The science behind Santa Claus

Christmas is coming! My favourite season of the year has begun, which means that is time to start celebrating with friends, buying presents for my loved ones, sending Christmas cards, etc. But most importantly, it is the time of year when our beloved Father Christmas, Santa Claus, along with his elves, have to start planning a long and exhausting journey that begins the night of 24 December in order to deliver presents to all the good children in every household around the world.

Santa getting ready to deliver presents. Image: public domain.

Here at Chalkdust we are already in Christmas mood (see our series of Christmas conundrums), but this time we wanted to show you a bit about the science behind Santa’s journey, in case you ever wondered. In addition, if you think you spend a lot of money during the Christmas period, we’ll show you how much money Santa has to spend on presents each year (according to our quick calculations).

We are not pretending to understand how Santa works his magic, but we thought it might be fun to apply some maths to the problem. So let’s begin.

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Christmas conundrum #2

It’s time for the second Chalkdust Christmas conundrum. But first of all, we can proudly announce last week’s winners. There were 82 entries to last week’s competition, of which 67 were correct. The randomly selected winners are:

  • Mike Fuller
  • Stewart Robertson
  • Catriona Shearer
  • Steven Peplow

Congratulations! Chalkdust T-shirts are on their way! The solution to last week’s puzzle can be found at the bottom of this blog post.

Now on to today’s puzzle. Four lucky people who submit the correct answer to the puzzle will win a copy of The Indisputable Existence of Santa Claus by Hannah Fry and Thomas Oléron Evans. If you want to know how great this book is, you can read our review of it here. The deadline for entries is Friday 15 December at 6pm.

Click here to download a printable PDF of this week’s puzzle

In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.

The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:

then you can deduce the following:

With the information given in the tree, you can work out the rest of the numbers.

Click here to download a printable PDF of this week’s puzzle

Once you have solved the puzzle, enter the number in the star at the top in the form below for a chance to win. The deadline for entries is Friday 15 December at 6pm. The winners will be announced in next week’s conundrum post, when you will also have a chance to win a copy of The Element in the Room by Helen Arney and Steve Mould.

The solution to conundrum #1

In last week’s conundrum, you were asked to find out who the icosahedral present was for. Stop reading now if you don’t want to know the answer yet.

Clue 5 told you that “the edges of Dominika’s present have an integer length, and her present has an integer volume”. The only Platonic solid that satisfies this is the cube, so that must be for Dominika.

Clues 1 and 2 tell you that Atheeta’s present has more faces than Emma’s, but fewer vertices. There are only two possible pairs of presents that satisfy this: the octahedron and the cube; or the icosahedron and the dodecahedron. As the cube is already taken by Dominika, the icosahedron must be Atheeta’s and the docedahedron must be Emma’s.

Finally, clues 3 and 5 tell us that the tetrahedron is Bernd’s and the octahedron is Colin’s.

So, the owner of the icosahedron was Atheeta.


Christmas conundrum #1

It’s finally time for the first Chalkdust Christmas conundrum. Four lucky people who submit the correct answer to the puzzle will win Chalkdust T-shirts. The deadline for entries is Friday 8th December at 6pm.

It’s nearly Christmas and you have wrapped up five presents for your five best friends: Atheeta, Bernd, Colin, Dominika and Emma. You are especially happy this year as each present is the shape of a different Platonic solid.

But in your excitement, you have just forgotten which present is for which friend. You can only remember the following facts:

  1. Atheeta’s present has more faces than Emma’s present.
  2. Atheeta’s present has fewer vertices than Emma’s present.
  3. The faces of Colin’s present are triangles.
  4. Three faces meet at every vertex of Bernd’s present.
  5. The edges of Dominika’s present have an integer length, and her present has an integer volume.

Who is the icosahedral present for?

Once you have solved the puzzle, enter your answer below for a chance to win. The deadline for entries is Friday 8th December at 6pm. The winners will be announced in next week’s conundrum post, when you will also have a chance to win a copy of The Indisputable Existence of Santa Claus by Hannah Fry and Thomas Oléron Evans.

This competition is now closed.


Chalkdust’s Christmas conundrums

Winter is coming. The temperature is dropping quickly (although not all the way to absolute zero) and the days are getting shorter. To cheer us up at this bleak time of year, somebody decided it was a good idea to have an annual celebration. No, not Isaac Newton’s birthday. We are talking, of course, about Christmas!

Ah, Christmas. What better way to spend the holiday season than relaxing at home, curled up by the fire with a good book. Or perhaps you’re the sort of person who prefers to unwind by tackling a Yule-themed puzzle or two. Or maybe you like to wear a fashionable, mathematical T-shirt that’s available in a variety of colours and any of the sizes that aren’t medium?

What about if you could do all three… at the same time‽

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Review of The Maths Behind by Colin Beveridge

You know what the biggest problem with The Maths Behind is? ‘Ice Col’ Colin Beveridge has basically covered every possible topic we can ever blog about on the Chalkdust website. This book explores the maths behind 57 everyday events: that’s more than a year of blog posts!

If this doesn’t strike you as a particularly large problem, then I reckon you will enjoy this book.

The first thing that strikes me about this encyclopedia of mathematical modelling is that it is very pretty. The publishers produce a lot of cookery books, and their designers have done a really rather good job of bringing these fifty-or-so topics to life. Most topics cover two to four pages, with large colourful graphics.

Stopping distances in The Maths Behind

Oh cool, stopping distances! What an interesting thing to write about.

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MathsJam 2017

Last weekend, seven us went to a conference centre near Stone in Staffordshire for this year’s MathsJam Gathering. In this blog post, we have collected together our highlights, which we present in approximate chronological order.

The train journey (Scroggs)

Playing Origins of World War I on the train.

The fun started before we even arrived. We spent the majority of the train journey playing Origins of World War I, a game taken from Sid Sackson’s A Gamut of Games. I won, which is unusual, especially when Bolt is one of my opponents.

The train journey was followed by the worst part of the weekend: carrying around 200 copies of Chalkdust over Stone station’s footbridge.

Saturday afternoon (Sean)

This was my first MathsJam, and I was amazed by the huge variety of the talks. Some people spoke about puzzley, gamey maths (which I had expected). Other people ranted or joked about mathematical errata from every day life (I should have expected this) and two people read truly beautiful poetry that genuinely moved me (I really didn’t expect this!). On top of the talks, everybody was lovely and there was an impressive supply of entirely adequate food for lunch. After my initial scepticism, I am already looking forward to next year!

Saturday lunch (Adam)

Saturday afternoon (Alison)

I strongly recommend giving a talk at MathsJam. Even if you have never attended before, you get so much out of presenting something interesting (or ranty) to a group of maths-obsessed people. It’s also the best way to meet other people after your talk: I spoke about Stupid Units and for the rest of the weekend people kept coming up to me with their favourite stupid unit. I now have enough units for five more talks!

If you are thinking of talking at MathsJam, absolutely go for it! They love it when new people speak. If you think your talk contains stuff everyone knows, trust me, it won’t. If you think it might not be mathematical enough (I was worried about this), you will be sent email addresses of people you can ask for guidance. If you are terrified of public speaking, go for it anyway! All the talks are only five minutes so it can be a great way of getting more practice talking to an audience, if that’s what you want. The moral of the story is: give a talk.

Saturday evening (Bolt)

TD and Bolt playing a game from A Gamut of Games.

This was my first MathsJam too and I also had a fantastic time. The Chalkdust delegation ran a table on Saturday evening where we taught people how to play some mathematically interesting games from Sid Sackson’s magnum opus, A Gamut of Games. Some of the other tables included: learning how to make delightful polyhedra using origami, learning how to play Go, a Markov chain game for generating new English words, and mathematical Dungeons & Dragons.

Later Saturday evening (Belgin)

On Saturday evening, after the mathematical Dungeons & Dragons was over, it was time for the MathsJam Jam: now here’s one singalong I couldn’t turn down! It was fun to sing (and laugh) along to rewritten versions of many famous songs. My favourite was Wonderwall, and I’m not even a fan of Oasis. The title was changed to Traversible, the lyrics were now about the postman tour problem, and to me it sounded better than the real thing!

The MathsJam room during the evening activities.

There were plenty of other mathematical versions of popular songs, and they were all hilarious. Popular maths indeed!

Later Saturday evening (TD)

While everyone else was having a little sing-song, I productively spent the evening learning about medieval French poetry with Adam Atkinson. One of the highlights was the following masterpiece:

Un petit d’un petit
S’étonne aux Halles
Un petit d’un petit
Ah! degrés te fallent
Indolent qui ne sort cesse
Indolent qui ne se mène
Qu’importe un petit
Tout gai de Reguennes.

(Hint: Read it aloud in your worst French accent. Spoiler at the bottom of the post.)

Even later Saturday evening (Scroggs)

After the MathsJam Jam, it was already quite late, but there was still plenty of time to try out a variety of the games that people had brought along. Highlights included Hare and Tortoise, Pinguin Party, and Dobble. I finally went to bed at around half past midnight, as Bolt was just starting a game of Settlers of Catan. He assures me that he won.

Sunday breakfast (Belgin)

Weetabix review: Tasteless! You have to add some honey/nuts/fruit/other stuff to make your breakfast taste of anything. And it soaks up milk like a sponge, so you’re left with no milk in your bowl. Maybe I’ll go for Wheat Bisks instead..

Sunday (Adam)

MathsJam weekend is a wonderful combination of everything I enjoy about pop maths. By sheer coincidence, the ethos of the weekend was distilled beautifully into session 2c on Sunday. Let me tell you about it. Six talks; five minutes each. If you exceed your time, Rick Astley plays you off over the speakers.

First, Glen Whitney brings out half a dozen huge 3D shapes that we helped make the night before. How many holes does it have? He whips out some play-doh, and shows that T-shirts are topologically the same as these giant creations.

Pedro in the middle of his trick.

Next, Sue de Pom is dressed up as Ada Lovelace and tells us some stories we don’t know about her (see issue 07). She ends with the sad tale of Ada’s death. No-one knows, but she is half a second from running over time, and Matt Parker deftly kills Rick before he can launch into this wildly inappropriate moment. It’s a win for the hidden tech.

Pedro Freitas shows us a card trick. Somehow cards can do subtraction? We debate how the trick works on the train home. Matthew and John Bibby do an amusing father-and-son two-hander, where only one of them has the slide clicker, and Geoff Morley shows us some classic portrait A4 slides musing over irrational or negative number bases. (Question: do you need a minus sign in a negative base?)

One of the many interesting object left on the table of things to play with (but give back afterwards).

Finally, Adam Atkinson, the aforementioned distributor of fine medieval French poetry, contemplates how large a statue of a hedgehog ought to be if he wants to place it on top of some obscure mountain near Catania. The audience erupts in applause.

This session was funny; it was touching; it was puzzling; it made you want to go and have a play. This spirit, one of earnestness and inclusivity, is not easy to cultivate. It’s extremely difficult to invite people from everywhere, based only on the criterion that they “like maths”, and then get them to bond over an assortment of five-minute talks. Among the delegates you’ll find amateurs who just enjoy playing with puzzles; you’ll find people working in universities; you’ll talk to people who engage with the public professionally. And yet what Katie, Matt and especially Colin have done is to make none of those differences matter. The conference is so full of things to do, ways to get involved, and people to make friends with, that you wonder why other conferences are so bad. Maybe the secret really is Rick Astley.

Sunday afternoon (Alison)

The winning cake.

Just before the final talks, it was time for the competition prizes. First, the prize for the best cake in the MathsJam Bakeoff. This was deservedly awarded to mathematician, crossnumber enthusiast and occasional poet Sam Hartburn.

After this, it was my job to award the prize for the competition competition. The competition was strong, but the winner of the competition competition was Katie Steckles, who beat all the competitions in competition with her competition. Competition competition competition competition competition competition. Competition.

Maybe the highlight of the prize giving was when Matt Parker won the prize for the most entries in a competition. His prize was a £5 voucher to spend on Maths Gear, an excellent shop for mathematical toys and games that just happens to be run by Matt Parker himself.

Another train (Scroggs)

After the end of the talks, it was time to get the train home. See you all next year!



Medieval French poetry (spoiler)

When read in a French accent, the poem sounds exactly like Humpty Dumpty. It is taken from Mots d’Heures, a collection of English nursery rhymes that have been “translated” homophonically into French.



Every schoolchild (and former schoolchild) has played around with typing numbers on a calculator, turning it so the display screen is upside down and giggling at the (usually rude) word spelled out. These words are called beghilos, named for the only letters you can make out of numbers on a standard calculator: b from 8, e from 3, g from 6, h from 4, i or l from 1, o from 0, and s from 5. Some variations use a 2 as Z and o as a capital D.

Using the traditional beghilos, there are over 200 possible words, although some of them are a bit rubbish like GI ( a martial arts uniform) and GHOLE (an anarchic term for ghoul, but sounds like it should be something else). Continue reading


Dispersion on the dark side of the moon

For the last fifty years, one of the most reliable ways of making sure that your artwork is seen by thousands of people around the world has been to stick it on the front of a (successful) album. Images used by artists like The Beatles, The Velvet Underground and The Clash are so famous not only because they adorn the fronts of CDs and LPs, but also because of the huge amount of branded merchandise that they have spawned. T-shirts, tote bags, coasters and Sex Pistols Virgin Money credit cards have ensured that album covers provide some of the most enduring modern works of art.

Given this, it might be easy to dismiss album art as a purely commercial exercise. But many artists also look to link their cover art with their music by visually representing some of the central themes. Perhaps it is not surprising, then, that some of the best album covers can be looked at through a mathematical lens. After all, mathematicians have always had ways to visualise abstract ideas, and there are easy connections to be made between physics and the psychedelic and cosmic imagery that was popular during the ‘golden era’ of the concept album. Let’s take a look at one of the most famous examples… Continue reading


In conversation with Cédric Villani

Early on a February morning, we’re standing outside one of the many trendy cafes in Fitzrovia. Down the street we spot a man striding our way, wearing a full suit, a hat, a giant spider brooch and hastily tying a cravat. It could only be superstar mathematician Cédric Villani.

Cédric is passing through London on his way back from the US, but this is no holiday. In his two days here, he is attending a scientific conference, giving a public lecture, and taking part in a political meeting. His packed schedule leaves the increasingly-busy Fields medallist just enough time to join us for breakfast.

Fields medal

One afternoon in early 2010, Cédric was in his office at the Henri Poincaré Institute in Paris, getting ready to pose for publicity photographs. The photographer, from a popular science magazine, was setting up his tripod when the office phone rang. Cedric leant over and picked it up. It was Lázló Lovász, president of the International Mathematical Union.

Fields medal ceremonies are held every four years, and six months before each ceremony, the winners are alerted by telephone about their success. During these six months, they are sworn to secrecy, but with the photographer in the room, Cédric suddenly realised that he might be in possession of the shortest-kept secret ever. By some miracle, the tripod had proved sufficiently interesting for the photographer, or perhaps he didn’t follow the English conversation, and the secret remained safe.

If you try too hard to win a Fields medal, you will fail.

Cédric had first realised that winning the Fields medal was a possibility at some point in 2004, when he was 31. Fields medals are only awarded to mathematicians under the age of 40, and until the phone call arrived, Cédric only placed his chances of winning at around 40%. “The prospect of winning the medal does put some pressure on you during your 30s. But everybody knows—it’s part of the common mythology—that if you try too hard to win it, you will fail.”

In August 2010, Cédric was officially awarded the medal at the International Congress of Mathematicians in front of 4000 mathematicians and journalists. Finally, he was allowed to celebrate: he did so by taking a dozen colleagues to a fancy restaurant in Germany, thereby relieving himself of half the CAN$15,000 prize money.

The Boltzmann equation and Landau damping


The Boltzmann equation can be applied up where the air is clear less dense. Image: public domain

While enjoying a hearty breakfast, Cédric explains his research to us. “In this room, we are surrounded by air. You can use the Navier–Stokes equations to describe this air. But at higher altitutes, where the atmosphere is more dilute, these equations do not work so well. Here, it is better to use the Boltzmann equation.” The Boltzmann equation describes the statistical behaviour of a gas, and Cédric has worked on two areas related to this equation: the influence of grazing collisions, where two particles pass very close to each other; and on the increase in entropy as time passes.

Cédric’s other work, completed with Clément Mouhot, looked at the mechanics of plasmas: high-energy soups of electrons and positively-charged ions which are formed by superheating gases. Roughly speaking, if a plasma is exposed to a brief electric field, then the electric field will become very small as time goes by. This decay effect is called Landau damping. In the 1940s, Lev Landau proved that this damping occurs for a linearised approximation of a plasma. Cédric and Clément proved this result for the full non-linear system of equations.

It was the work in these two areas that led to Cédric being awarded the Fields medal, although he has worked in other areas as well. Imagine you have a large pile of sand and a hole to fill (with the same volume as the sand). How should you go about moving the sand to fill the hole, while minimising the total work you have to do? This is an example of an optimal transport problem.

He used the ideas of entropy from his study of the Boltzmann equation and applied them to this problem, and used this to establish a link between the non-Euclidean curvature of a manifold and properties of the entropy. This led to a “whole bunch of research related to non-Euclidean geometry”.

Career choices

Academia is where my heart belongs.

If the young Cédric had had his way, his research life would be very different. “When I was a kid, I wanted to go into palaeontology. I recently had a great discussion with Jack Horner, the world’s most famous expert on the subject—‘Mr Dinosaur’, and it was like reconnecting with my youth.”

So is he happy in mathematics academia? “Academia is where my heart belongs. I like industry, and I sit on the advisory boards of several companies, but I’m an academic guy. My research has not had an application so far that I am aware of. But, with applications, when they come it will be much later.”

Traces of Cédric’s early passion can still be spotted though. He owns a cuddly toy dinosaur called Philibert, and leaves maths books open to keep him entertained. Years later, he found that Alan Turing, one of his greatest heroes, used to do the same with his teddy bear at university.

Grumpy Gauss

Grumpy Gauss, oil on canvas. Christian Albrecht Jensen (1840)

In fact, Turing is the hero in his recently-penned graphic novel,  Les Rêveurs Lunaires. Excited readers will be disappointed, however, as “even though England is everywhere in the book, English publishers have not yet been interested in making an translation.” This is a double-shame, as you will remember from Chalkdust issue 04 that comic books about maths are `hot’.

He is, however, less sure whether he would like to travel back in time to work with Turing or other mathematicians. “People like Gauss—so fascinating, so superhuman. But he was known for being rather grumpy; maybe it would not be so pleasant! Then take Riemann—a genius! But a bit depressive; maybe he was not so fun to work with. I’m not sure if he would want to see me.”

A day in the life of a Fields medallist

Life is rarely routine for Cédric. In a usual year he travels to 20–25 countries, and has roughly 30 different appointments each week. When he can, he enjoys a quiet family breakfast at home. The contents of this breakfast have not changed since he was a child, and include bread, jam and hot unpasteurised milk. For today, however, he makes do with a full English with scrambled eggs.

I never give fashion advice. I always tell people: “find your own way”, as I did find my own way.

Dairy products seem to feature heavily in Cédric’s day-to-day life. Impressively, he is able to visualise every shelf in his favourite cheese shop and name, in turn, every item on sale. This is very important to him, as otherwise he could return home from grocery shopping to find himself without one of his many favourite cheeses.

He is in London to give a lecture to the public, something that he spends a large amount of time doing these days, “much more so than to mathematicians. But both are good: different feelings, different preparations.” Overall, since winning the Fields medal and gaining fame, Cédric claims that his time for research has been “divided by hundreds”.

Indeed, the public lecture is not his only commitment in London. He is currently attending a meeting at the Royal Society about the numerical abilities of animals. This meeting included great revelations about the mathematical abilities of frogs—evidenced through their calls involving sounds of varying number and length—as well as fish, bees and chimpanzees. “One of the crazy things that emerged from this conference is that the tendency to put small numbers on the left and large numbers on the right is not merely a side effect of how we write numbers. You can also find this—in some sense—in newborn chicks and fish.”

When in France, Cédric is recognised everywhere he goes, and is (still) posing for photographs. He is regularly featured on the covers of science magazines, and is often confronted by giant billboards of his face. If you are planning on winning a Fields medal, do not panic: he assures us that you will quickly get used to this.


Cédric enjoying a popular maths magazine

Cédric enjoying a popular maths magazine. Image: Chalkdust

When we meet Cédric, the French election is in full flow. As part of his stay in London, he is attending a meeting for the candidate he describes as the “young, centrist guy”. He is one of seven scientists on a board that provides scientific policy advice to the European Commission. However, he doesn’t recommend becoming too involved in politics, as he thinks there is no way to find time to pursue both a serious research career and a serious political career.

“The current political climate is far from science in general. Science, as a field, is much more respected by society than politics. So there is reputation to be lost by going into politics. But the most popular politician in French history is Napoleon, and he was keen on mathematics, and a big protector of mathematicians and scientists. He was elected to the academy of sciences, attending when he could, and enjoyed discussions with many of the best mathematicians of his time. But he was always late…”

Keen not to be late himself, Cédric finishes his eggs and heads off to his next commitment. It would seem, however, that Cédric does not always listen to his own advice: in June he became an elected member of the French parliament, as a member of the young, centrist guy’s party.

TD, Scroggs and Yiannis The Undergrad enjoy Cédric's company

TD, Scroggs and Yiannis The Undergrad enjoy Cédric’s company. Image: Chalkdust