### Review: Who’s Counting, by John Allen Paulos

We asked guest author Elliott Baxby to take a look at John Allen Paulos’ latest book, Who’s Counting.

Mathematics is an increasingly complex subject, and we are often taught it in an abstract manner. John Allen Paulos delves into the hidden mathematics within everyday life, and illustrates how it permeates everything from politics to pop culture – for example, how game show hosts use mathematics for puzzles like the classic Monty Hall problem.

The book is a collection of essays from Paulos’ ABC News column together with some original new content written for the book, on a huge range of topics from card shuffling and the butterfly effect to error correcting codes and COVID, and even the Bible code. As it’s a collection of separate columns, it doesn’t always flow fluently – I did find myself losing focus on some of the topics covered, particularly ones that didn’t interest me as much. This was mainly down to the content though – the writing style is extremely accessible and at times witty.

The book included some interesting puzzles and questions, which were challenging and engaging, and included solutions to each problem – very helpful for a Saturday night maths challenge! I even showed some to my friends, who at times were truly puzzled. I loved the idea of puzzles being a means of sneaking cleverly designed mathematical problems onto TV game shows. It goes to show maths is everywhere!

I enjoyed the sections on probability and logic as these are topics I’m particularly interested in. One chapter also explored the constant $e$, where it came from and where else it pops up – a very interesting read. It does deserve more attention, as π seems to be the main mathematical constant you hear about, and I appreciated seeing $e$ being explored in more depth.

This book would suit anyone who seeks to see a different side of mathematics – which we aren’t often taught in school – and how it manifests itself in politics and the world around us. That said, it would be better for someone with an A-level mathematics background, as some of the topics could be challenging for a less experienced reader.

It’s mostly enjoyable and has a good depth of knowledge, including questions to test your mind. While I didn’t find all of it completely engaging, there are definitely some points made in the book that I’ll refer back to in the future!

### Aperiodical News Roundup – December 2022

Here’s a roundup of the maths news we missed in December 2022.

## Maths News

The leap second, referred to in this Independent article as a ‘devastating time quirk’, is finally being abolished. This has been covered in a bunch of places, mostly being quite rude about the leap second, including a writeup in the New York Times where it’s referred to as ‘a kludge, a bain, a pain in the little hand’ (£), and this Live Science article (‘pesky’). A committee at the International Bureau of Weights and Measures apparently nearly unanimously voted in support of Resolution D, meaning there won’t be any leap seconds from 2035 until at least 2135.

Anti-maths news! Princeton mathematician Rachel Greenfield (pictured left – photo by Dan Komoda/Institute for Advanced Study), working with Fields Medalist Terry Tao, has posted a disproof of the periodic tiling conjecture. A preprint titled ‘A counterexample to the periodic tiling conjecture‘ is now on the ArXiv, and if it’s correct, means that any finite subset of a lattice which tiles that lattice by translations, must tile it periodically. There’s a nice explanation in the Quanta writeup!

Meanwhile there’s been a new claimed proof of the 4-colour theorem, which is non-constructive (meaning it doesn’t rely on finding a colouring for every possible map, but proves the theorem generally). Some people have been skeptical about the proof, including in this statement from Noam Zeilberger, which links to a Mastodon discussion with John Carlos Baez. (via Neil Calkin on Mastodon)

Another claimed proof – this time of the sunflower conjecture. A k-sunflower is a family of k different sets with common pair-wise intersections, and the conjecture gives conditions for when such a thing must exist.

ArXiv has posted a framework for improving the accessibility of research papers on arXiv.org – their plan is to offer html as well as PDF versions of papers. (via Deyan Ginev)

## Events

Bright-trouser-wearer and mathematician Marcus Du Sautoy is offering a free OU online course, entitled ‘What we cannot know’. Find out how he manages to break the rules of reality by facilitating you knowing something that it’s by definition impossible to know, by signing up online for the 8-week course (which can also be accessed without signing in but then you don’t get a badge).

As part of their Elevating Mathematics video competition, the National Academies Board on Mathematical Sciences and Analytics (BMSA) invites early career professionals and students who use maths in their work to submit short video elevator speeches describing how their work in mathematics is important and relevant to our everyday lives, with a $1000 Prize for the best video. And finally, in a rare instance of us linking to the Hollywood Reporter, Hannah Fry is to front a science and tech series for Bloomberg, entitled The Future With Hannah Fry. Sounds great! It’ll be available on Bloomberg’s Quicktake streaming service and will explore breakthroughs in artificial intelligence, crypto (not clear if -graphy or -currency), climate, chemistry and ethics. ### Particularly mathematical New Years Honours 2023 It’s that time of year when we take a look at the UK Government’s New Years Honours list for any particularly mathematical entries. Here is the selection for this year – if you spot any more, let us know in the comments and we’ll add to the list. • Paul Glaister, Professor of Mathematics and Mathematics Education, University of Reading. Appointed CBE for services to education. • Dan Abramson, headteacher of King’s College London Maths School. Appointed OBE for services to education. • Kanti V. Mardia, Senior Research Professor, Leeds University. Appointed OBE for services to Statistical Science. • Jeffrey Quaye, National Director of Education and Standards at Aspirations Academies Trust, PhD in Mathematics Education and Chartered Mathematics Teacher. Appointed OBE for services to education. • Charlotte Francis, maths teacher and entrepreneur. Appointed Medallist of the Order of the British Empire for services to education. Updated 2/1 to add Dr. Jeffrey Quaye, HT The Mathematical Association on Twitter. ### How to fold and cut a Christmas star This week and last I hosted a series of public maths talks featuring disabled presenters. I’ll post about how that went later, but for now I just want to share this clip of me filling time spreading Christmas joy. This is a party trick that Katie Steckles showed me: you can fold a piece of paper and then make a single cut to produce a five-pointed star. I showed how to do it by following the instructions I’d been told, and then recreated the steps just starting from the insight that when you make the cut, all the edges of the shape need to be on top of each other. Maybe you’ll show someone else how to do it during the Christmas holiday? This doesn’t only work for stars: there’s a theorem that you can make any polygon by folding and a single cut. Erik Demaine has made a really good page about the theorem, with some examples to print out and links to research papers. Katie can cut out any letter of the alphabet on demand, which is impressive to witness! ### Aperiodical News Roundup – November 2022 Here’s a roundup of things that happened online in November that we didn’t cover here at the time! ## Maths Research News According to an article on philosophy news site Daily Nous, an international symbolic logic journal printed then shortly retracted two articles, one entitled “The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic” and the other “There are Infinitely Many Mersenne Prime Numbers. Applications of Rasiowa–Sikorski Lemma in Arithmetic“. After a discussion on MathOverflow, mistakes were found in both papers, and the journal’s editor posted: Recently two articles on the applications of the Rasiowa-Sikorski Lemma to arithmetic were published online in Studia Logica without proper examination and beyond reasonable standards of scholarly rigor. As it turned out, they contained an irrrepairable mistake and, consequently, have been retracted from the journal’s website. The papers will not appear in print. Studia Logica editor-in-chief Jacek Malinowski (via Catarina Dutilh Novaes on Twitter, whose thread includes some clarifications.) According to Conway’s Life, a blog which documents developments in research around Conway’s Game of Life, on November 9, 2022 Pavel Grankovskiy discovered that 15 gliders can make any pattern in Conway’s game of life. Given a particular shape, the gliders can be set up to create it (eventually) beating a recent record of 16 gliders. (via Oscar Cunningham on mathstodon,xyz:) Fields medalist Terry Tao reports some progress on the union closed sets conjecture, an open problem in combinatorics, which has seen rapid developments thanks to (in Tao’s words) ‘maths at internet speed’. ## Other News As of 11th November, applications for Young Researchers for the Heidelberg Laureate Forum 2023 are open. If you or someone you know is a researcher in maths or computer science at undergrad or postgrad level, and would like to spend a week next September in a lovely town in Germany meeting the world’s most decorated mathematicians and computer scientists, you should consider applying! The latest issue of The Mathematics Enthusiast is a special issue collecting 29 reviews of popular maths books by maths educators, including Matt Parker, Hannah Fry, Eugenia Cheng, Simon Singh and Jordan Ellenberg among many others. If you’re looking for new pop maths book recommendations, it’s a good place to start! It was announced earlier this month that having discovered sufficiently many very big and very small numbers, it’s time for some new SI prefixes: ronna-, ronto-, quetta- and quecto- have joined the ranks of things that make numbers bigger and smaller, allowing you to describe itty bitty quantities as small as$10^{-27}$(ronto) and$10^{-30}$(quecto), as well as chonky numeros in the region of$10^{27}$(ronna) and$10^{30}$(quetta). The earth weighs 6 ronnagrams, and Jupiter is about 2 quettagrams. “‘R’ and ‘Q’ were the only letters left in the English alphabet that hadn’t been used by other prefixes.” Richard Brown, National Physical Laboratory And in computer news, Google Chrome now supports MathML core, a language for describing mathematical notation embeddable in HTML and SVG. (via axel rauschmayer) ### What Can Mathematicians Do? A series of online talks about maths I’ve put together a series of online public maths presentations, to take place in the last couple of weeks of term before Christmas. This came about after a few people on the Talking Maths in Public WhatsApp group complained that we can hardly ever take up requests for a speaker to deliver a fun maths talk due to our disabilities, usually because of the difficulty of travelling to and from an event. I quipped that we should set up a series of talks for non-commutative mathematicians, and then I was told that the department’s EDI committee had a load of money sitting unused in its budget. So I decided to use some of it! ### Aperiodical News Roundup – October 2022 ## Research AI research company DeepMind said that their AlphaTensor system has discovered a new way to multiply matrices, citing this as the first such advance since the Strassen algorithm was proposed in 1969. AlphaTensor found thousands of algorithms for multiplying matrices of different sizes, but most were not better than the state of the art. Specifically, it found an algorithm for multiplying $$5 \times 5$$ matrices in $$\mathbb{Z}_2$$ in just 96 operations. There’s a paper in Nature describing how the algorithm was found. It’s not all over for us humans just yet, though: the DeepMind announcement prompted two algebraists at Linz University, Jakob Moosbauer and Manuel Kauers, to see if they could do even better. After a few days of thought, they published The FBHHRBNRSSSHK-Algorithm for Multiplication in$\mathbb{Z}_2^{5\times5}\$ is still not the end of the story on the arXiv, giving an algorithm which does the multiplication in only 95 steps.

Meanwhile, in other computers-helping-humans news, the Lean 3 library mathlib has made it to 100,000 theorems, none of which have been left as an exercise for the reader.

## Events

The IMA and LMS have joined forces to offer a new university access programme called Levelling Up: Maths, which aims to address the difficulties that young people of Black heritage face in STEM. A-level students can join the programme, and will be able to access teaching and mentoring in virtual tutorial groups with Black heritage undergraduates, as well as events with Black guest speakers. The programme is also supported by the RAEng, BCS, IOP RSC, MEI and STEM Learning, as well as the Association for Black & Minority Ethnic Engineers (AFBE-UK) and Black British Professionals in STEM (BBSTEM).

What Can Mathematicians Do? is a series of free online public maths presentations organised by Newcastle University’s School of Mathematics, Statistics and Physics, covering a wide range of topics such as how colours mix, how to make a mint on the stock market, and how to pick your next Netflix binge. Aimed at students in school years 10 to 13, the talks are all given by disabled presenters: to show that anyone can be a mathematician, and mathematicians can do anything.

And finally: last weekend, a group of maths communicators (including several Aperiodical editors and regulars) put together a live online 24-hour Mathematical Game Show, featuring mathematical games, games with a mathematical twist, the maths of games and games about maths. The show has raised nearly £5000 for a collection of excellent charities, and the whole show is available to watch back in half-hour or 1-hour segments.

## And finally

Nick Berry of the Data Genetics blog has died. The site ran for over a decade, and was described by Alex Bellos as ‘one of best examples of maths outreach on the web […] A brilliant cabinet of curiosities’. Nick passed away peacefully at home on Saturday October 8th after a long battle with cancer. (via Alex Bellos on Twitter)

Phil Goldstein, aka magician Max Maven, has died. Max Maven popularised the Gilbreath principle, which underlies a host of astonishing mathematical card tricks. (via Colm Mulcahy on Twitter)