The true work of the
mathematicianeconomist is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proofpiece of research. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematicaleconomic research is to be completely stuck.
It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.That's pretty much how I feel about research. Another analogy is that research is like solving a Rubik's Cube: You're about to put the last piece in place and you find you have to go back 25 moves and start over.