Characteristic Classes

This story is part of a series entitled Leaving Mathematics. See also:
1. The Baltimore Snowstorm; 2. The Italian School; 3. Characteristic Classes

Rainer noticed the pattern halfway through July. He had constructed smooth surfaces in a certain four-dimensional smooth algebraic variety, using the Chern classes of vector bundles. He noticed that he could anticipate these surfaces’ Hodge numbers. “This seems to amount virtually to something like a non-existence result,” he wrote, later that day, in an email to a junior faculty member at another school.

Rainer soon sank into a deep depression. “I go full days without saying a single word,” he told Diego, over the phone. Continue reading

Ruminations

Jalāl ad-Dīn Rumi informs math and life.

mathnavi

A page from Rumi’s Mathnawi.

“It’s very perverse, what you’re doing,” Professor Vyacheslav Shokurov said, one afternoon in his office chair, with a skepticism characteristic of the mathematician. “One usually begins with examples – examples not treatable by the existing theory. One then develops new theory.”

Shokurov peered at me for an instant, and then lifted his hands from his lap. “But you’ve developed the theory first. And now you go looking for examples.”

My mathematical research had been stalled for about two weeks, for exactly this reason. Continue reading

A Fragile Truth

My four-week psychiatry rotation at Western State Hospital landed smack in the middle of peak general election season. And, oddly enough, these two experiences have yielded remarkable similarities. In both cases, I have been forced to entertain various versions of the truth.

Many of the patients here at Western State are psychotic. Our known and stated goal, then, is to return these patients to reality-based thinking. Only then might they qualify for discharge. This exercise has presented philosophical challenges. Certainly, sometimes, our job is easy. One of our patients, who signs her forms as Michelle Obama Prince Harry Elizabeth Queen Zealand, communicates with Russia, Germany, Berlin, Jerusalem, East Germany, West Germany, South Germany, and Russia, by radio, television, and satellite, including the satellite in the backyard of her palace, which she built, and in which we currently reside. Another patient, though, gave me pause. Continue reading