MATHEMATICIANS have long tried, and failed, to solve the Riemann Hypothesis, a stubbornly unyielding math problem. Good luck to whoever tries to figure it out. For the first correct proof, a $1 million prize will be awarded by the Clay Mathematics Institute.

Similarly, two successive Microsoft chief executives have long tried, and failed, to refute what we might call the Single-Era Conjecture, the invisible law that makes it impossible for a company in the computer business to enjoy pre-eminence that spans two technological eras. Good luck to Steven A. Ballmer, the company’s chief executive since 2000, as he tries to sustain in the Internet era what his company had attained in the personal computing era.