I have been working on trying to prove a uniqueness theorem regarding the Riemann constant vector (RCV) as well as develop an algorithm for computing the RCV that does not grow exponentially with the genus of the curve. The latter is especially important since, the number of cases I need to check in my current algorithm, as well as the complexity for checking each case, grows exponentially with the genus. This makes computing, say, a genus five RCV nearly infeasible on my machine.
(Granted, I don’t have the patience for computations that take more than a minute but I think I set my software performance standards pretty high.)
It has been frustrating trying to come up with a more direct version of this algorithm. So when I read the following from a recent New York Times article on Terry Tao I couldn’t help but laugh. (And relate.)
… The steady state of mathematical 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.
There have been a lot of moves that I have taken back. Hopefully, I will force this devil to change strategy soon.