Another thing that hits home with me about Isaac Asimov’s autobiography is some of his college experiences.

I still recall from the first I read it back in the 70s that he had the same experience with calculus that I had. That is, I had always thought of myself as having a special relationship with math, not that I was a prodigy or anything, but it was always a subject that I did well in.

I especially liked geometry because of its logic, and while I might not pick up on new ideas on my first encounter, once I had them, they generally stayed with me. I didn’t have to memorize rules and theorems and whatnot; when the time came to take the tests, I could always reason things out once again. Not perfectly, mind you, as I still tended to schussle, so I’d generally get a B on tests because I’d make careless mistakes.

The point is, I thought I had a special relationship with math.

And this followed me into my first course in calculus, the differential variety, at Penn State, which I did well in without much trouble.

But then when I took integral calculus, suddenly nothing was coming easily anymore. I had to really struggle to get through it.

And I realized that math was no longer my thing.

Young Isaac, while he was certainly far more proficient than I ever was, had a similar experience:

My biggest disappointment, however, was integral calculus. Until now for thirteen years, all the way from arithmetic to differential calculus, I had understood math without any trouble—even if I weren’t mathematician enough to join a math club. In integral calculus, I found suddenly that I had to sweat it out.

It was a horrible and embarrassing situation to get a B in a math course. I realized I had encountered my ceiling of comprehension in mathematics and I took no more courses in the subject.

But that’s not all.

He actually flunked some of his courses as well.

Now the circumstances were entirely different, and he was under a vastly different environment than I was. After all, he was a Jew in a college that took only a very limited number of Jews at that time, for example. And he was taking some far more advanced courses at a younger age than I ever did. And of course, over all he did way better than I did.

By the way, I have since met several folks who had a similar experience with calculus. It seems that integral calculus is something of a barrier that separates the wheat from the chaff, in a mathematical sense so to speak.