The Aperiodical

Presented by Katie Steckles and Peter Rowlett, episodes of Mathematical Objects will take an object, real or abstract, as inspiration to chat about a mathematical topic. This introduction explains the idea ahead of the first episode, coming soon.

As part of our special Apéry takeover today, I chatted to mathematicians Ben Sparks and James Grime, to find out what we know about the mathematics Apéry did – it’s an enjoyable 10-minute listen.

Cushing was injured in a serious maths accident recently (he fell out of the bath) so I wanted to assess the damage to his number-wrangling faculties. Fortunately, there’s the National Numeracy Challenge, which begins with a test to pinpoint your weak areas. National Numeracy is a charity that wants every adult in the UK to “reach a level of numeracy skills that allow them to meet their full potential.” Well, if there’s one thing we’ve got, it’s bags of potential. So I called David up and we took the test together. Because I had my fears about how it might go, I recorded our conversation. You can listen to that below. You’ll probably get the most out of it if you follow along with the test yourself, by going to nnchallenge.org.uk and signing up. It only takes a minute! WARNING: Spoilers ahead         We got to Level 2! And it turns out it did give us certificates! More information Take the National Numeracy Challenge (or, since you’re reading this site, share that link with your relatives) National Numeracy

MathsJam is an annual conference in the UK, and a monthly night in pubs around the world, organised respectively by mathematician and juggler Colin Wright, and stand-up mathematician Matt Parker. We cornered Matt and Colin at the MathsJam conference last November, and talked to them for just over half an hour about the conference, the pub nights, and a disturbing amount about cake. Here are some links to the things we talked about: MathsJam website MathsJam conference website @MathsJam, on Twitter MathsJam Bake-off entries, 2013 Matt’s maths mug

David and I sat down again and talked about maths a bit more. I’m calling this number 1 because it suits both our counting systems: David can call this the first podcast of a new series, and I can say the one we put out under All Squared was number 0. Everyone wins! Here follows a long rambly list of things we talked about, and some things we alluded to too. The button to actually play the podcast is down at the bottom of the post. Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory The probabilistic method Swiss cheeses, rational approximations and universal plane curves (The one with the excellent bibliography) A cheaper Swiss cheese Alice in Switzerland: The life and mathematics of Alice Roth Meromorphic function Carrots for dessert Orange peels and Fresnel integrals Cake Cutting Mechanisms The University of Auckland has lots of kiwis in its logo. Newcastle University only has one lion. Computer analysis of Sprouts with nimbers Nimbers On Numbers and Games How to eat 4/9 of a pizza On the Cookie Monster Problem 100 Essential Things You Didn’t Know You Didn’t Know Garfield’s proof of the Pythagorean theorem Napoleon’s theorem Arithmetic derivative David really does have a big tattoo of $\pi$ on his chest. Tukey tallying There exist infinitely many twin primes iff there are infinitely many primes $p$ such that $(p^2)^{\prime\prime\prime} = 1$. The Princeton Companion to Mathematics (warning: auto-playing “podcast”) A CBE is not quite as worthy as a Knight or a Dame The book with the pictures of nudey ladies is Groupes Stables, by Bruno Poizat. The French edition with the pictures is very hard to get hold of (we had to do an inter-library loan through the university), but the foreword to the English translation is superb, and basically boils down to “je ne regrette rien”. The proof that $\sqrt[n+2]{2}$ is irrational because of Fermat’s Last Theorem, which was retold at MathsJam by Julia Collins. That came from the MathOverflow question, “Awfully sophisticated proof for simple facts”. Congruent number Matrix determinant fact Determinants and Matrices by A.C. Aitken (possibly shonky PDF copy) Pfaffian The 15 stupid proofs that the primes are infinite were published in the latest issue of Paradox (PDF), the magazine of the Melbourne University maths and stats society. They’re on page 17.

We haven’t done one of these for absolutely ages. Since all three of us were at the big MathsJam conference a couple of weekends ago, we decided to introduce a local minimum into the fun curve by sitting down and talking about how this site’s doing. Actually, we ended up talking about the MathsJam baking competition for absolutely ages. When we got round to talking about the site, we mentioned: Council orders maths & Sudoku to be removed from mathematician’s gravestone Prime gaps update All Squared, number 10: maths journalism From the mailbag: dual inversal numbers Carnival of Mathematics 104 Submit a thing to the next Carnival of Mathematics

Evelyn Lamb is a professional mathematician who has taken up journalism on the side. She received the AAAS Mass Media Fellowship last year, and spent the summer writing for the magazine Scientific American. We talked to her about maths journalism, the challenges involved in making advances accessible to a wider audience, and the differences between blogging and print journalism. Here are some links to go with the things we talked about: AAAS Mass Media Fellowship Evelyn Lamb. Evelyn on Twitter. Roots of Unity, Evelyn’s blog at Scientific American. The AMS Blog on Maths Blogs, edited by Evelyn Lamb and Brie Finegold. Solved? 80-year-old puzzle of the infinite sphere, New Scientist‘s coverage of last year’s invariant subspace ‘proof’. Adam Goucher’s blog, Complex Projective 4-Space. Evelyn’s Carnival of Maths post.

We have an unusual All Squared podcast for you this time. My good friend David Cushing has been asking to do a podcast for absolutely ages. We couldn’t decide on a single topic to talk about, so instead I suggested we just sit down and chat about maths in general, like we do when there isn’t a microphone in front of us. We talked for about an hour and a half, but because I’m completely stupid we lost a big chunk of it when the microphone switched off. To make things even worse, we recorded in a room with a ridiculously loud fan, so there’s that to contend with. Anyway, we talked about some fun stuff, so I think it’s worth listening to. Here are some links relevant to the things we talked about. David would like you to know that $5 \times 16017 = 80085$. The book David brought was Topology, by James Munkres. Brouwer’s fixed-point theorem says that for any continuous function $f$ with certain properties mapping a compact convex set into itself there is a point $x_0$ such that $f(x_0) = x_0$. The pancake theorem is referred to by MathWorld as “a two-dimensional version of the ham sandwich theorem”, so CP wins. The ham sandwich theorem says that the volumes of any $n$ $n$-dimensional solids can be simultaneously bisected by an $(n-1)$-dimensional hyperplane. The hairy ball theorem says that there is no nonvanishing continuous tangent vector field on even-dimensional $n$-spheres – there’s always a point on the sphere where the function is zero. The black hole information paradox says that it’s possible for a black hole to destroy information. In 2004 Stephen Hawking conceded his bet that information is destroyed, so CP wins again. (Guess who’s writing this summary) The book CP brought was Only Problems, Not Solutions by Florentin Smarandache. It turns out he’s a bit of a character! The family of sequences which contains a sequence for each digit, except inexplicably 1, was “Primes with $n$ consecutive digits beginning with the digit $D$” Problem 102 of Only Problems… contained this cool diagram: We can’t remember what “the Russian book” was. Sorry! The powerful numbers are sequence A060355 in the OEIS. Paul Erdős made a conjecture on arithmetic progressions. The Bee Gees consisted of brothers Barry, Robin, and Maurice Gibb. That’s three people: a powerful triple. $x^2 – 8y^2 = 1$ is a Pell equation, and the reason why the continued fraction representation of $\sqrt{8}$ generates consecutive pairs of powerful numbers. The Muddy Children puzzle is a good introduction to public announcement logic. The slides we were looking at were “The Muddy Children: a logic for public announcement”, by Jesse Hughes. Analysis vs Algebra predicts eating corn? David was playing Wuzzit Trouble by InnerTube Games. It was reviewed here by Colin Beveridge last month.

This is the second and final part of our interview with Colm Mulcahy. Last week we talked about card magic; in this part we moved on to the subject of Martin Gardner and the gatherings of interesting people associated with his name. We’ve tacked on some blather we recorded about the British Science Festival in Newcastle to the end of this podcast. Listen in to hear what we think about maths! (We’re broadly in favour of it.) Here are some links to go with the things we talked about: Martin’s autobiography, Undiluted Hocus Pocus, came out last month. Here’s a review in Plus Magazine. Mathematics Awareness Month in 2014 will be on the theme of “Magic, Mystery and Mathematics”, to celebrate Martin Gardner’s centenary. The Gathering 4 Gardner happens every two years. The next one is in 2014, but it’s invitation only! Celebrations of Mind happen all round the world to carry on the Gardnerian spirit. You can look at a map of all the events and register your own at the official site. Colm’s book Mathematical Card Magic: Fifty-Two New Effects is published by CRC Press, priced £19.99/$29.95 and available from the booksellers in general.

Colm Mulcahy is an original Aperiodical contributor (Aperiodicontributor?) and friend of the site. He’s spent the last year and a bit writing his new book, Mathematical Card Magic: Fifty-Two New Effects. It came out a few weeks ago, so we thought it was a good opportunity to talk to him and find out just what’s so great about mathematical magic tricks. Actually, we had that thought quite a while ago and if we’d been the least bit organised this podcast would’ve come out the same day as the book. As it happened, we first arranged to talk to Colm back in May, and then it took literally three months before we actually managed to record the interview. … And then it took us three weeks to edit it up and upload it. Sorry! Because Colm had so much interesting stuff to say, we’ve split the interview into two parts. In this first half we talk about the book and mathematical card magic; in the second part, out next week, we talk about Martin Gardner and the Celebration of Mind. Mathematical Card Magic: Fifty-Two New Effects is published by CRC Press, priced £19.99/$29.95.