# 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!

• This should obviously be CW, but I support this question existing in the hope that my future children will get me cool math gifts. – Alec Rhea Dec 11 '20 at 22:47
• This is entirely not the right website, but I’d like to see what answers you get anyway, so let’s hope the “vote-to-closers” are too busy closing homework questions and let this one survive at least for a while. – Gordon Royle Dec 11 '20 at 23:11
• Please, keep this question open. It is one of a very few holidays treats we can have in MathOverflow in the depressing time we have. – Piotr Hajlasz Dec 12 '20 at 0:16
• Are you sure that Dad is not an MO regular? – Gordon Royle Dec 12 '20 at 12:54
• Am I allowed to go against the grain and suggest not getting your dad a math-related gift? Maybe I am not "mathy" enough but I usually find such gifts a bit boring/easily forgotten (ok, I love the suggestion below about Hagaromo chalk!) – Remarkably Unremarkable Dec 12 '20 at 22:54

I'm surprised no one has yet suggested a lifetime supply of Hagoromo chalk.

• Sadly, those of us who already purchased a lifetime supply (well, a 10 year supply) haven't been able to use it while teaching remotely on our iPads. :( – Joe Silverman Dec 12 '20 at 0:57
• @Joe: Not with that attitude... – Asaf Karagila Dec 12 '20 at 9:39
• @AsafKaragila Sorry, not quite sure what "attitude" you're attributing to my post. It was meant to partly reflect sadness that such a gift wouldn't be of immediate use, with an underlying unexpressed hope for the future that by the following Christmas we'll be back in the classroom and reunited with our students. But as always, it can be difficult to exactly convey one's meaning in a short online comment. And BTW, I think Deane's suggestion for a gift is excellent. – Joe Silverman Dec 12 '20 at 13:31
• @Joe: That's a joke, suggesting that you're expecting to fail using the chalk with an iPad. It's a common joke, e.g. "I don't think I can eat a 2kg steak.", "Not with this attitude you can't.", etc. – Asaf Karagila Dec 12 '20 at 13:32
• @AsafKaragila Ah, I see, that completely went by me. Makes a lot of sense now. – Joe Silverman Dec 12 '20 at 13:39

Obviously, a closed, non-orientable, boundary-free manifold.

• I can confirm that this is a good answer. A former high school math teacher I know keeps his copy on display in the kitchen. – KConrad Dec 11 '20 at 23:24
• I also confirm, and used this many times for all kinds of gifts to mathematicians. They also have scarfs, knit hats and many other non-orientable things for sail. – Alexandre Eremenko Dec 12 '20 at 2:46
• THE CUCKOO'S EGG!!!!!!!!!! – Bob Jarvis - Reinstate Monica Dec 12 '20 at 16:55
• My wife bought one of these for me, and I can confirm that it is a good gift (I'm not even in math, I'm in computer science). Before she bought it, she asked my brother if it was a good idea and he said, "of course!" She asked, "but what's the point of it?" He replied, "that it's a Klein Bottle." – Moshe Katz Dec 13 '20 at 0:33
• if you're really cheap you can turn the label of an e.g. water bottle into a Moebius strip. – AlexArvanitakis Dec 13 '20 at 1:00

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”.

• If they ship many of these... things... I wonder what is the plural of gömböc :) – Qfwfq Dec 12 '20 at 2:27
• Well, the internet tells me: Gömböcök. – Fred Rohrer Dec 12 '20 at 6:58

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".

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 mathematical gift that I enjoyed was a triple of solids of constant width.

• I imagine these feel very nice to roll around in your hand together. I imagine that you don't really have a sensation of one rolling over the "edge" of the other because of the constant width? I would be very curious to play with these. – Steven Gubkin Dec 12 '20 at 14:24
• The nice thing is to put a book on three of them and see how it stays stable and parallel to the floor. When I got the gift it did not work for me because I missed one of the solids in the box and tried it on two. – Gil Kalai Dec 12 '20 at 17:03
• @StevenGubkin I've never held these, but I imagine you'd still feel it as you roll over an "edge" - constant width does not imply that the center of mass is at the geometric center, so you could still have differently stable positions depending on the orientation. The top right image, for example, looks like it's sitting stably on its base, but would fall stably to the bottom right image if tipped far enough over the "edge", so I think you'd feel it behave differently as you rotate it. I'm also very curious for hands-on experience. – Nuclear Hoagie Dec 14 '20 at 18:55

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.) Perfect for the set theorist: https://www.geoponicsinc.com/collections/christmas/products/wooden-cardinal-ornaments-assorted • I hope that either you already have these, or your family follows you on MathOverflow! – Matt F. Dec 13 '20 at 2:43 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! • What kind would you recommend? – Deane Yang Dec 12 '20 at 2:33 • This heavily depends on each individual. I would personally pick a cheap bic pen to work with over a fountain pen 24/7/365 (even 366 if it comes down to it). – user347489 Dec 12 '20 at 7:18 • @user347489 Are you left-handed? – wizzwizz4 Dec 12 '20 at 12:31 • @wizzwizz4: For my part, I am left-handed, and find that I smudge much less with a good fountain pen than with most roller-balls. The idea that lefties don’t like fountain pens is a bit of a misconception in my experience — it’s just a matter of individual tastes either way, I think. – Peter LeFanu Lumsdaine Dec 12 '20 at 14:45 • @mlk I love pencils too. They are pretty much like fountain pens, but much worse. The point is that when you write with a pencil or a fountain pen you have some feedback (if you know what I mean) and that makes your writing so perfectly satisfying. Bic pen (mentioned by someone) has no feedback and that makes it so bad. – Piotr Hajlasz Dec 12 '20 at 23:20 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 • Great suggestion! – Deane Yang Dec 14 '20 at 1:53 • This. My (former) grad students jointly got me one for hitting 50. In Notre Dame colors, too. I think they overdid it a bit, getting back to Erasmus of Rotterdam is a bit much. But it is still very nice. Keeping it in my office. Framed. – Jyrki Lahtonen Dec 14 '20 at 22:20 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. Illustrating Mathematics, Ed. Diana Davis, 2020. ISBN: 978-1-4704-6122-5. AMS link. Several beautiful mathematical T-shirts could be found here: https://www.tembelone.com • Nice, I like the rooted tree drawn in the upwards direction. – Gordon Royle Dec 12 '20 at 10:31 • See also "p-adicts" T-shirt : bonfire.com/p-adicts – Watson Dec 14 '20 at 13:59 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.)

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.

• I remember realizing that slide rules use a log scale to convert multiplication into addition. Such a nice application of an abstract fact for a concrete, practical purpose. – Nik Weaver Dec 12 '20 at 16:19
• @NikWeaver I recently bought two slide rules and now I'm awaiting a third one in the post. A month before buying my first slide rule, I also got myself a few Soroban abacuses and a Sudoban abacus, as I was curious about them. I was intrigued by some Asians who worked natural logarithms on acabuses. And exponents and roots too. So I bought them. I am struggling to get the hang of them. Have you ever used them? youtube.com/watch?v=q62hQVfVGxU – Rita Geraghty Dec 12 '20 at 16:46
• I have a vintage slider rule after my grandfather who was an engineer. Unfortunately, I do not know how to use it, but I promised myself I will learn it. – Piotr Hajlasz Dec 12 '20 at 18:47
• Oooh. Great idea. I used to drool over slide rule catalogs. – Deane Yang Dec 12 '20 at 19:00
• @MattF. probably soroban abacus (Japanese abacus) – KingLogic Dec 14 '20 at 2:22

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.

You may adopt a polyhedron in their name!

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.

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.

• I think it safe to assume that the OP will weigh our suggestions against all the non-mathematical gift options that he/she can evaluate without our assistance. – Gordon Royle Dec 14 '20 at 8:57
• @GordonRoyle - I completely agree. – Chris Leary Dec 14 '20 at 16:18

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.

• It looks great. I like the contrast of different textures in the drawing. Did you draw this yourself? – Mozibur Ullah Dec 13 '20 at 12:13
• @MoziburUllah thanks so much! Yes, I drew it myself - it is just pen on paper. – user141903 Dec 13 '20 at 12:22
• You really should bring out a book or at least publish them on the web. I'd certainly buy a copy! – Mozibur Ullah Dec 13 '20 at 12:26
• @MoziburUllah thanks! I do have some posted here: erincarmody766.wixsite.com/mysite-3 And I would happily sell you one (this one even), I can send it to you - just email me erincarmody766@gmail.com. And good idea on the portrait book! – user141903 Dec 13 '20 at 12:42
• They're great. I see you're a writer as well. I've always liked Alice so I bought the book to see how she got on in her further adventures. – Mozibur Ullah Dec 13 '20 at 13:00

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.

https://math-sculpture.com/ carries a large variety of, well, varieties.

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.

Treat him like a person, a math degree is a just a piece of paper, it doesn't define you.

• I would say it definitely signals his interests and life experience. And choosing a present for someone based on their interests and experiences is definitely a human thing to do (or so I have been told by humans). – Kimball Dec 12 '20 at 20:43
• You seem to be one of those people that just loves to get upset over anything someone does. Buying a gift based on someone's interests and passions is nice, and does not at all mean that you are not treating someone like a person.... – user2520938 Dec 13 '20 at 11:50
• This is what I was thinking. Lots of mathematicians have other interests! – Mozibur Ullah Dec 13 '20 at 12:16

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

• Do you mean this Joy Division? – Basil Bourque Dec 13 '20 at 1:52
• Yes. Of course, if the Dad prefers something more classical, perhaps a vinyl LP of the Sex Pistols first release, or perhaps something by Mr Iggy Stooge? – Lysistrata Dec 13 '20 at 11:19

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.

I would say something related to tiling, so obviously https://mcescher.com/shop/ is the place.

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 .

An extravagant tiling related possibility:

Image:Solarflare100

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.