We physics students at Columbia U. called him "Professor Backwards" because we so rarely saw him frontwards at the blackboard.

Often a little late, he would enter the amphitheatre where 100+ of us took his course in "Electromagnetism", go to the blackboard with his notes, and begin to write equations on the board -- without so much as a "Howydoo".

For the entire hour -- of this course, given three times a week -- he'd keep his front toward the blackboard, covering it with equations. When he talked, he'd mumble to the blackboard, and we'd try to understand him, while rapidly taking notes.

We often said that, if we met "Professor Backwards" on the walk, coming towards us, we wouldn't recognize him until he passed us and we saw his back.

We learned how difficult he was the first day of the course. He entered, a little late, faced us -- in one of his few confrontations -- frowned and said, "You should know that I resent teaching this course. I'm doing important research, and haven't time to teach sophmores!"

Pupin, the physics building on the Columbia Campus, had several of these amphitheatres, with eight blackboards at the front of the room, in four columns, with upper and lower blackboard. When a prof finished with a lower blackboard, he yanked a pulley cord, raising this up, lowering a blank blackboard down, to work on. An assistant would enter when he neared the last column of blackboards and erase the ones on the left, to use again. Prof. Backwards often covered the eight boards three times in a session -- in long derivations, some of which require two or three days to complete.

We learned early that he sometimes made mistakes in his copying or in his notes: a "variable A" might become "B" without warning; a "plus" sign might accidently become "minus", and vice versa; multiplication might become division, and vice versa; differentiation might become integration, and vice versa; vectors might become scalars, and vice versa. When questioned by a student, Prof. Backwards might acknowledge one or more of these -- face turned resolutely toward the board.

One afternoon, six of us from this course were trying to figure out a difficult derivation. It didn't seem to make sense. After nearly a frustrated hour, I had an idea. "Look. He knows where's he's going. Let's start at the end and work backwards -- correcting to make the end-part make sense." The others agreed. We began this, and continued it the next day, finally working back to the beginning -- changing here and there -- to obtain a derivation that seemed to make sense.

"How'll we know it's right?", some one objected.

"We'll ask him. But, Hays, you're the only one free at his office hour. And you started this. So you'll have to show him this version."

I started on a Monday. Prof. Backwards entered the anteroom where I sat with other students, glared at us all and went into his office, without calling any of us for the entire hour -- then left, huffily.

On Tuesday, he reluctantly allowed two students to come in for consultation. Similarly, on Wednesday and Thursday. On Friday, he entered the room, glared at me. "Oh, you again. Ok. Come in."

I nervously showed him the corrections, one after another. He agreed to all of them. When our reconstructed derivation was confirmed, Prof. Backward said, "Ok. That's taken care of. Go along and study it. I have some work to do."

This took my breath away. "Sir, do you realize how much work we had to do to work this out?"

"Yes. I can imagine. Good for you! Good for you! Now, go study it!" Clearly, Prof. Backwards thought it the duty of students to correct their professor's mistakes.

Many years later, I read Sören Kierkegaard's comment, "Life can only be understood backwards, but must be lived forwards." And I realized that one jazzed up version of this is, "My derivation can only be understood backwards, but you must study it forwards."