The perfect necklace for the special mathematician in your life. Image: Sarah Wood, used with permission.

Looking for a gift that says, “Hey, I know you like math”? Look no further. There is an embarrassment of riches when it comes to wonderful mathematical things to give to people, but here are some of the coolest items I’ve seen this year.

To read

I wrote reviews of Jordan Ellenberg’s How Not to Be Wrong and Richard Schwartz’s Really Big Numbers earlier this year, and both would make good gifts.

Albert Michelson’s Harmonic Analyzer was a 19th century machine that used gears to perform Fourier analysis mechanically. Bill Hammack, a chemical engineering professor at the University of Illinois Urbana-Champaign has made a superb set of YouTube videos that show the machine in action. He, Steve Kranz, and Bruce Carpenter have also put together a beautiful book illustrating exactly how it worked. Bonus: if you’re cheap, there is a free pdf version of the book available at the website.

The Mathematician’s Shiva by Stuart Rojstaczer is about family, grief, the immigrant experience, and the Navier-Stokes problem. Few novels center around mathematicians, and while some of the characters in this book are a bit stereotypical, he portrays many mathematicians with complexity and sympathy, and I was drawn in to the story.

Zombies and Calculus by Colin Adams is not for the squeamish, and I’m squeamish. But if the mathletes in your life don’t mind a few bashed-in brains, they can probably handle this book. The book gently introduces mathematical concepts such as tangents, curves of pursuit, and exponential growth within the framework of an over-the-top zombie apocalypse story.

John Napier gave birth to the logarithm 400 years ago, and there’s a new biography of him by Julian Havil that explores not only his mathematical work but also his personality and the treatise on the Book of Revelation that he thought he would be remembered by. Bonus points if you give the recipient of this book a slide rule too.

Oliver Byrne’s edition of Euclid’s Elements. This is a reprint of the 1847 edition of the Elements that uses beautiful diagrams in primary colors to illustrate the proofs.

I haven't gotten my hands on a copy yet, but with a title like Things to Make and Do in the Fourth Dimension, I'm guessing Matt Parker's new book will be pretty fun.

To see and do

A crochet kit and Crocheting Adventures with Hyperbolic Planes by Daina Taimina. You know the mathematician in your life wants to make some negatively curved objects out of yarn!

A mathematical beading tutorial or beautiful beaded beads from Gwenbeads.

Baby’s first number sets puzzle. It’s never too early to teach your little one about the different types of numbers we use. I could quibble about the relative size of the rationals and irrationals, but this is a really cute wooden puzzle that can help you introduce the child in your life to the numbers they’ll need to know later. This is from the NausicaaDistribution Etsy shop, which also sells a variety of cute statistics-related items.

Anything from Mathsgear. Their shapes and solids of constant width are probably my favorite items, but there are other fun things in the shop, too.

Anything from Henry Segerman’s Shapeways shop. There you can order 3-d prints of stereographic projection models, quaternion monkeys, and many, many other pieces of mathematical art.

A Klein Bottle opener by Bathsheba Grossman. (Note that it only opens orientable bottles, so unfortunately you can’t open a Klein bottle with a Klein bottle opener.) Klein bottles can also be obtained in glass or wool from kleinbottle.com.

Beautiful hexagons, in the form of Alex Wild's bee-related photography. (Warning: don't click if you don't want to see bees.)

To wear

Emmy Noether around your neck! The SarahWoodJewelry Etsy shop has tons of cool jewelry celebrating famous women in history, but the Emmy Noether pendant called to me. (This bracelet of a 14th century picture depicting a woman teaching geometry is pretty great, too.)

A hypercube around your neck! Sadly, this pendant actually only exists in three dimensions, so it’s really just a projection of the four-dimensional hypercube, but it’s pretty cool anyway.

A space-filling curve around your neck! DMCK makes mathematically inspired scarves in cheerful colors.

The Enigma Machine around your neck! I kind of want all the ties in the Cyberoptix Etsy shop, but this one seems particularly appropriate for fans of math, computer science, and/or Alan Turing. Their ruler necktie would also come in handy for emergency measuring situations. The mathematician you give this to might be interested in knowing that there are either 85 or 177,147 ways to tie a tie, depending on how you count.

Geometry Daily around your neck! Scarves and pocket squares based on designs from Tilman's beautiful Geometry Daily tumblr.

To give

If the mathematicians in your life don’t need more stuff, perhaps they would appreciate a donation to a math-related cause.

CHAMP, the Cougars and Houston Area Math Program, is a math enrichment program for high schoolers from underserved areas in Houston. It is run by volunteers, so there is very little overhead, and every dollar counts.

Translate Grothendieck’s biography. Or at least help pay for a translation into English of part of Winfried Scharlau’s biography of the late, enigmatic mathematician Alexander Grothendieck.

Disclosure: I received review copies of some of the books I recommended and some solids of constant width from MathsGear when I visited during the summer, but I have received no other free items or compensation for these recommendations, and no one has asked to be included on this list.