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.
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.