Sometimes They Surprise You

In my course on the history of modern mathematics, we just covered the emergence of calculus. After devoting most of two class sessions to Newton, I briefly discussed Leibniz' contributions, mainly by contrasting his foundational ideas and notation with Newton's. Then I asked for questions. One of the students raised a hand. "Why did Leibniz develop calculus? Newton needed it for his work on motion and gravitation. What was Leibniz' motivation?"

I paused. Blinked. Said, "That's a good question, and I don't know the answer. I'll look into it."

I'm still not sure. I've poked around a little and have some general ideas, but... I'm not sure. I'm also not sure why the question never occurred to me.

On an unrelated but thematically similar note, a former student of mine dropped by and asked me if I'd ever heard of "inconsistent mathematics", a mathematical metatheory that avoids Russell's Paradox and its kin by allowing, under certain circumstances, statements which are both true and false. I was ready to dismiss this as obvious crankitude, but I looked it up and... there's something there. I'm going to have to take a closer look. I thanked the student for bringing it to my attention, and he hurried off to class happily. (If you're curious, one reference is Inconsistent Mathematics.)

Sometimes they surprise you.