Two Wrong Questions

By the time I took that Calculus final, the course already felt less like a subject and more like unfinished business. I had repeated enough mathematics courses with the same professor to know the classrooms, the books, and the familiar feeling of seeing material I had once failed to understand. This time I decided there would be no excuse. I worked through every problem in the red-covered book until I no longer wanted to see the book again.

Then the exam began, and I could not solve the questions.

That kind of failure feels different when you have studied seriously. If you arrive unprepared, the explanation is waiting for you. When you have prepared for weeks and still understand nothing, the mind begins searching for another cause, and the most convenient one is yourself. I left the room convinced that I had somehow become much less intelligent than I had believed.

Later I learned that two of the questions were wrong. The professor himself could not find their answers.

Relief arrived first, then irritation. For several hours I had been treating broken questions as evidence about my own ability. Nothing about my preparation had changed, yet the meaning of the exam changed completely once I learned that the problems themselves did not work.

It was not the only strange moment I remember from those courses. After another exam, a friend and I met outside and compared the answer to the last question. “Thirty-three,” I said. He had the same result, and for a few minutes that number felt like proof that the universe was still organized.

There was also the professor’s appeal procedure. When I asked whether students could object to final grades, he said of course. When I asked how, he explained that I only had to find him at the university within the next two weeks, then added that I probably would not find him.

A right existed. Access to the right was another matter.

Years later, I remember very little of the mathematics from that exam. I remember the red book, the number thirty-three, and the extraordinary relief of discovering that sometimes the student is confused because the question is wrong.