I’ve been remembering my high school calculus teacher, Mr. O’Byrne, over the last few days.

It started while I was reading a lengthy article about neural networks and how they’re trained using backpropagation and analytic gradients. There’s not that much calculus involved, just a few partial derivatives, but it’s more than I’ve used in decades. The author was describing these gradients as the limit of some function as a variable h approaches zero. And it all came rushing back. There I was, a teenager in Mr. O’Byrne’s calculus class, learning about slopes, tangents and limits as h approaches zero.

To be honest, Mr. O’Byrne was not one of my favorite teachers. I didn’t dislike him, I just didn’t find him particularly dynamic or inspiring.

Perhaps that’s because he was close to retirement by the time I showed up in his class. Maybe he was tired and worn out. He was a large man in both height and girth, with thinning, wispy white hair. I remember he seemed to be in poor health, often short of breath and coughing wetly into a neatly folded white handkerchief.

But his lessons sure stuck.

On the last day of school Mr. O’Byrne bade us all farewell with a traditional Irish toast, “May you be in heaven a half an hour before the devil knows you’re dead.”

Most of us remember one or two special teachers who inspired us or challenged us or coached us. Yet even the ones we don’t remember as fondly, the ones who gave of themselves year after year without fuss or flamboyance also helped us and left their mark. They deserve a toast too.