Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.
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
Our original prize crossnumber is featured on pages 64 and 65 of 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.
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…
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.
But this is still a conjecture, and mathematicians have been unable to prove whether it is true or false.
Alison Clarke, a doctor who works at hospital in Norfolk, has decided that the twin prime conjecture is…
FALSE.
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.
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).
The winner of the Book of the Year 2023 was picked from the shortlist by the Chalkdust editors:
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.
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:
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.
Maths is a fickle world. Stay à la mode with our guide to the latest trends.
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
Forget SUVAT—turns out all we need to solve mechanics problems is an omelette and doner kebab.
‘The Unknown’ is a villain for the ages. We tried to get ChatGPT to write this column, but it was too good.
Dumaker, CC BY-NC-SA 3.0
Ask ChatGPT about Chalkdust for some fabricated lore.
Gary Lineker currently recruiting one centrist pure mathematician and one centrist applied mathematician for another guaranteed hit.
I can’t do that on my journey to work.
Be it House of Games prizes or Death in Paradise murder weapons, public spreadsheets have the data.
No one wants to know they’re row 301, mate.
Another mathematical win for independent researchers!
Great Expectations would have been much less interesting.
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 $\square$.
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.
$\boldsymbol{\square}$
