[Image taken from here]
We've established that a node in the Bitcoin network doesn't need to trust its neighbors to tell the truth, it only needs to trust in math. Here is a bit more detail on that.
You may have heard of Bitcoin "mining", and wondered what that is. Bitcoin mining is searching for a solution to a mathematical puzzle. In a nutshell, the first node to find such a solution earns the right to append the next block of transactions to the blockchain, and pocket some Bitcoin as a reward. The solution found by the node is called "Proof of work", because it is a piece of evidence that the node has spent a significant amount of computational work on the mathematical puzzle.
However, it shouldn't really be called proof of work, because it hasn't been mathematically proven that there isn't an easy way to obtain a solution. Rather, we believe that there is no easier way to find a solution than "brute force" grunt work, because to this day no mathematician has published a cleverer method. So really, rather than trust in math, we trust in mathematicians!
To summarize, when you use Bitcoin, you don't need to trust a bank, but you do need to trust the (unproven) assumption that the underlying mathematical puzzles actually require significant computational work.
To learn more, check out the next episode!
