Welcome to the 101st edition of the Carnival of Mathematics. The Aperiodical took over running the Carnival when it launched in April 2012, at Carnival 85. Although it’s conventional to celebrate round number anniversaries (and even though I’m left-handed), we decided for a combination of reasons not to make a big deal out of Carnival 100 – instead inviting maths author Richard Elwes to host it on his blog – and instead to make the more exciting number 101 into our big celebration of how long the Carnival’s been running.

The Carnival of Mathematics has always been run on a voluntary basis by maths bloggers, rounding up posts they’ve seen and that people have submitted. It’s been organised by several different people throughout its history, and hosted by dozens of different blogs; it’s made friends with other maths blogging carnivals; and in this age of RSS, Twitter and link sharing, it’s still a great resource to find interesting stuff collected in one place. For more information about the Carnival, and an FAQ, please visit the Carnival of Mathematics page.

So, to kick it off in the conventional manner, here’s some facts about the number 101, and why it’s superior to 100:

- It’s greater, literally
- It’s a prime number
- It’s a palindromic number, that is, it’s the same written backwards as forwards
- It forms a pair of twin primes with 103, and it’s the sum of five consecutive primes (13 + 17 + 19 + 23 + 29)
- It’s the only known prime number which is written only in alternating 1s and 0s in base ten
- It’s also a dihedral prime number, which means it reads the same if you type it in a calculator and turn it upside down.

Another interesting fact is that more books are published with a title starting ‘101’ than starting ‘100’, which is clearly because it’s better.

Before we commence properly, I’d just like to thank everyone who’s submitted posts to the Carnival this month – some people send in their own work, while others submit things they’ve found and enjoyed. Your contributions are greatly appreciated. On with the Carnival!

Different Sizes of Infinities, at Homeschool Math Blog

A lovely simple explanation of the different sizes of infinities. Maria Miller says: “This is one of the areas of math I’ve always felt was FASCINATING, AMAZING, awesome, mind-boggling!!!” She’s not wrong.

How Tall is an Alpaca, at Deathsplanation

Alison Atkin talks us through some death and statistics – and why ‘average age at death’ isn’t necessarily as illustrative as people take it to be.

Why Randomness May Not Mean What You Think It Means, at io9

A discussion of the different types of randomness – nice to see this on a blog which covers a range of diverse topics from pop culture and film to pictures of sharks eating other sharks.

Lemma, Proposition, Theorem and Corollary at Grad Studies in Control

Yao-Hong Kok talks us through what these terms mean, how they occur in mathematical research papers and how best to use them in your own writing.

How To Win at Pointless, at The Aperiodical

Aperiodical semi-occasional contributor Paul writes what we hope will be the first in a series about the mathematics of TV quiz shows, starting with inverse-points extravaganza/tea-time sensation Pointless.

Jason and Jacob – Unfathomable Minds at Math-Frolic

An account of some cases of mathematical savantism. Shecky R says: “Just a quick glance at the always-interesting subject of brain functioning and mathematical talent.”

Integer Sequence Review Mêlée Hyper-Battle DX 2000 – The Grand Finale, at The Aperiodical

Since no real-life carnival would be complete without a competitive game in which the outcome is very slightly rigged, take a look at this, the final in the Aperiodical’s stormingly popular Integer Sequence Review Competition. If you haven’t already seen them, you should also read the earlier rounds.

Next, some posts I’m loosely categorising as education-themed:

Matrix Notation, at Clayton Aldern’s blog Compatibilism

Clayton says: This longform post, targeted at a general audience (i.e. not necessarily having a math background), is an urge to teach mathematics so as to appeal to the intuition. The piece does so through a review of Gilbert Strang’s Linear Algebra and Its Applications.

Heavy metal or blue jeans? No, just maths from the Irish Times / Science

Peter Lynch writes about Cambridge University’s Wranglers – not their glee club, but a group of elite mathematicians.

Regents’ Recap – June 2013: More Trouble With Functions, at Mr Honner’s blog

Patrick Honner says “This piece exposes yet another serious mathematical error on a high-stakes state math exam in New York. […] This is just the latest example of serious mathematical misunderstanding from the authors of these high-stakes exams, as seen in my on-going series that critical reviews these tests.”

Next up, a couple of interesting editorials about mathematics in general, and its place in the world.

Why Maths Needs Public Speakers, at Fix Epsilon > 0

This blog is written by a mathematics undergraduate at Imperial College London, and in the past has covered the experiences and feelings of being a maths student. In this post, the author discusses their interest in public engagement, and gives examples of speakers that have inspired this.

Mathematics, at Electrolights

A fairly lengthy discussion of the concept of mathematics as a language, and what this means for those teaching and studying it.

These next few entries involve nice bits of code:

Form Follows Functions, at Maxwell’s Demon

Aperiodi-pal Edmund Harris presents some beautiful interactive graphs which get a bit four-dimensional.

Paley Graphs in Sage, at Yet Another Math Blog

David Joyner says: “Paley graphs have some pretty cool properties and there is some Sage code to help you draw your own.”

Worlds Colliding: Convert a Digital Photo into an Excel Spreadsheet at AccountingWeb

Matt Parker (stand-up mathematician and Aperiodi-friend)’s photo/spreadsheet conversion website is now finally online, and Twitter has been rife with screengrabs of spreadsheets of photos (in some cases, spreadsheets of photos of spreadsheets of photos). David Ringstrom has written a blog post about it, with appropriate levels of enthusiasm.

And to finish, a couple of short posts.

All Men are Men, at Enigmania

EnigMan presents a paradox.

Montessori’s Worst Nightmare, at Mathematics Under The Microscope

Alexandre Borovik leaves a quick note about a depressing trend in computer-based maths education.

So, that’s a round-up of maths blog posts we’ve enjoyed this month. Since the Carnival of Mathematics started, this has happened roughly every month, which means we have quite a large back catalogue of hand-picked nice blog posts. In case you haven’t yet seen enough amazing maths bloggery yet, here’s a selection of quasi-randomly chosen nice posts from the historical past since 2007 when the Carnival began.

**From 2012**: I can’t believe I have to explain to the Guardian that the moon is larger than a jogger, at andrewt.net; featured in Carnival 87

**From 2011**: Links to Enthuse about Mathematics, at Travels in a Mathematical World (at The Aperiodical); featured in Carnival 76

**From 2010**: Is the British Voting System Fair, at Tim Gowers’s Weblog; featured in Carnival 65

**From 2009**: Puzzle: Who Am I?, at JD2718; featured in Carnival 60

**From 2008**: Look, say, walk at Two Star’s Livejournal; featured in Carnival 43

**From 2007**: Clarkkkkson, at Everything2; featured in Carnival 6

(Prior to March 2009, the Carnival was posted fortnightly, if you were wondering about the numbers.)

That’s all for this Carnival of Mathematics, until next month! If you’ve been inspired by reading all this to blog about mathematics yourself, or if you see any other blog posts around the local internet you think deserve inclusion, we accept submissions through the Carnival of Mathematics page on this website. Also, we’re always looking for people to host future Carnivals, and if you’re interested in doing so, please get in touch.

The next Carnival of Mathematics, rounding up posts from the month of August, will be hosted by Michelle at My Summation. See you then!

“It’s the only known prime number which is written only in 1s and 0s in base ten”

You don’t mean any 0-1 strings because of 11, or 19 1’s. Or 10101101 to mix it up a bit.

Maybe numbers of the form 10000…000001? They seem tenaciously composite, checking with the amazing applet at http://www.alpertron.com.ar/ECM.HTM

Apologies – I mistyped what was in my head. I’ve now corrected it to what it should have said!