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Source: www.vnbitcoin.org June 3, 2014 – 06:01

The equations provide a way to prevent...

2014-01-26 14:02:30 by -

..double spending.
Suppose I sent you 10.5 BTC and turned around and sent that same 10.5 BTC to somebody else (perhaps one of my own wallet addresses)?
Who does it belong to?
The answer to that question depends on the Bitcoin blockchain.
Typically, the second transaction will get rejected by the entire network.
There may be cases where approximately half of the network thinks the coins belong to you, and the rest of the Bitcoin network thinks the 10.5 BTC belongs to the other address.
At this point, we say the blockchain has "forked"