that central authority.  However, there is no central authority in Bitcoin and these blocks need to verified in some way.  Many Bitcoin Miners all over the world are compiling these transactions.  At the end of the compilation they essentially print a lottery number at the bottom.  Each miner is doing this millions or billions of times per second. (Source: http://cointext.com/bitcoin-mining-whats-it-all-about/)