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I always assumed it was a bit like SHA hashing. Yes, collisions are theoretically possible. But they're so unlikely that it can be used as a unique identifier for most purposes.
That is not at all what this article is about. The headline is terrible.
The research is suggesting that there may exist "per-person" fingerprint markers, whereas right now we only use "per-finger" markers. It's suggesting that they could look at two different fingers, (left index and right pinky, for example) and say "these two fingerprints are from the same person".
When they say "not unique", they mean "there appear to be markers common to all fingerprints of the same person"
The truth is more interesting than the headline
Precisely. We've always known that identical fingerprints are not just possible but more common than the regular folk would imagine. The point is that the statistical probability of two individuals being in the same room at the same time and related to the same crime with the exact same fingerprints are so low as to make fingerprint ID good enough.
Multiply that by fingerprint evidence being often partial and damaged and how few shits the penal bureaucracy gives about people they've already decided are guilty
~~Excepting of course identical twins~~
Edit: apparently I was wrong
They tend to have different fingerprints for the same reasons they will have differing birthmarks.
Identical twins do not have identical fingerprints, because fingerprints are not only genetic. They might be close or somewhat similar, but rarely identical. They can be distinguished as different individuals by regular pedestrian forensic techniques.