## 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.

$\boldsymbol{\square}$