Re: unique mathematical hash
Yes hashes are clearly not unique (and hence the article is just plain wrong about that).
Any dedupe system that assumes they are unique and doesn't verify the data is the same after getting a hash match is insane and should not be used. It doesn't matter how low the probability is, I do not want to risk my data getting destroyed because it just happens to have the same hash as some other data.
And yes there are programmers out there dumb enough to assume the hashes are effectively unique because the probability is so insanely low of them having a collision and then treat them as if they were actually unique. Some day their customer is going to pay for that mistake and they might not know it for a long time after it happens.