What's a great christmas present for someone with a PhD in Mathematics? Christmas is just around the corner and I haven't bought all the gifts for my family yet ( yeah, )
My Dad has a PhD in Mathematics, he works in Graph theory and his thesis was about Quasiperiodic tilings.
What do you think would make a good gift for him?
I'll appreciate anything you could think of!
Thanks for reading, hope you have a great day .
p.s.: after reading all the tags in this website I think this is the right one for this kind of question? please correct me if I'm wrong!
 A: I'm surprised no one has yet suggested a lifetime supply of Hagoromo chalk.
A: Perhaps he would like a hand-drawn portrait of his favorite mathematician (or himself!).  This is one of Kurt Gödel.  I'm a mathematician and artist and love to draw portraits of mathematicians.

A: If your dad is currently teaching, perhaps a useful gift for him is a really comfortable chair (and desk maybe). Personally, since all my teaching duties this year have been done from home, I'm sitting the most part of the day, and I've been struggling with a lot of pain in my back.
A: Obviously, a closed, non-orientable, boundary-free manifold.
A: I would like to suggest Joel David Hamkins' book Proof and the Art of Mathematics. My wife will give it to me this Christmas, and I couldn't look forward to it more.
A: Just hint at their mathematical side, e.g. give them the complete collection of Joy Division albums. And maybe a matching T-shirt...
Joy Division 2020
A: An extravagant tiling related possibility:

Image:Solarflare100
A: I would say something related to tiling, so obviously https://mcescher.com/shop/ is the place.
A: My school had some of these and I loved them.  You can order them here.  More stuff here.
Also: lots of math sculptures at https://bathsheba.com .
A: Treat him like a person, a math degree is a just a piece of paper, it doesn't define you.
A: Although I am a programmer, I highly recommend this book:
https://www.amazon.com/Math-Book-Pythagoras-Milestones-Mathematics/dp/1402788290

Math’s infinite mysteries and beauty unfold in this follow-up to the best-selling The Science Book. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

I have a local publisher version with a different book cover and overall design. The book covers fairly complicated topics written in an easy-to-understand style targeting a broad range of readers.

I believe a guy with a Ph.D. in math can enjoy interesting math facts in a relaxing way.
A: I myself work on graphs and studied quasiperiodic tilings, and I warmly recommend XKCD and its goodies, in particular the volume 0 book, the log-scale height poster, and its other books!

A: Bit expensive, but a Gömböc might be a nice desk toy...
Added: the on-demand 3D-printing site shapeways has a category for mathematical art
https://www.shapeways.com/marketplace/art/mathematical-art
One of these is a model of the generalised hexagon of order 2, due to my close colleague John Bamberg. (I get no commission if you buy one.)
https://www.shapeways.com/product/QZP8BGTE2/generalised-hexagon-of-order-2
The bipartite incidence graph of this geometry has diameter 6 and girth 12 and 126 vertices and is often called Tutte’s 12-cage, so it rates highly on “graph-theory content”.
A: This is not out yet, so it would a present for Christmas 2021 and beyond, but this coffee table book of photographs of mathematicians' chalkboards looks very, very cool:  Jessica Wynne, "Do Not Erase: Mathematicians and Their Chalkboards".
EDIT:
It is published now.
A: Complex dynamics generates a wealth of fascinating fractals which are perfect for posters. So I would say a Mandelmap poster can be a good gift.
A: A book of interviews of famous mathematicians could be good. I have in mind particularly More Mathematical People, which I've gotten a lot of mileage from here at MathOverflow.
A: A good red wine from Bodegas Langa (Spain)

A: The Museum of Mathematics gift shop has possibly the most well-curated collection  I know of.  It features so many things that I'd want and so few that I actually need, and that's practically the definition of a good gift.
https://shop.momath.org
A: A mathematical gift that I enjoyed was a triple of solids of constant width.

A: Nate Eldredge will generate a random mathematical paper for you (with authors of your choice) for free or you can order a printed randomly generated book (I’m unsure whether these can be personalized). See his blog here.. He will donate $5 to the AMS for all books sold.)
A: I think a twisty puzzle like a Rubik's Cube is a nice gift, especially if your recipient is interested in puzzles or group theory. I suggest avoiding the Rubik's brand cubes because those turn terribly and going for a Chinese company speedcube.  In my extremely limited experience with abstract algebra, I've found being able to see concretely commutators and generators is greatly rewarding and helps my intuition.
A: Lot of choice from  Quasi periodic tiling designs for table mats by 3d printing ( choose a flexible plastic for rolling up thin sheet after breakfast ). Ask him for his  favorite tiling .. penrose, arabesque...
A: It is common in Iran that students gift "Rubaiyat Omar Khayyam" that can be found in Amazon easily.
A: I figured someone would mention this, but since no one has, I will. If our dad likes mathematical history in a personal vein, the Math Genealogy Project will create a personalized history of his mathematical predecessors, PhD advisor by PhD advisor, with some branching. And if he's had PhD students of his own, those can be included. One of my colleagues has a framed one on his wall and it's always fun to look at. In many cases, the trail goes back to the 18th century, or even earlier.
https://www.genealogy.math.ndsu.nodak.edu/posters.php
A: A fountain pen, of course. If you do mathematics you have to write a lot. I write about 6,000 pages per year (I know it is crazy that I know that number) and the the best writing tool ever created is a fountain pen. My father gave me my first fountain pen when I was 12 and now I have more than 30 of them. I poisoned my kids with the love to fountain pens too, but they are jealous, because they think I might love fountain pens more then them, and I will not comment on that. Merry Christmas!
A: Perhaps a slide rule for your father. It is an instrument used for calculating exponents, roots, logarithms, etc. Slide rules predate calculators. Sadly, they are obsolete today. You can still find vintage slide rules at Etsy.
Below is an example.

A: One can also make a donation in the giftee's name, to something that mathematicians benefits from. Say, donate to OEIS (The On-Line Encyclopedia of Integer Sequences), Sage, or Wikpedia.
A: You may adopt a polyhedron in their name!

A: For mathematicians of a certain age, an old-fashioned chalkboard would be welcome. (This one, https://www.amazon.com/dp/B01N7U3GSV/ is 17”x23” for only $12 at the moment.)
A: In the vein of coffee-table books, I like
Mathematicians: An Outer View of the Inner World
by Mariana Cook. It contains photographic portraits of 92 mathematicians, along with a short autobiographical essay on each one. The book was originally published in 2009 and many of the subjects are since deceased; as time goes on it serves increasingly as a record of a bygone age in mathematics.
A:       

Illustrating Mathematics,
Ed. Diana Davis, 2020.
ISBN: 978-1-4704-6122-5.
AMS link.

A: Several beautiful mathematical T-shirts could be found here:
https://www.tembelone.com

A: I think it's fine to get a technical book.  If he has two, your father can give away the one his kid didn't inscribe.
I don't know combinatorics well enough to identify the classics (although I do recall having been told that Lovasz's Combinatorial Problems & Exercises is one of the great books of the genre).   Instead I offer a few generic suggestions:
Aigner, Ziegler & Hoffman, Proofs From The Book.
Monastyrsky, Modern Mathematics In Light of The Fields Medal.
A: https://math-sculpture.com/ carries a large variety of, well, varieties.
A: 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.
A: I quite enjoy reading autobiographies or good scientific biographies of mathematicians (and other kinds of scientists) whose work has influenced the fields that I study. But I don't necessarily seek them out, preferring a casual opportunistic approach. I would be quite happy if someone were to give me such a book as a gift. It might be possible to please your father in a similar way.
Some extra research is required for this option though. Because the audience for biographies of this kinds is fairly narrow, many of them are out of print, if they even exist. Used book sellers are to be be consulted for good measure.
A: I think it would be hard to find a math book or a book about math that would be a sure fire gift for a mathematician. My suggestions are: (1) a classy chess set, and (2) an electronic keyboard, both of which speak to a "mathematician mind" in different ways. Two other possibilities: electronic chess set and electronic sudoku set.
