Thanks!  

I agree that the chance of those assumptions being broken is not worth worrying about; it would be like worring that three nuclear reactors may melt down and explode at the same time.  

However I would dispute the assertion that the two assumptions that I listed are "well grounded in reality" -- in the same sense that, say, physical laws like gravitation, conservation of energy etc.  are.

Basically the only "proof" of those two assumptions is that many bright people have spent lots of time trying to find fast ways to solve those problems, over the last 40 years, and failed. But that is not a statistically significant result, because the space of all algorithms, even of modest size, is extremely large; so even all that work has explored only an infinitesimal fraction of it.

For the physical laws, in contrast, one can argue that all our collected experience and measurements are statistically significant  "proof" that they work, at least in the realms that we have experienced.  Doubting them (in those realms) is certainly a waste of time.

Moreover, the techniques that we scientists use to find fast algorithms are such that we can only find "obvious" ones, in a sense. So there may exist a relatively short algorithm that quickly solves the bitcoin mining problem, say; but, even if we find it somehow, and check that it works in quintillion of cases, we may be unable to understand how it does it.  (You are aware of the Collatz problem I suppose.)

(You are not referring to the P != NP conjecture I suppose?  It is just as uncertain, but it has absolutely no relevance to those two assumptions in the bitcoin protocol.)

(By the way, until the 1980s many people were quite certain that the linear programming problem could not be solved in polynomial time, because many bright people etc. etc..  Some even had started to build a theory of "LP-complete problems".  Then a Russian mathematician found a polynomial algorithm, by thinking out of the box.)