A manager once told me he'd never hire a PhD because once they complete the specialized work we hire them for, they inevitably get put on something outside their specialty - like your linked xkcd - and then their acceptance as experts along with that behavior causes real problems.
Another time I had an older PhD moved to my area (outside his) where we were trying to meet a number of objectives. He said in a meeting that "it is mathematicaly impossible" to achieve one of our performance goals. I quietly went back to the lab and ran my new control algorithm and documented hitting that goal. Never refuted him, just filed the incident away in my head.
Edit: People being arrogant or know-it-all is probably not especially correlated with having obtained a PhD, but more with overall frame of mind, and I find this comment to be a uselessly negative ad-hominem.
Also people bringing this up remember the one time the PhD was wrong, while discounting the 99 times the PhD was right and kept them from doing a lot of fruitless work.
Sorry, but I think it's correlated in two ways. One is that very bright people, which I think includes most PhD-havers, are especially used to being right. When they have the rare experience of being ignorant and wrong, they may struggle with it much more than others. Two, academia is a bubble. I think that's great; I love that we have a place where people who are deeply interested in something can focus entirely on that. But it necessarily means that they're less likely to know about things outside that bubble.
That's not to say it's a perfect correlation. I know plenty of people with PhDs who don't have the problem in the XKCD cartoon. But I too am careful hiring PhDs in tech jobs. Professional work is just very different than academic work. It takes time to learn it for people whose main focus is the theory. After all, "In theory, theory and practice are the same. But in practice..."
I once worked with a PhD who claimed that basically any novel bit of coding was a "research problem", and thus not worth bothering. Using a hashtable to speed up an algorithm? Research problem. Using raw TCP instead of HTTP for a long running connection? Research problem. Implementing a graph algorithm you could read up on Wikipedia? Research problem. I think it was only when I solved three of those "research problems" in one week that he finally shut up.
But you actually don't have a proof you solved these tasks! Where is the arxiv preprint? Make sure all LaTeX is syntactically correct, and double-check that your chosen citation style is according to its latest edition!
