Happy New Year! And welcome to the first Carnival of Mathematics of 2014. The Carnival is a monthly roundup of blog posts on or related to mathematics, from all over the internet. Posts are submitted by authors and readers, and collated by the host, whose blog it’s posted on. This month, the Carnival has pulled in here at The Aperiodical, and we’re all ready with our party hats for the celebration of mathematical blogging that implies.

First of all, in Carnival tradition, I should throw out some facts about the number 106, as this is the 106th Carnival. Unfortunately, 106 is possibly the most boring number I’ve ever considered, although I did manage to scrape together the following, thanks to some helpful tweeters (follow the links to see who):

• It’s the sum of two squares (81 + 25). This means that, in particular, $\sqrt{106}$ is the length of the hypotenuse of a right-angled triangle whose other sides measure 5 and 9. In fact, this also means that a circle of radius $\sqrt{106}$ centred at the origin would have precisely 8 lattice points on its edge.
• Its prime decomposition is $2 \times 53$, which means there are precisely two groups of order 106, namely the cyclic group of order 106 and the dihedral group of order 106.
• The number of possible mathematical trees with 10 roots is 106, which means that if you join a piece of string to the end of each finger, there are 106 ways to connect them all into a tree. Do it! Send photos!

It’s also been pointed out that the sum of the first 106 digits of pi is prime, that it’s the first number over 100 which is the product of two primes, and that it’s a type of Peugeot. Thanks, Twitter!

Anyway, on with the show. Roll up, roll up! Catch some blog posts which were posted in December!

Being the end of the year, and people being somehow convinced that an arbitrarily-assigned number increasing is somehow a significant event, several places have posted roundups of the year. The Wolfram blog, for one, has collated the ten most popular blog posts from 2013, plus some special mentions. White Group Mathematics, who will be hosting next month’s Carnival, has posted a mildly entertaining roundup of science, technology and education goings-on in 2013. And, in what can only described as meta-meta-meta-linking, in this Carnival rounding up blog posts, I’m linking to MatthewMaddux’s roundup of the posts made on their blog this year, many of which link to stories about maths education.

On a related note, Matifutbol presents a round-up of the numerical and cultural properties of the number 13, and the number 14, as we move from 2013 to 2014. In the spirit of temporally-inspired reflection, Evelyn Lamb over at Scientific American has been reading – and pondering on – transcripts of Felix Klein’s 1893 lectures on the state of (then) modern mathematics and maths teaching in Germany.

Those with an interest in propositional logic should be wary of reading Tim Gowers‘ blog post ‘A small paradox‘, which may well blow their minds, as he somehow manages to construct a demonstrably false statement before your very eyes. And for those who are really serious, Secret Blogging Seminar (written by a group of PhD mathematicians at Berkeley) discovers a result in category theory via an old example.

Everyone loves data representation, right? Mapping Ignorance blog has posted a lovely piece about proportional symbol maps (the ones where there’s a blob of appropriate size over a geographical region). On the bad side of data representation, Colin Beveridge at Flying Colours Maths deconstructs some terrible graph abuse in the Maths Police Christmas Special.

Over in the recreational maths department, Tony Mann has written about Five curious and interesting mathematical objects, while Kevin Houston reports on the recent Radio 4 Maths and Magic programme, which featured some tricks performed at the MathsJam conference.

A fantastic blog you should check out if you can is that of Peter Woit, who posts disturbingly regularly on topics in maths and physics (mostly physics, but that’s forgivable). This month, his posts included:

• A summary of some discoveries made in the wake of Edward Snowden’s revelations about the NSA, and how they relate to elliptic curve encryption;
• The latest news on the abc conjecture;
• The news that Facebook founder Mark Zuckerberg and Russian entrepreneur Yuri Milner will fund the $3m Breakthrough Prize in Mathematics, which will be awarded to mathematicians… for… doing stuff?

Fans of reaction-diffusion systems will be interested to read Simon Gladman’s account of a node-based interface for playing with them (made using Apache Flex), while maths teacher Patrick Honner presents an interesting anecdote about meeting Fields medalist Cedric Villani.

Two number theory-related posts:

• Aperiodichum and occasional guest star David Cushing has been thinking about arithmetic progressions of square numbers, and how their properties translate to triangular numbers.
• Shecky Riemann, at Math-Frolic (who were the host of the Carnival before last), recounts a nice fact about progressions of prime numbers from Richard Elwes’ book. He also reminds us of what could well be my favourite XKCD comic of 2013.

Speaking of XKCD, quantum computer scientist Scott Aaronson has posted an explanation of his research, using only the 1000 most common words in English – inspired by the XKCD comic ‘Up-Goer Five‘.

And to finish off, here’s a song about the 48th Mersenne prime, discovered earlier this year, by geek songstress Helen Arney, which featured in the More or Less specials which went out on the BBC World Service over the holidays.

That’s it for Carnival 106! The next Carnival will be hosted at White Group Mathematics, and submissions close on 5th February, so if you see any good maths blog posts this month, please submit them.