I was so glad to be involved with this project of Hannah Hoffman. She had inquired on Twitter whether mathematicians could provide a proof of the irrationality of root two that rhymes. I set off immediately, of course, to answer the challenge. My wife Barbara Gail Montero and our daughter Hypatia and I spent a day thinking, writing, revising, rewriting, rethinking, rewriting, and eventually we had a set lyrics providing the proof, in rhyme and meter. We had wanted specifically to highlight not only the logic of the proof, but also to tell the fateful story of Hippasus, credited with the discovery.

Hannah proceeded to create the amazing musical version:

If the square root of two was rational

It then would have to be fractional.

If it was a over b

Then you must see

This could not be actual

For a-square over b-square would equal two

But this certainly would not do

With a bit of effort as we plod

We see a could be neither even nor odd

And this would be counter factual.

Typo: a proof of the irrationality of two

Oh dear! Now fixed.