Julie Rehmeyer explains a math. strategy

One strategy in attacking a difficult math. problem is to break it up in to a number of hopefully simpler problems. Sometimes an opposite strategy also works as Julie Rehmeyer explains in Creeping up on Reimann:

"Mathematicians attack really hard problems like the Riemann hypothesis with a strategy that might initially seem odd: they try to prove a claim that is even bigger and bolder than the original one. By embedding the problem in a larger context, they can build bigger tools to attack it.

To see why that might be useful, imagine that a mosquito is pestering you. If you can't manage to swat it, you might instead try a bug bomb, killing every insect in the room—and being sure to get that darn mosquito in the process. Thus killing all the bugs might be easier than simply killing the one wily mosquito. This technique of generalization is the same one that brought down both Fermat's Last Theorem and the Poincaré conjecture."