Mathematically unlikely and infinite are extremely different things, and it also depends on what exactly you are looking at when comparing two fingerprints.
If you are going on trial, and comparing a very small patch of fingerprint (2mm x 2mm) found at a crime scene to a spot the same size on a subject’s finger, then it’s possible that you mistakenly matched incorrectly.
If you are comparing an entire set of 10 fingerprints from a previous arrest to a new arrest with 10 fingerprints, then it’s mathematically unlikely that you’re going to mistakenly match.
If an iPhone is looking at a single fingerprint and comparing it to what is stored, then it’s extremely unlikely that any specific person can trick it, but if 100,000 people try, it will probably find a false match at some point, because the accuracy of what is being compared is compromised by the need for speed, and low number of false negatives (the real user needs to be able to log in quickly, and every time, with few failures.)
When saying absolute terms of “every fingerprint is unique” you have to put some qualifiers on it to make it true.
“Unique among any human who ever lived or will ever live” is also very far from “unique among the 8 billion or so currently living humans” or “unique among the humans currently in a comparable age range/state of health/… in terms of finger size/wrinkles/…”.
Adding onto this, in cryptography this field of study is called “Biometric Failure Rates” (at least it was called that in my beginner course). A good introduction would be this article.
Mathematically unlikely and infinite are extremely different things, and it also depends on what exactly you are looking at when comparing two fingerprints.
If you are going on trial, and comparing a very small patch of fingerprint (2mm x 2mm) found at a crime scene to a spot the same size on a subject’s finger, then it’s possible that you mistakenly matched incorrectly.
If you are comparing an entire set of 10 fingerprints from a previous arrest to a new arrest with 10 fingerprints, then it’s mathematically unlikely that you’re going to mistakenly match.
If an iPhone is looking at a single fingerprint and comparing it to what is stored, then it’s extremely unlikely that any specific person can trick it, but if 100,000 people try, it will probably find a false match at some point, because the accuracy of what is being compared is compromised by the need for speed, and low number of false negatives (the real user needs to be able to log in quickly, and every time, with few failures.)
When saying absolute terms of “every fingerprint is unique” you have to put some qualifiers on it to make it true.
“Unique among any human who ever lived or will ever live” is also very far from “unique among the 8 billion or so currently living humans” or “unique among the humans currently in a comparable age range/state of health/… in terms of finger size/wrinkles/…”.
Adding onto this, in cryptography this field of study is called “Biometric Failure Rates” (at least it was called that in my beginner course). A good introduction would be this article.