The British Prime Minister Rishi Sunak has announced that all students will study maths to age 18. The response has been varied, with commentators from both within mathematics and from non-mathematical backgrounds weighing in (with varying degrees of nuance).

However, this isn’t planned to happen soon – only to start the work to introduce this during this Parliament, with actual implementation to happen at an unspecified point in the future.

It’s worth noting that there is a shortage of maths teachers, with nearly half of schools currently using non-specialist maths teachers, according to the *TES*.

The fact this might make maths a political football is a bit of a problem – the opposition Labour party say “they’ve nothing to offer the country except double maths”. (As much as we love maths, we’ll agree there are more important things to worry about at the moment).

The Chrome browser, and eventually other browsers built on it such as Edge and Opera, can now render MathML without any additional libraries as of version 109. Chrome briefly had some support for MathML, which was removed in 2013 due to lack of interest from Google. The developers who were working on it have kept plugging away, funded by the open source software consultancy Igalia.

Until now, the only reliable way to display mathematical notation on the web has been to use a JavaScript library such as MathJax or KaTeX, which do all the work of laying out symbols using generic HTML elements.

Now, you can just put MathML code in a page and expect most browsers to display it, like this:

$$\int \frac{1}{{x}^{2}+1}$$

There’s still a need for MathJax and the like: writing MathML code is no fun, so they’re still useful for translating LaTeX code, and MathJax adds a range of annotations that help with accessibility. But this is a step towards mathematical notation being much easier to work with on the web!

The US National Academies have released a series of posters “Illustrating the impact of the mathematical sciences”.

CLP’s place of work still has some Millennium Maths Project posters clinging on to the walls, older than almost all of the students, so maybe it’s time for a refresh! *(via Terence Tao)*

Tim Austin is the new Regius professor mathematics at Warwick. *(via Warwick Mathematics Institute)*

A bit of bureaucracy news: the Council for the Mathematical Sciences, comprising the five learned societies for maths and stats in the UK, is creating a new Academy for the Mathematical Sciences. It looks like the societies for the different sub-disciplines have acknowledged they need to work together, though this gives off a “now you have n+1 standards” smell. They’ve got a nice logo, though.

The Financial Times style guide changed so that ‘data’ is always singular, pragmatically following common usage. FT writer Alan Beattie said it best: “For anyone opposed, I’d like to know what your agendum is.“

The London Mathematical Society will hold a ceremony in London on 22nd March to officially award the Christopher Zeeman medal to the 2020 and 2022 medallists, Matt Parker and Simon Singh.

The ICMS in Edinburhgh has launched a “Maths for Humanity” initiative, which will be “devoted to education, research, and scholarly exchange having direct relevance to the ways in which mathematics, broadly construed, can contribute to the betterment of humanity.” *(via Terence Tao)*

Yuri Marin has died. The Max Planck Institute has posted an obituary describing his life’s work. One of his PhD students, Arend Bayer, collected some memories in a Mastodon thread.

William ‘Bill’ Lawvere has died. There is a page on the nLab describing his life’s work.

]]>In December I organised a series of online public maths talks called *What Can Mathematicians Do?*

The recordings of the talks are now online, free for anyone to watch. You could go to the official page I put up on Newcastle University’s website, or you could just watch them here!

First, Tanya Gleadow talked about the maths of drawing with lasers, and I stepped in at the last minute to talk about the Herschel enneahedron:

In the second session, Abi Kirk talked about Euler’s formula for polyhedra, and Amy Mason shared a method for deciding what to watch next on Netflix:

Third, Chetna Petal talked about her mathematical career in “I introduce myself as a mathematician… yes, really” and then Lucy Rycroft-Smith talked about the maths of menstruation (yes, really!)

In the penultimate session, Sophie MacLean showed how to get rich by applying maths to stock trading, and Lauren Gilbert talked about her experiences as a disabled physics student at Newcastle:

Finally, Naomi Wray enthused about the dozenal system for writing numbers, and Matt Mack described how to make art using the Travelling Salesman Problem:

So there you go!

I reckon the series was a moderate success: I did gather ten disabled mathematicians to talk to the public about maths, but the format didn’t work too well. We tried to time the sessions so that schools could take part in the last week of school, but didn’t get much take-up. I don’t know if I should have been more persistent with reminding teachers who signed up about the sessions, or if it just wasn’t practical. It was interesting to work with BSL interpreters for the first time, and I’m glad to have made contact with all of the speakers, some of whom I hadn’t worked with before.

]]>The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>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!

]]>π is an irrational number that is equal to 3.1415926535 (to 10 digits). Things could have been different, however, if Dr. Edward J. Goodwin succeeded in passing Indiana Bill No. 246. This bill would have completely changed π and mathematics as a whole.

In 1894, Dr. Goodwin, a physician who dabbled in mathematics, claimed to have solved some of the most complex problems in math. Among these was the problem of squaring the circle, which was proposed to be impossible by the French Academy in 1775. This is impossible due to the fact the area of a circle is $\pi \cdot r^2$, where $r$ is the radius, and the area of a square is $s^2$, where $s$ is the length of each side.

This was proven by Ferdinand von Lindemann in 1882, and is what makes squaring a circle impossible.

In order to square a circle, $\pi \cdot r^2$ must be equal to $s^2$. For example, if $r=1$, we would have $\pi \cdot 1^2 = s^2$, or $\pi = s^2$. This would mean that each side of the square is equal to the square root of π, and since π is transcendental, there’s no algebraic expression that could describe π.

Regardless, Goodwin claimed to have done it, and published his paper to *American Mathematical Monthly* in 1894. It was gibberish, and no amount of understanding in mathematics would make his work comprehensible. He claimed nine different values of π across his many works, with one claim going as far as $9.2376\ldots$, “the biggest overestimate of π in the history of mathematics” (*A History of Pi*). When his theories weren’t becoming popular, he decided to take them to the Indiana State Legislature on January 18, 1897.

Goodwin had convinced his state representative, Taylor I. Record, to introduce House Bill 246 (Indiana Bill No. 246). House Bill 246 would make Goodwin’s method of squaring the circle a part of Indiana law. However, those in the legislature either didn’t understand or didn’t even glance at the bill – and the House Committee on Canals decided to pass it. Dr. Goodwin’s ridiculous bill was now headed to the senate.

At the statehouse where the senate took up the bill was Professor Clarence Abiathar Waldo, a mathematics professor from New York. When Waldo heard what the bill was about, he was shocked to discover he was in the middle of a debate on a fundamental principle of mathematics. He decided to intervene and talk to the senators about the repercussions the bill would have on everything mathematics, and was able to stop the bill from passing the second chamber.

After Waldo’s intervention, it was clear to everyone that the people involved in the attempted passing of the bill, including Dr. Goodwin, were all wrong, and it was ridiculous to define mathematical truth by law.

]]>The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>Rational numbers, when written in decimal, either have a terminating string of digits, like $\frac{3}{8}=0.375$, or produce an infinite repeating string: one well-known example is $\frac{1}{7}=0.142857142857142857…$, and for a full list of reciprocals and their decimal strings, the Aperiodical’s own Christian Lawson-Perfect has built a website which generates a full list.

I’ve collected some interesting observations about the patterns generated by the cycles of recurring decimals, and in particular several relating to $\frac{1}{7}$.

For anyone interested, there’s a surprising connection between reptend primes and Fermat primes.

The recurring cycle for $\frac{1}{7}$, which is $142857$, has a length of $6$ digits – and when the length of the cycle produced from a fraction is one less than the denominator of the fraction, the cycle is a **maximum** recurring cycle. When the denominator is a prime number $>5$, the rational number will always produce a recurring cycle, and many primes produce a maximum cycle. Such primes are called **reptend primes** and the first fourteen are $7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167$ (OEIS A001913).

The decimal expansion of general fractions of the form $\frac{n}{7}$ also have the interesting property that it contains the same digits in the same cyclic pattern for any value of $n$ up to $6$, but with the start digit shifted along each time: $\frac{2}{7} = 0.285714285714285714…$, $\frac{3}{7} = 0.428571428571428571…$ and so on.

This is not unrelated to the fact that $142857$ is the first **cyclic number**, and the only one not beginning with zero. Cyclic numbers (OEIS A180340) are so named because when a cyclic number $n$ is multiplied by the numbers from $2$ to $n-1$, it contains the same digits in a different order.

$142857 × 2 = 285714$

$142857 × 4 = 571428$

$142857 × 5 = 714285$

$142857 × 6 = 857142$

If we multiply by multiples of $7$, an interesting pattern appears, which when an addition is applied, shows a further connection:

$142857 × 7 = 999999$

$142857 × 14 = 1999998 \rightarrow 1 + 999998 = 999999$

$142857 × 21 = 2999997 \rightarrow 2 + 999997 = 999999$

$142857 × 392 = 55999944 \rightarrow 55 + 999944 = 999999$, where $392$ is $56 × 7$

Multiplication by any number greater than $7$ but not a multiple of $7$ can also be seen to produce, via an addition, more cycles of $142857$:

$142857 × 9 = 1285713 \rightarrow 1 + 285713 = 285714$

$142857 × 37 = 5285709 \rightarrow 5 + 285709 = 285714$

$142857 × 127 = 18142839 \rightarrow 18 + 142839 = 142857$

$142857 × 3123 = 446142411 \rightarrow 446 + 142411 = 142857$

$142857$ is also a **Kaprekar number** (OEIS A006886) – when squared, the two halves of the number sum to the original number. Examples include $45^{2}=2025$ for which $20+25=45$, and $297^{2}=88209$ for which $88+209=297$. For our cyclic number, $142857^{2}=20408122449$ and $20408+122449 = 142857$.

Dattatreya Ramachandra Kaprekar (1905-1986) was an Indian mathematician who said of himself, “*a drunkard wants to go on drinking wine to remain in that pleasurable state. The same is the case with me in so far as numbers are concerned”.*

Adding subsets of digits of cyclic numbers can also be seen to create interesting patterns:

\[14+28+57=99 \qquad 142+857=999 \qquad 1428+5714+2857=9999 \]

We can play the same trick with the second cyclic number $0588235294117647$: $94117647+05882352=99999999$; and using the third cyclic number $052631578947368421$ we have $947368421+052631578=999999999$.

We can also play with squares of subsets of the digits of cyclic numbers:

\[857^{2}-142^{2}=714285 \qquad 94117647^{2} – 5882352^{2}=8823529411764705 \]

For other prime denominators, we don’t always get cyclic patterns like this. The denominator $3$ gives two different cycles, $33333…$ and $66666…$ as does the denominator $13$ ($0769230769230769…$ and $1538461538461538…$). The denominator $11$ yields five different cycles. (For more, read Conway and Guy’s The Book of Numbers).

There is an extraordinary outcome for the set of proper fractions with prime denominator $19$. The maximum recurring cycle for $\frac{1}{19},\frac{2}{19},\frac{3}{19},…..\frac{18}{19}$, when laid out in tabular form, produces a magic square: its rows, columns and leading diagonals have the total $81$.

0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 |

1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 |

1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 |

2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 |

2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 |

3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 |

3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 |

4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 |

4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 |

5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 |

5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 |

6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 |

6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 |

7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 |

7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 |

8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 |

8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 |

9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 |

The first row of the table is the recurring cycle for the rational $\frac{1}{19}$, and the second row is the cycle for the rational $\frac{2}{19}$. The digits for each subsequent row continue in a similar way leading to the final row, the cycle for the rational $\frac{18}{19}$.

Another nice pattern here is the remarkable fact that the cycle $052631578947368421$, the recurring section from $\frac{1}{19}$, can be generated from the the powers of $2$. Writing the powers of two in subsequent rows, starting on the right, and then adding the columns gives:

1 | |||||||||||||||||||||||||

2 | |||||||||||||||||||||||||

4 | |||||||||||||||||||||||||

8 | |||||||||||||||||||||||||

1 | 6 | ||||||||||||||||||||||||

3 | 2 | ||||||||||||||||||||||||

6 | 4 | ||||||||||||||||||||||||

1 | 2 | 8 | |||||||||||||||||||||||

2 | 5 | 6 | |||||||||||||||||||||||

5 | 1 | 2 | |||||||||||||||||||||||

1 | 0 | 2 | 4 | ||||||||||||||||||||||

2 | 0 | 4 | 8 | ||||||||||||||||||||||

4 | 0 | 9 | 6 | ||||||||||||||||||||||

8 | 1 | 9 | 2 | ||||||||||||||||||||||

1 | 6 | 3 | 8 | 4 | |||||||||||||||||||||

3 | 2 | 7 | 6 | 8 | |||||||||||||||||||||

6 | 5 | 5 | 3 | 6 | |||||||||||||||||||||

1 | 3 | 1 | 0 | 7 | 2 | ||||||||||||||||||||

2 | 6 | 2 | 1 | 4 | 4 | ||||||||||||||||||||

5 | 2 | 4 | 2 | 8 | 8 | ||||||||||||||||||||

. | . | . | . | . | 6 | ||||||||||||||||||||

. | . | . | . | . | . | 2 | 1 | 0 | 5 | 2 | 6 | 3 | 1 | 5 | 7 | 8 | 9 | 4 | 7 | 3 | 6 | 8 | 4 | 2 | 1 |

$142857$, the recurring cycle for $\frac{1}{7}$, similarly occurs in this sequence of infinite additions. It begins with $7$ at the top, and each subsequent row is obtained by multiplying by $5$ and moving the end of the number to the left one each time. The cycle $142857$ is produced by adding the columns generated.

7 | ||||||||||||||||||||

3 | 5 | |||||||||||||||||||

1 | 7 | 5 | ||||||||||||||||||

8 | 7 | 5 | ||||||||||||||||||

4 | 3 | 7 | 5 | |||||||||||||||||

2 | 1 | 8 | 7 | 5 | ||||||||||||||||

1 | 0 | 9 | 3 | 7 | 5 | |||||||||||||||

5 | 4 | 6 | 8 | 7 | 5 | |||||||||||||||

2 | 7 | 3 | 4 | 3 | 7 | 5 | ||||||||||||||

1 | 3 | 6 | 7 | 1 | 8 | 7 | 5 | |||||||||||||

6 | 8 | 3 | 5 | 9 | 3 | 7 | 5 | |||||||||||||

3 | 4 | 1 | 7 | 9 | 6 | 8 | 7 | 5 | ||||||||||||

. | 0 | 8 | 9 | 8 | 4 | 3 | 7 | 5 | ||||||||||||

. | 4 | 9 | 2 | 1 | 8 | 7 | 5 | |||||||||||||

. | . | . | . | . | . | . | 7 | 1 | 4 | 2 | 8 | 5 | 7 | 1 | 4 | 2 | 8 | 5 | 7 |

I was surprised to discover in David Wells’ excellent Penguin Dictionary of Curious and Interesting Numbers that the points (1,4) (4,2) (2,8) (8,5) (5,7) and (7,1), formed by overlapping pairs of the digits in the $\frac{1}{7}$ cycle, lie on an ellipse, called the one-seventh ellipse:

Better still, we can concatenate pairs of digits from the cycle. The points created, (14, 28), (42, 85), (28, 57), (85, 71), (57, 14) and (71, 42), also lie on an ellipse, shown below:

Wells also stated that the points determined by the period of $\frac{1}{13}=0.076923076923….$ lie on a hyperbola. To find the equation of this conic, I contacted Professor Marc Chamberland – a co-author of the paper ‘*A Generalization of the One-Seventh Ellipse*‘. Marc sent this explanation in his reply:

Using the notation from our paper, we let $a=0, b=7, c=6$ and $S=9$. Theorem 1 implies that the points $(0,7), (7,6), (6,9), (9,2), (2,3)$ and $(3,0)$ all lie on a conic. Putting these points on the bivariate quadratic curve $Ax^{2} + Bxy + Cy^{2} +Dx + Ey + F = 0$, we can solve for the coefficients: $A = 141, B = 134, C=9, D = -1872, E = -684, F = 4347$.

Marc Chamberland

The conics were a huge and fascinating surprise but I don’t know if there is any conclusion or use for their connection to the cycles. However, there is a connection to the final part of the Pascal pentalogy as the paper A Generalization of the One-Seventh Ellipse makes use of Pascal’s Hexagrammum Mysticum Theorem.

If you’ve found this interesting, the following links are intended for any reader wishing to look further into the content:

- In particular, I recommend Tony Padilla’s Numberphile video explaining how the cyclic permutations are formed.
- MacTutor biography of Dattatreya Ramachandra Kaprekar, which includes some more number patterns
- You can read more about Cyclic numbers, Midy’s Theorem, Artin’s Constant and the general bivariate quadratic curve at Wolfram MathWorld.

As part of the 24 Hour Maths Game Show which took place at the end of October 2022, our own Christian Lawson-Perfect designed a maths/games crossover gameshow format to end them all – a mashup of hexagon-fighting TV quiz Blockbusters, and his own personal obsession: interesting mathematical factoids. Welcome to Blockbusters of Interesting Maths!

The premise of Blockbusters of Interesting Maths is simple. Start by collecting three maths communicators – in this case, me (**Katie Steckles**), Sheffield Hallam Uni maths lecturer and recreational maths fan **Alex Corner**, and mathematician and juggler **Colin Wright**. Colin is a self-described “torturer of adults and confuser of children”, but to clarify, he mostly does that using interesting maths. Alex teaches on the SHU Game Theory and Recreational Maths module with our own Peter Rowlett, and was prepared to have a good go at coming up with some interesting facts. I, on the other hand, have come across far too many interesting maths facts in my time, and can definitely half-remember most of them.

Between us, we’re pitted against Christian’s board of randomly chosen words – from Ogden’s Basic English, a collection of 850 common English words, from which he’s deliberately removed a chunk of the mathematical and scientific terminology. To make our way across the board, we pick a letter and find the word hiding behind, and are then charged with coming up with some kind of interesting maths fact relating to that word.

Christian’s judgement on whether our maths fact was interesting enough is final, and we’ve got to make an unbroken line from one edge of the board to another. If we fail to come up with a sufficiently interesting fact, or our fact is deemed too tangential to the word in question, that tile is blocked off.

Since we could never do anything the easy/conventional way, instead of a tessellation of hexagons, CLP’s gone for the Cairo pentagonal tiling, so each cell is only adjacent to five others instead of six. His web gadget, a version of which can still be found online for anyone to use (BYO interesting mathematicians), was deployed live on the Game Show to challenge the three of us, and the below is a blow-by-blow of what went down, with links to some of the things we talked about.

We’ve also included some additional facts from Christian, who is also a font of interesting maths facts and is making up for the fact that he didn’t get to play himself. Next time!

My initial instinct was to pass over to Colin, as he’s got a whole bit about calculating the distance to the moon using a pendulum, but instead he gave some interesting facts: the distance to the moon is pretty much exactly about 10 earth circumferences (~40 megametres), and it creates tides on opposite sides of the earth at the same time.

**Christian**: I can’t remember if anyone talked about all the different ways of counting a lunar month… I like the word sidereal and have no idea how many syllables it has.

We failed to come up with sufficient interesting maths for this – a bit of discussion about publishing results before someone else who’s working on them was deemed to be too depressing.

Alex talked about the work of Alan Turing on abiogenesis – mathematical models that can be used to describe patterns found on animal fur, including leopard spots and zebra stripes. Christian confirmed this was to do with reaction-diffusion models.

**Christian**: Back in 2008, a Simon Scarle published a paper connecting Turing’s work on reaction-diffusion to his other work on computability, through simulations of cardiac arrhythmia on the Xbox 360. I’ve never known what to do with this information. If you want to play with reaction-diffusion models yourself, there’s a good simulator called Ready, which we wrote about it in 2012.

I waffled briefly about the history of counting and the Ishango bone, which is an interesting historical artefact linked to early mathematical activity, and which it turns out I’d got mixed up with the Lebombo bone, which is an even older one.

Colin took this as a verb, and talked about predator-prey dynamics, particularly related to pursuit predation, including ambush and persistence behaviour in hunting. For each type of hunting, the animal has to weigh the probability of a successful catch against the amount of energy expended on the chase.

After a brief digression about which direction the real line points in (since we’d missed the opportunity to connect the board top-to-bottom, which most of us hadn’t realised was a thing), Alex couldn’t think of anything to say, so we lost this one.

After mentioning the mathematical use of the word, I managed to just about describe a particular maths problem this reminded me of that involved chasing something that’s swimming in a river (Christian mentioned this was covered in Dara Ó Briain’s School of Hard Sums, and it turns out there’s a writeup on Marcus Du Sautoy’s blog), and we then went on to another puzzle about a cat in a pond, which Ben Sparks has done a great video about.

**Christian**: Talking of interception reminded me of this fun paper describing a strategy for avoiding being intercepted while mapping an unfriendly subway system.

Colin covered a couple of topics – starting with control theory, which Colin compared to riding a unicycle. The trick is to keep the wheel under you, by (e.g) pedalling faster if you’re falling forwards, which can be understood by solving fairly straightforward differential equations – as unicycling robots often do.

He also talked about controlling a dog’s behaviour, and how rewarding good behaviour every time means the effect of training wears off more quickly, whereas rewarding it randomly some of the time means the effect lasts longer – this is related to spaced repetition as a learning technique.

Back over to Alex, who took electrical inspiration and used it as a chance to talk about capacitor laws. There were lots of nice relationships between different physical laws and it all got a bit physics, and as a result was rejected by Christian, so we lost this one.

I took the opportunity to talk about mathematical crystal structures, bond angles and 3D lattices (and got in a Kathleen Ollerenshaw mention). Christian also connected it to the structures of viruses, and mentioned Hamish Todd’s lovely videos.

Colin riffed on ratios in mixtures, from concrete to cake recipes, and then moved on to mixed techniques. Combinatorics, for example, uses a variety of different techniques you have to try in different combinations in order to solve a problem, and Colin explained how maths research, particularly in applied contexts, a mixture of techniques can be most powerful. Von Neumann showed that mixed strategies are always more effective in game theory!

After a brief digression about profit-loss models in economics, I jumped in with a mention of the version of internet protocols used in communication with objects in space, which Colin then ran with – talking about comms in trading (which relies on the speed of light to make sure transactions are instantaneous). A client-server model can be used, and in some contexts, equations from fluid mechanics are even used to describe how packets of information are moved around.

With that, we finally managed to satisfy Christian’s mathematical interestingness quotient and successfully connected the opposite sides of the board.

If you’d like to rewatch this or any other part of the 24 Hour Maths Game Show, you can find links to each segment on the website, and you can still donate to our charities by visiting 24hourmaths.com/donate.

]]>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)*

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.

]]>- 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.

Get the full list from gov.uk.

Updated 2/1 to add Dr. Jeffrey Quaye, HT The Mathematical Association on Twitter.

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