Indeed.

But money was not created by academics. It evolved over centuries and the monetary media concerned were chosen by ordinary people, not academics, based on their ability to see and verify the integrity of the said medium.

The more you can see and verify, the more valuable the monetary medium. The less you can see and verify, the less valuable the monetary medium.

I don't need to convince you of that principle. Satoshi already understood it and built it into bitcoin. The fact that there is no counterparty underwriting the numbers in a bitcoin address means that the public is the caretaker and counterparty and therefore has to see everything. That includes the balances at all addresses, the transaction ID and the movement at each end.

Saying that "it's all taken care of by math" is b.s. The shadowcash experience has demonstrated that and ring signatures, stealth addresses and all other toytown trainspotter spyware are now toast because of it. (They always were to me, I just didn't expect a practical example to arrive so soon).