Because bitcoin is an algorithmic solution to exactly that problem - trust in a distributed system, casually known as the Byzantine Generals Problem, or Two Generals problem [1].
The innovators and early adopters were motivated by their understanding of the utility in finally achieving a solution to that problem in the context of digital currency (not historically possible for digital currencies till the invention of 1) the Internet and 2) the BitTorrent protocol, so essentially a major breakthrough and first in human history). They provided the critical mass, social proof, and wealth effect that then drove later adoption.
Just to nitpick a bit, the Two Generals problem is actually different than the Byzantine Generals Problem. 2GP deals with the (simpler) case of achieving consensus in a distributed system with unreliable communications. That is, messages can be reordered, lost or arbitrarily delayed, but end hosts are assumed to be trustworthy. BGP deals with the aforementioned scenario where nodes can be malicious as well.
Yes, good distinction. I should have linked the Byzantine Fault Tolerance page [1] since it describes that distinction better. Not sure why I went with Two Generals since I looked at both.
The innovators and early adopters were motivated by their understanding of the utility in finally achieving a solution to that problem in the context of digital currency (not historically possible for digital currencies till the invention of 1) the Internet and 2) the BitTorrent protocol, so essentially a major breakthrough and first in human history). They provided the critical mass, social proof, and wealth effect that then drove later adoption.
[1]:https://en.wikipedia.org/wiki/Two_Generals%27_Problem