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.