Over the years, I've told colleagues and friends about things I have seen or experienced. Many times, people have said that I should write them down so that they won't be lost and forgotten, since some of them might be useful parts of our history. I've been writing them down, without being sure what I would do with them. I decided to gradually post them on this website, and see what reactions I get. I suggest reading from the bottom up (starting with the August 2017 post "The Meritocracy"). Thoughtful and kind feedback would be useful for me, and would help me to revise the exposition to make it as useful as possible. I hope that while you read my stories you will ask yourself "What can I learn from this?" I'm particularly interested in knowing what you see as the point of the story, or what you take away from it. Please send feedback to asilverb@gmail.com. Thanks for taking the time to read and hopefully reflect on them!

I often run the stories past the people I mention, even when they are anonymized, to get their feedback and give them a chance to correct the record or ask for changes. When they tell me they're happy to be named, I sometimes do so. When I give letters as pseudonyms, there is no correlation between those letters and the names of the real people.

Saturday, June 5, 2021

My Superpower

This begins a series of vignettes on the same theme.

Part 1:

I stared at the test question. The test was in a group theory course I was taking at a math summer camp for talented high school students. We were asked to prove that a certain statement was true. I struggled with the problem for awhile, and finally wrote in the answer space, "I must have a fundamental misunderstanding of group theory, because it seems to me that ..." and I went on to explain how I concluded something that was in direct contradiction to what we had been asked to prove.

After the test, the students gathered around to discuss it. My friends had all come up with proofs for that question. No one else seemed to have a fundamental misunderstanding of group theory, the way I had. I sighed.

That test question shook my self-confidence. I thought I knew right from wrong, at least in mathematics. That was the beauty of math; you know whether you're right. I had thought I was good at it. Clearly, I was wrong. How depressing.

I was awed by the brilliance of the top students. Many of the best ones had impressive backgrounds---they had highly educated parents, went to unusually good high schools, and had already taken courses at universities. I wasn't in their league. I managed to do well on some of the tests by doing well on the problems they looked down on and didn't bother with, namely the routine ones that required very fast and accurate computation by hand. I was great at those (but that wasn't my superpower).

One of the counselors told me, "Congratulations! You're the only one who aced the test." I didn't know what "aced" meant, and I was too embarrassed to ask. When the professor handed back the graded tests, I had a score of 20 points. That seemed odd. Twenty points was the maximum. Why hadn't he subtracted points for my fundamental error in understanding?

The professor pointed out to the class that he had made a mistake, and accidentally asked us to prove something that wasn't true. I was the only one who realized it. Those who gave an incorrect proof had one point taken off.

I felt bad about getting credit for realizing the problem was wrong, since I had realized no such thing. It hadn't occurred to me that such an intelligent professor could make a mistake. I only thought that I must be stupid.

While I wondered if it was fair for my fellow students to lose a point due to the professor's mistake, I was happy to be the only one who aced the test. And I was amazed that such smart students could write incorrect proofs and not realize they were flawed.