MD5 theoretical question Ok, so this is a very possible stupid question, but one of those things that has sat at the back of my mind for a while.

We all know that MD5 has issues, and these have been known for about a decade.  So this is theoretical.  I'm not considering using it for anything.

Question is this.  If MD5 generates a 32 digit number in hex, given that 32 is finite, and we can hash longer and longer values, didn't we know from the offset that MD5 had to have collision issues?
Basically all hash functions have this "problem". Pretty much all are finite in length.

The real problem happens when collisions can be generated in less work than brute force. Due to the birthday problem with an $n$-bit hash function we would expect to see a collision after computing $n/2$ digests. If $n$ is large enough (say $n=160$) we would not expect any realistic adversary to be able to generate collisions.

A hash function is broken when someone can demonstrate collisions in fewer than $n/2$ operations.