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.

Sunday, June 10, 2018

A test of character

For a problem I was working on, I needed to know the answer to a particular mathematics question. Hoping that specialists in the area would know the answer or could figure it out, I asked around.

At conferences, I met one specialist after another whose knee-jerk response was "It's trivial." They seemed to expect me to be satisfied with that, but I pointed out that I didn't just want the answer, I wanted a proof. They couldn't produce one, and seemed annoyed with me.

The top people in the field didn't behave that way. They thought about it briefly and decided they didn't know.

I learned that rather than going through the usual routine of "It's trivial" and "But I'd like to know a proof," it saved time to begin with "I've asked Serre, Tate, and Mazur and they didn't know. But it's closer to problems you've worked on, so I thought you might be able to help."

How did the specialists respond? In a sage and serious tone, they replied "Oh, that's a very hard problem."

But it was the same problem that had been "trivial" a few months before. I wondered whether "It's trivial" had less to do with the mathematical question itself, than with the person I was asking, and (perhaps) their perception of me.

Then I asked Ralph Greenberg the question. We had a long mathematical discussion. He came up with cases where the result held, and other cases where it didn't. (It turned out to depend on whether the field was a finite field, a number field, a function field, etc.) 

Since then, I think of Ralph as a hero (and a "mensch"). And I think of that mathematical question as a test of character.