"Google is the home to world-class engineers working on the world’s hardest problems". World-class engineers: true. World's hardest problems: false. Unless google has a secret space program, cold-fusion reactor, cure for cancer, desalination, etc... Perhaps I am naive but monetizing searches, email and other things doesn't count as any of the world's hardest problems.
At this point I consider Calico to be a part of Google (although separately incorporated). Not sure about you but I definitely see "extending the average life expectancy of the human population" as a difficult problem.
But even discounting this (naysayers will cry foul at the fact that it technically is a separate company), I think organizing the world's information is certainly an extremely difficult problem. And certainly one that Google is attempting to solve in more ways than search.
Also - self driving cars? Certainly you will agree that is not trivial.
I think you may be confusing "problems that would have the biggest potential impact on humanity" with "problems that are hard to solve". Which is not to say that curing cancer or colonizing mars is easy. But in what way is, say, desalination harder to do than creating a search service that wants to make all information "universally accessible and useful"?
> Perhaps I am naive but monetizing searches, email and other things doesn't count as any of the world's hardest problems.
Working on monetization isn't, AFAIK, what Google engineers do, that's what Google business folks do.
Google engineers work on things like natural language processing for conversational search, or predictive algorithms for identifying information needs in advance and providing them at the right time without requiring an active search -- and that's just for Google's fairly prosaic mainstream products, not the GoogleX/Calico/etc. moonshot kind of work.
Even boring problems at Google are done at mind boggling scale, but the work that Google is doing on machine learning alone, what Ray Kurzweil is trying to do, is one of the hardest problems in history.
The everyday things you use, like Google Maps, have incredibly sophisticated pipelines behind them. I'm not talking about serving up image tiles, I'm talking about the software that processes satellite, aerial, and street view imagery and stitches everything together into a coherent whole, while doing things like using machine learning to recognize signs, text, objects, building outlines, etc.
It all works so smoothly and so well most of the time that people don't even know all of the work that goes into it. Just parsing a question for meaning in search is a very very hard problem. What Siri does is kind of a joke compared to what's really required to make things work as they should.
Self-driving cars could make a big dent in the ongoing loss of a million lives a year to road accidents. As far as I'm concerned, that's up there in the category of things you listed.