## How would Michael Palin say “Quod erat demonstrandum”?

by

The letters QED (or the unabbreviated “quod erat demonstrandum” [“which is what was to be proved”]) are often used to indicate the end of a formal proof.  This longstanding tradition goes back to a style of proof writing, where the culminating sentence of the argument gives a recapitulation of the statement of the theorem; the QED places a stamp of finality on the discussion.

In modern typesetting, the QED has been largely replaced with typographic symbols; typically a solid or hollow rectangle or square is used to demark the end of the proof.  (The cynic in me wonders if these just serve as flags for when the reader should take up reading carefully again.)

How does one indicate the end of a proof in a classroom setting?  Often I will scribble out a square (or whatever symbol our textbook uses); sometimes I’ve written out “Q.E.D.”.  Often I’ll pause, then solicit questions and comments.

But apparently I much more frequently channel Michael Palin.

Today I gave a final exam in Real Analysis II.  This group of students has gotten to work with me on proofs for a full year, so they know my quirks and foibles better than most.

On the last page of the final, most of the students ended their last proof with the phrase:

“And there was much rejoicing.”

This isn’t a phrase I’ve consciously chosen to use in class, but it rings true enough as something I’m sure I *have* said on occasion.  But if it made this much of an impression on the students, I wonder if I use it all the time, not just occasionally.  Hmmm.

Come to think of it, it isn’t such a bad replacement for Quod erat demonstrandum.  Captures the feeling of a good solid proof, well-understood.  And it is much more evocative than a box.

### 11 Responses to “How would Michael Palin say “Quod erat demonstrandum”?”

1. Michael Lugo Says:

In very informal notes my proofs end “we win!” (I’m not sure who “we” are here.)

2. Barry Leiba Says:

I always liked “Q.E.D.”, but I’m partial to “La voilà,” as well. I could get used to “…and there was much rejoicing.” Any excuse for a Monty Python reference is a good thing.

3. Brent Says:

I always taught my students to say “booyah!” at the end of a proof. =)

4. Jason Baldus Says:

Mine has always been “Hooray!” for my Geometry classes, and “Hooray.” for my Algebra 2 classes. I like “we win!” and “booyah”. On some days, it’s “Hiya!”, “Boom”, “Party time”, or I draw little pictures of fireworks. Mostly, it’s just “Hooray.”

5. CTV Says:

I’ve always liked Q.E.D. It has class.

“And there was much rejoicing” has a certain charm too, I could definitely see myself using it. I wonder what it would be in Latin, though. An online translator gave me the no doubt incorrect “Quod illic eram ultum tripudium” abbreviated QIEUT which is almost like QUIET.

6. Brent Says:

My wife (who studied Latin) suggests it should be Q.M.G.E., “quod multum gaudendum erat”.

7. theCountess Says:

This has inspired me to reevaluate my end-of-proof symbol. I was always box kind of gal, but it got boring pretty fast. I tested out a bunch of symbols on my homework once, ending each proof with a different one, finally settling on some derivative of the box. Still boring when compared to Monty Python…

Also, if you anagram quod erat demonstrandum, you can get fun things like “our trodden madman quest” 🙂

8. Batman Says:

I’ve always told my students – especially those just starting to write proofs – that the end-of-proof symbol is an opportunity to show off some creativity and/or artistic skills. I still use the “halmos”, but my students have used things like a sun, cube, star, stick figure, happy/sad face (determined by their level of approval of the problem), fish, and plenty of others I’ve forgotten.

My favorite was by a fellow student in grad school whose last name was Parrot. He drew a parrot head, and he could do it in under 2 seconds.

9. Amanda Says:

I’m a big fan of QED, but at the end of really tough ones I write OMG!

10. A=B implies that 1=1, therefore… « 360 Says:

[…] Finally, adding these two equations gives us , which reduces to the equation 1=1.  QED. […]

11. TwoPi Says:

When I interned at AT&T, as a joke I set up LaTeX code to print a tiny death star AT&T logo as the QED symbol.