Very often people say that Bitcoin is a system where you do not need to trust people, just math. I suggest to look at this problem from another angle. Now I will try to prove that this is a system of trust between people.
Imagine for a moment that aliens flew to Earth, met us and they liked Bitcoin. They watched mining, installed an ultrafast internet connection and flew away. On their planet, they gave their scientists the opportunity to set up production of miners, and the total hashrate began to increase rapidly (and it is easy to hide from which planet the blocks come). Mining pools have become very small and now occupy no more than 0.1% of the total processing power. As it turned out, their mathematicians have moved much further, and do not consider the current Bitcoin developers intelligent people at all. New changes began to appear in the protocol, which were first understood by scientists from the Earth. All the changes raised the productivity, security, anonymity of Bitcoin.
Now questions to think about:1. If at some point (due to communication delays), double spending attacks occur, and it is not at all possible to establish who did that — there could already be no identified pools-how to find a social consensus as to what is good, and what is bad?2. What if scientists from the Earth at all ceased to understand the mathematics on which the changes were based? (Who generally understands how ZCash works? Even SegWit/Lightning Network is understood by a few percent of people who develop applications on Bitcoin). Can a large investor now call his friend Peter Todd, and ask — “Hey, can you tell me, what risk will I face if I update?”
In the end, trusting Bitcoin, we trust not just mathematics. We trust MATHEMATICIANS. Which we know. If there are more than one, we can sleep at least a little bit better. Discussions between these mathematicians help us understand that they are in consensus at least about something (and it happens publicly on forums, let’s say when DAO hack comes).
And one more question — who does your mother trust when you say “Mom, keep all the money in bitcoins” — you or Satoshi Nakamoto / Core Dev / 51% hashrate?
Bitcoin is about SOCIAL consensus, which is reached using math, but only among people who know and understand each other.