It's an interesting concept, but his main sell was anonymity, and and we all know by know there's no such thing. The blockchain can be traced back.
The math behind it is solid, as long as we don't find a quicker way to solve the discrete logarithm problem of elliptic curves. Unfortunately, that's exactly what Shor's algorithm for quantum computers does, so as soon as you can have a multiple qubit quantum system, bitcoin is in peril (same with RSA encyrption, BTW).
You should also look at the weaknesses before investing:
https://en.bitcoin.it/wiki/Weaknesses