### QED 1

Some time ago, I went through a proof of the quadratic formula with the pre-AP kids. It was part of our notes. I put the proof in their homework. The proof was an extra credit question on their test. At the end of the proof, when we had arrived at our destination, I wrote on the board: *QED*.

I turned to the kids.

“*Quod erat demonstrandum*,” I said. I rolled the r’s. I flattened the vowel sounds. I did my best to sound exotic.

“What’s that!?” a student asked.

“That which was to be shown,” I said. “It’s latin”.

And I repeated it again.

### QED 2

We did another proof a few weeks ago. Frankly these proofs are not so much proofs *per se* as derivations. So yeah. We derived something else. And when we got to the end, I wrote: *QED*.

One of the students said, “Tell us what that stands for again, Mr. Hasan.”

Of course, they knew what it stood for. What they were asking for was the *latin*. They wanted to hear it.

“*Quod erat demonstrandum*,” I said. I rolled the r’s. I flattened the vowel sounds. I did my best to sound exotic.

### Professor Langebartel

When I was an undergraduate at the University of Illinois, I took a *Differential Equations and Orthogonal Functions* course from Dr. Langebartel. He was awesome, so awesome that when I needed a math elective to finish my minor I chose *Tensor Analysis* simply because he taught it.

Dr. Langebartel once stopped a lecture and asked us, “Who was the greatest mathematician in history?” He waited briefly, but this was a rhetorical question. He answered it himself.

“Eudoxus,” he said.

We were in an auditorium in Altgeld Hall (which is going to get a facelift soon). I can still hear his booming voice in that large hall drawing out his sibilants: *Eudoxxxxxusssss! *And he told us a story about Eudoxus.

It was a surprise to have a professor give historical context in a technical course. No other professors I had did this. He was the one from whom I first learned *QED*. And I still remember how exotic it sounded for him to draw out the latin pronunciation. Clearly my students feel the same way.

*My students thank you for those lessons, professor.*