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Aperiodical News Roundup – April 2021

Top news this month: Pure mathematicians at Leicester have opened a GoFundMe to pay for legal support in their fight to keep their jobs. The London Mathematical society has published a letter making the case for pure maths at Leicester, and there’s a petition you can sign.

Culture

Hannah Fry has a new TV show about maths and sport, on BT Sport and YouTube, called It’s A Numbers Game (or IT’S A NUMB3R5 GAME, if you believe the logo). She’s joined by Pippa Monique, Ugo Monye, Andrew Mensah and Dr Nick Owen. It’s on each Saturday on both BT Sport and YouTube. There are some resources for kids aged 5 to 14 on Twinkl, to go with the show.

Erasmus EUR2 coin

Awards

Dr. Marie Davidian is the recipient of the 2021 Marvin Zelen Leadership Award in Statistical Science. (via Harvard Biostatistics)

UK mathematicians Yuhka Machino and Jenni Voon earned gold medals at the 2021 European Girls’ Mathematical Olympiad, and the UK team as a whole finished third. (via the UK Mathematics Trust)

Events

The Institute of Mathematics and its Applications is again running a series of online talks.

The first talk at the 6th May event will be from Nick Higham who has been awarded the Gold Medal award in recognition of outstanding contributions to mathematics and its applications. This will be followed by Jane Leeks and David Abrahams discussing future developments in mathematical sciences knowledge exchange.

There will be a couple more talks on the 25th of May to do with modelling and Covid-19.

More information: IMA Mathematics Online series


The London Mathematical Society is offering two summer placements – a Library and Special Collections Summer Placement (working with the LMS’s special collections) and an Equality and Diversity – Success Stories Placement (putting together profiles of successful mathematicians), both of which are paid hourly at three days a week for 8 weeks over the summer, and would suit prospective postgraduates with an undergraduate degree.

More information: Jobs at the LMS


The International Congress of Mathematicians is running a surprising maths videos contest. Prizes include a grant to attend ICM 2022 in St Petersburg, which won’t be much use to LGBT+ mathematicians, whose existence in Russia is illegal, or Azat Miftakhov, a student at Moscow State University who has been detained by Russian authorities for two years. If that doesn’t faze you, the ICM has produced an example of a surprising maths video:

Proof news

Kelsey Houston-Edwards writes in Quanta magazine about a proof of the Erdős-Faber-Lovász conjecture on colouring hypergraphs. The preprint by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku and Deryk Osthus is available on the arXiv.

Also in Quanta magazine (if you can pay people to write maths news, they write maths news! Who knew?), Erica Klarreich writes about a counterexample to the unit conjecture on group algebras, presented at the end of a talk by Giles Gardam, and Steve Nadis writes about a recent proof of a special case of the Erdős-Hajnal conjecture in graph theory. That guy Erdős sure made a lot of conjectures.

Over on the mersenneforum.org, where seekers of new and exciting prime numbers hang out, it’s been reported that a new probable prime repunit has been found – it’s got a record 5794777 decimal digits, all of which are the digit 1. (via Ed Pegg)

Other news

Version 3.0 of SnapPy, program for studying the topology and geometry of 3-manifolds, has been released. (via Jordan Ellenberg)

Early Family Math is a new free maths resource website for children from 6 months to 6 years old. At the moment it has a lot of resources for activities, and some maths story books. They say that videos are forthcoming.

And finally, there’s a fundraiser for Mathematicians of the African Diaspora, which hosts the largest searchable database of mathematical scientists of the African Diaspora in the world, and is looking for funding to expand its database and reach a wider audience so it can continue to inspire the next generation of Black mathematicians. (via Edray Goins)

My robot draws TeX

For my birthday I got an EleksDraw pen plotter. It’s a cheap and cheerful example of the form: a pair of orthogonal metal rods with a pen on the end, attached to electric motors. The idea is that I can connect it to my computer and the computer can direct it to draw things. It arrived as a kit, so first of all I had to descend from the astral plane of pure thought and – shudder – screw the bits together.

The #plottertwitter hashtag is a constant source of inspiration, where people around the world share pictures of the amazing, beautiful things they’ve made their pen plotters draw, often with the AxiDraw plotter, which differs from mine in that nobody seems to have had to attach 200g of batteries as ballast to the pen holder to overcome friction on the knacky sliding rail.

My pen plotter. The end closest to the camera is the pen holder, which has had two AAA and one C battery stuck to it with electrician's tape.

The basic idea of a pen plotter is that the pen holder is free to move in the plane, constrained by the lengths of the two axes. If there’s a pen in the holder and paper underneath as it moves, then a drawing happens. The pen holder can move up and down, to lift the pen away from the paper so it can move without drawing.

The instructions you can give the plotter are quite straightforward: move in a straight line to these coordinates; move the pen up or down; move back to the ‘home’ position. It’s a lot like the turtle drawing robot I played with in primary school.

A robot turtle. Its shell is clear plastic, through which you can see lots of electronics and a pen holder.
A Valiant turtle robot, similar to the one I used in primary school. Photo from National Education Network.

You can either directly write a list of instructions for the plotter, or write some code that takes a vector image and produces a corresponding set of instructions. SVG is a widely-used vector graphics format, so it’s a common choice of input for pen plotters.

This was very pleasing to watch.

So I was playing around with my pen plotter, getting it to draw space-filling curves and geometrical diagrams, when I decided that I should get it to draw text. It turns out that there are a few ready-made “fonts” for plotters that give paths to write letters with strokes instead of filling in shapes, so that was nice and easy.

But then I wanted to write mathematical notation, and I remembered: MathJax has an SVG output! It didn’t take long to write a bit of JavaScript that takes some maths written in LaTeX and gets MathJax to produce the corresponding SVG code and insert it into the picture, ready for my plotter to draw.

The remaining problem is that MathJax’s fonts produces shapes that should be filled in, which is easy on a computer screen, but the pen plotter just draws their outlines. That’s not much of a problem, though: I just had to trace over the symbols in Inkscape, and replace each instance of a MathJax symbol with my single-stroke traced version.

The pen plotter hovering over a piece of paper, on which is drawn some mathematical notation. Each of the symbols has been drawn in outline.
Success! But it looks like a mathematical crime scene with those outlines.

There are squillions of symbols in the TeX fonts, and I didn’t want to have to trace them all before I could draw anything, so I decided to do it bit-by-bit. I added a step to my MathJax → SVG tool to capture any symbols in the output that hadn’t been traced yet and produce an SVG file I could load into Inkscape. After tracing over those symbols, my code absorbed them into its library of replacements. I wasn’t too careful to be precise with my traced symbols – I wanted it to look as much like handwriting as I could manage.

Some mathematical notation drawn in a jumble on a page. The symbols are drawn with single strokes instead of outlines.
My first few traced symbols. They already look a lot better, and more like handwriting, than the standard TeX fonts.
A passage of text with inline mathematical symbols drawn on paper.
Starting to draw TeX inline with plain text. The font I chose for the plain text made it look a bit too much like the product of a typewriter. The text is from Éléments de Géométrie of 1885 by L’Abbé M. Reydellet, another birthday present.
Another passage of mathematical text. This time the plain text is drawn in a style that looks more like natural handwriting.
This looks much better! The text is drawn from Philip Ording’s brilliant 99 Variations on a Proof.

The fantastic thing about MathJax is that it does a lot of work to match its output with the size of the surrounding plain text, so the results looked really good straight away.

I decided to draw some mathematical postcards to send to my maths pals. On one side I drew a picture, and on the other side I wrote a passage of text about it, often with plenty of mathematical notation.

Eight postcards drawn on colourful paper. They each feature a different mathematical diagram.
The “front” sides of my first batch of postcards.
Eight postcards, each with a passage of text including inline and standalone mathematical notation.
The “back” sides, with explanations of the diagrams. You can see a few places where the pen went awry or failed to drop down, so I had to make it draw over some sections a couple more times.

I’m particularly pleased with this formula for the length of a toilet roll, drawn from the paper How long is my toilet roll? – a simple exercise in mathematical modelling by Peter R. Johnston:

I’ve put all of my plotter-related code online. If you just want to make your own postcard, here’s a tool you can use to write a postcard with mathematical TeX.

Some different ways of multiplying numbers, vectors and matrices

Here’s a quick video I recorded at the end of my work day, inspired by this tweet.

Aperiodical News Roundup – October 2020

Here’s a roundup of mathematical stories from the month that’s just been.

The enormous difficulty of telling the truth about escalators with statistics

Earlier this year, when getting the train to work was still a thing for me, I noticed this statistic:

Did you know? 95% of the time escalators were working in the last four weeks.

The permutation clock

52 playing cards arranged in a grid

I recently had an idea: map the Unix time (seconds since 1st January 1970) to shufflings of a deck of cards. Each second would correspond to a different ordering of the 52 cards.

I wanted to think about how mind-bogglingly huge $52!$ is: $52!$ seconds is more than $2 \times 10^{60}$ years. So even if you spent your entire life watching this thing, you’d leave this world having seen basically none of the possible permutations. Happily, Wikipedia reckons that the heat death of the universe will happen in about $10^{100}$ years, so there’s plenty of time for me to enact my plan.

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