My father is a retired mathematician who loves to immerse himself in history documentaries, particularly around wartime or famous figures. He loves historical gossip - i.e. things most people don't realise about past events and people. Start with someone nearly everyone's heard of, and add something interesting about them that most people wouldn't know. Then write it in a whimsical style, and he's happy as Larry.
Any recommendations, please?
Do you think your father would most enjoy an academic book or one written for a well-educated but more general audience? If the latter, this is a wonderful question to ask your local independent bookseller. Staff at bookshops are paid to be knowledgeable about their stock, love this kind of puzzle to solve, and could probably help you find a recent title your father won’t have read yet!
Edited to add: many independent stores aren’t currently open for browsing but are glad to give recommendations over the phone and ship your order.
One of my favorite works of popular history is Nathan Miller's Founding Finaglers (1976), a study of American history centering around corruption. The 1st chapter features the man who kidnapped Pocahontas, the 2nd chapter is about New York being a city of pirates circa 1700. There's one about the Yazoo Fraud, Civil War profiteering, etc.
Other than that, it's hard to find books that aren't overly specific. There's a lot of fun to be had with say, Andrew Jackson's crazy ass, the Election of 1876 or Garfield's strange assassination, but they're not things I have read whole books on. Another thing I can recommend though is the Medical History of American Presidents site by Dr. John Sotos.