Bitcoin is "secure" until P!=NP.
if someone one day finds out that P is equal to NP, then bitcoin will not be safe anymore.
But if this happends also everything that atm is considered secure will not be anymore (e.g. homebanking).
Apart from that, Bitcoin is not just cryptography.
There are many companies that allow users to purchase sell and manage bitcoins, if their servers are not secure, then also bitcoins that they manage are not secure and can be stealed.
Moreover, Social Engineering is always there, waiting for you to make a mistake.
So, Bitcoin is secure? In my opinion, the answer is no. Nothing is secure because humans are weak, easy to control, and most of the time: Stupid.