The birthday paradox basically says that you can expect a collision when you've explored the square root of the problem space. For birthdays, you expect a collision in a group of sqrt(365) ~= 19 people.
For a 256-bit hash, you expec a collision in a group of 2^128 hashes. That is still huge. Absent a weakness in the hash being found, it's unlikely anyone will ever generate two colliding hashes.
For a 256-bit hash, you expec a collision in a group of 2^128 hashes. That is still huge. Absent a weakness in the hash being found, it's unlikely anyone will ever generate two colliding hashes.