I have a personal, and highly idiosyncratic reply. My idea of a great Christmas gift would be a nice bottle of Scotch, or, as my daughter and son-in-law once gave me, a case of Guiness. Unlike a lot of mathematicians, when I stopped work for the day, week, or term, I really didn't want to do anything math related: puzzles; Rubik's cube; chess. I really dislike games of strategy. My wife (also a mathematician) likes really hard Soduko and Kakuro. I prefer crosswords (New York Times, especially). I tell her that if I were going to work that hard with numbers, I would rather work on a research problem. It is for certain that I would not like a mathematical gift for Christmas, birthday, anniversary, or whatever. Maybe your Dad is a crossword fan?
I also dislike getting clothing for gifts as no one understands my likes, or dislikes. If my rant discourages you from getting a math gift, or any gift at all, I apologize. All in all, I would try to choose something safe, which of course is no help at all to you. Nonetheless, have a Happy Christmas, and I hope you get to celebrate with your Dad, circumstances permitting.