Thinking Outside the Box (...well, sort of)

 Oh, we'll revisit Futility Closet today, this time for "Airy's Paradox":

https://www.futilitycloset.com/2021/10/08/order-3/

A Grim Paradox

 You've likely heard of Thomson's Lamp paradox (or you can look it up), but have you heard of the Grim Reaper paradox:

https://www.futilitycloset.com/2021/10/02/the-grim-reaper-paradox/

The Paradox That Splits Philosophers Down the Middle (Newcomb's)

 Alex Bellos on Newcomb's paradox:

https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/nov/28/newcombs-problem-divides-philosophers-which-side-are-you-on

Of Fallacies and Paradoxes (...and sums)

 One statistician's "top 10 fallacies and paradoxes in statistics" (read the entire thread, and/or look up further info on Wikipedia):

https://twitter.com/MaartenvSmeden/status/1356147552362639366

....and for your bit of humor to start the day (or, whenever you read this):

https://twitter.com/Thalesdisciple/status/1356455290342764544

Yes or No

Been reading a review copy of a wonderful new book (due out in March) by Matt Cook from MIT Press, entitled “Sleight of Mind,” all about one of my favorite topics… paradoxes. It’s chockfull of them, and I’ll do a fuller review closer to the publication date, but will entice you with just a few fun, simple one-sentence logic puzzles (variations of the “liar paradox”) that appear near the start of one section of the volume:

“Answer truthfully, yes or no: Is ‘no’ the correct answer to this question?" 

“Now answer this one truthfully: Is ‘yes’ the correct answer to this question?” 

“What about, ‘Does this question have an answer?”

…and I’ll leave you to contemplate these on your own. 
(but essentially, for one of them neither answer works, for one of them both answers work, and for one of them only one answer fits).

Looking Forward and Backward (at books)

Since listing my favorite math books of 2015, I was recently reminded that the new Barry Mazur/William Stein volume on the Riemann Hypothesis is due out at the end of January 2016:
http://amzn.to/1lZuxxb

Too late for Christmas, but what a great start to the new year. David Mumford calls it "a soaring ride." I suspect once out, this short volume will be THE book (out of many available) to introduce folks to possibly the most important unresolved, far-reaching conjecture in all of mathematics. (...Perhaps I already know my favorite book of 2016!)

Meanwhile, I just obtained a couple of fine prior books on paradoxes, and feel safe recommending both well-ahead of finishing them. Roy Cook's 2013 "Paradoxes" is a good, fairly standard treatment of what I believe is one of the most important topics in all of math/philosophy, for bright high-school-level-and-above students.

Stanley Farlow's 2014 "Paradoxes In Mathematics" looks to be an especially wonderful introduction to several of the classics for middle-to-high-school students particularly, in breezy but broad-covering fashion. I was previously unaware of this succinct little volume from Dover, and am delighted to have stumbled upon it. Again a great stocking-stuffer for that distinctively math-inclined youngun on your list.