Dear Dirichlet, Issue 19

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to

Dear Dirichlet,

I’ve decided to set myself a physical challenge. I’m going to train up and apply for BBC One’s primetime show of contenders versus professional athletes. Any top tips for how to best prepare myself?

— Where’s Wolf, Derby

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Prize crossnumber, Issue 19

Our original prize crossnumber is featured on pages 64 and 65 of Issue 19.


  • In this crossnumber, each clue is satisfied by both the entry and the reverse of the entry. For example, if the clue for a 4-digit entry is `multiple of 5′ then the entry could be (for example) 5105 or 5225 (as these numbers reversed are 5015 and 5225 which are also multiples of 5), but it could not be 4125 (as this number reversed is 5214 which is not a multiple of 5).
  • There is only one solution to the completed crossnumber. Solvers may wish to use the OEIS, Python, a graphical calculator, etc to (for example) obtain a list of cube numbers, but no programming should be necessary to solve the puzzle. No entries end with 0. As usual, no entries begin with 0.
  • One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
  • To enter, submit the sum of all the digits in the row marked by arrows using this form by 8 October 2024. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 November 2024.

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Cryptic wordsearch, Issue 19

Cryptic #7, set by Kelpie: Download as a PDF or read on!

The clues below all have solutions contained within the grid. All solutions are read horizontally or vertically with no diagonals. When you have found all the
clues the remaining letters should dance around to tell you where you are.


  • Northern Briton with extra time announced ‘round up an engineer’. (5,7)
  • Average? That’s unkind. (4)
  • Changing optics at my approaching limit. (10)
  • Most important irreducible number. (5)
  • Our favourite agony uncle from tired child wriggling their first day away. (9)
  • A function sounds like a signal (4)
  • Lyrical poem for studying evolution. (1,1,1)
  • Magazine formed from mark on Horseman’s jacket with hesitation removed. (9)
  • Tony’s atom created by mixing iron core in my sink. (8)
  • Greek land measurement. The study of distance and shape. (8)
  • Initially pretty direct evidence for studying changes. (1,1,1)
  • European satellite created Elements. (6)
  • Description of many spectres from American sentence ending inside the heads of all Irish children. (9)
  • Loop, approximately without a line’s limits. (6)
  • Ranking the best decimal base. (3,3)
  • Heads of London metropolitan schools form learned society. (1,1,1)
  • Whole numbers found from Riemann summation with helping replaced by hesitations. (8)
  • The first programmer? They adore fabric. (8)
  • Bisection of glass regardless of optimism. (4)
  • The usual dancing Roman with article removed. (4)
  • Comes in linear and abstract flavours, used to solve equations. (7)
  • Mathematician from French farm, not initially elegant, but a model. (6)

The zero knowledge proof, Issue 19

There are loads of statements where, despite years of trying, mathematicians have failed to determine whether they’re true or not. We reckon we’ve waited long enough: it’s time to let someone make the final call.

This issue, we ask someone who doesn’t work as a mathematician to finally decide the correctness of…

The twin prime conjecture

Two prime numbers are twin primes if one of them is 2 larger than the other: for example, 5 and 7 are twin primes. Pairs of twin primes appear to become rare as numbers get larger, but the twin prime conjecture says that however large you go, there will always be a pair of twin primes that are larger.

Twin primes

But this is still a conjecture, and mathematicians have been unable to prove whether it is true or false.

Is it true?

Alison Clarke, a doctor who works at hospital in Norfolk, has decided that the twin prime conjecture is…


As somebody who has a A-level in mathematics (B), and has read nearly
half of Vicky Neale’s excellent book Closing the Gap, I can authoritatively say that the twin prime conjecture is false.

Just think about it logically: there are lots of primes at beginning; you have your 3s, your 5s, your 7s, all bunched up like bananas. The number 2 manages to be the only even prime because it’s so small. But as numbers get bigger, the primes get more spread out, and numbers are more likely to have factors. It’s just common sense that the larger a number is, the more factors it has.

So the idea that you can have two massive numbers $x$ and $y$ where $y=x+2$ and $x$ and $y$ are both prime is just counterintuitive. If there are infinitely many primes that are just two apart, then it’s just as likely that there will be infinitely many primes that are just one apart—and we all know that that’s impossible.

Anyway, I’m off to read the second half of Vicky Neale’s book to find out if I’m right.


Book of the Year 2023

A few weeks ago, we announced the shortlist for the 2023 Chalkdust Book of the Year. We award two prizes: the Chalkdust Book of the Year (as chosen by our editors), and the Chalkdust Readers’ Choice (as voted for by our readers).

Chalkdust Book of the Year 2023

The winner of the Book of the Year 2023 was picked from the shortlist by the Chalkdust editors:

Once Upon a Prime

Sarah Hart

This book (Amazon UK, Waterstones) is her book which explores the relationship between mathematics and literature.

You can also read our full review of Once Upon a Prime here.

Chalkdust Readers’ Choice 2023

As well as picking our favourite from the shortlist, we held a vote for our readers to pick their favourite. The runaway winner of this poll was:

That’s Mathematics

Chris Smith & Elīna Brasliņa

This book (Amazon UK, Waterstones) is their book , which brings to life the Tom Lehrer song That’s Mathematics.

You can read our full review of That’s Mathematics here.


What’s hot and what’s not, Issue 19

Maths is a fickle world. Stay à la mode with our guide to the latest trends.

HOT Darts

Is this the world’s most mathematical sport? Lightning-fast arithmetic, probabilistic analysis and complex trajectories. You can’t beat a bit of bully!

Bully doll original image: Humor Blog, CC BY 2.0

NOT Projectile motion problems

Forget SUVAT—turns out all we need to solve mechanics problems is an omelette and doner kebab.

HOT AI generated content

‘The Unknown’ is a villain for the ages. We tried to get ChatGPT to write this column, but it was too good.

The Unknown

Dumaker, CC BY-NC-SA 3.0

NOT Trusting AI content

Ask ChatGPT about Chalkdust for some fabricated lore.

HOT Getting mathematical opinions from podcasts

Gary Lineker currently recruiting one centrist pure mathematician and one centrist applied mathematician for another guaranteed hit.
The Rest is Mathematics

NOT Reading papers to form opinions

I can’t do that on my journey to work.

HOT Using spreadsheets to log your favourite TV show

Be it House of Games prizes or Death in Paradise murder weapons, public spreadsheets have the data.

NOT Using spreadsheets to rank your first dates

No one wants to know they’re row 301, mate.

HOT The new Dear Dirichlet mug!

Dear Dirichlet mug

HOT Finding an infinite game of beggar my neighbour

Another mathematical win for independent researchers!

NOT Spending an infinite amount of time playing beggar my neighbour

Great Expectations would have been much less interesting.


The big argument: What’s the best way to end a proof?

QED, argues Sam Kay

Quod erat demonstrandum: that which was ‘to be demonstrated’. Doesn’t it just sound cool? If you’re not already convinced, let me guide you through this page viz the correct way to sign off your proofs.

This glorious Latin abbreviation was integrated into society rather early on, with its roots in ties with Greek mathematicians Euclid, Archimedes et al (ca 300 ACN). Although Latin is less-widely used today, it still serves purpose in lots of secondary school mottoes.

Okay, sure, some school kids might not like the use of Latin phrases as it makes them sound ‘pretentious’, ‘pompous’, etc. Well, to those claiming this is the MO of pretentious people, would you be one to strike your PhD from your CV? In this day and age, AD 2024?

Once I was typing a proof by contradiction into Overleaf. But the font I used didn’t have a symbol, and was instead printed as the universal ‘missing character symbol’, ie $\square$!

There is so much more freedom when using Latin abbreviations. In PDE theory we often talk about the existence of solutions. After one of these proofs, one may want to use QEC, which was to be constructed. Other equivalent forms are QEF, which was to be done, or QEI, which was to be found out.

And that concludes my argument. QED.

PS: this argument should be titled QED vs $\square$.

$\square$, argues Clare Wallace

Obviously the square is the better choice. Look at it: $\square$. It’s elegant. It’s understated. It says, “oh, this old proof? I just had it lying around.”

Paul Halmos introduced the $\square$ notation for the end of proofs, inspired by end marks in (non-maths) magazines, in the 1950s—and lots of people still call it the ‘halmos’. Honestly, I’d be on board with anything he has to say about writing and typesetting maths.

And as I keep telling my fellow Chalkdust editors, I think the more we can do to make maths look more appealing, the better. I’d even argue that we should take more inspiration from magazines and newspapers: more colour! more pictures! more clickbaity article titles!

OK, maybe not that last one. But the point is: QED feels needy. It’s trying to show off with abbreviations. “Look at me,” it says. “I’ve stuck some unnecessary Latin at the end of this proof, because I’m clever.”

On the other hand, $\square$ is just cool. It’s not impressed by dead languages. It’s here to do a job, and it’s done it. It’s letting the maths speak for itself. It’s got nothing to prove.