I have a PhD in physics and I read Hawking's book as a child.

You just got me to realize that while I've read many physics popular books that have been "simplified enough that the common person can get something out of them, but not so much that they become meaningless", maths books that achieve the same are much rarer, I think.

I'm a purely amateur mathematician and not a physicist at all, but I completely agree with you that maths is missing this "midway between pop-math and real-math-textbook" kind of book.

One book that I can't recommend more highly is William Dunham's "Journey Through Genius". He picks ten or so the greatest proofs in math over the centuries, then proceeds to give you all the historical background about why they were created, who created them, etc, and then proceeds to give the full details of the proofs themselves. Including showing places the proof is considered wrong by modern standards.

It's my favorite "semi-pop-math" book, I highly recommend it.

True. Math is drier than physics. But Terrence Tao is well known, and there are a lot of nerds on the planet. The last popular math book I read wasn't good (Humble Pi; a Comedy of Math Errors), but I did enjoy e.g. How to Lie with Statistics, and, to a lesser extent, Innumeracy. I would buy Tao's book, probably.