It is the time of year for predictions: predictions for 2011, predictions for the next decade, predictions for the unspecified future. I searched a bit for predictions in mathematics, but it seems mathematicians are too wise to engage in this dubious activity. I found only two predictions:
(1) Two New Scientist writers, Samuel Arbesman and Rachel Courtland, predict that 2011 will not see the $P=NP$ problem resolved.
(2) Sir Michael Atiyah
suggested that the conjectured self-adjoint operator that could explain the Riemann hypothesis might be the Hamiltonian of quantum gravity
Of course it is a stretch to call Atiyah's suggestion a "prediction." And every conjecture in mathematics is a prediction! Nevertheless, in the spirit of New Year's, I would be interested to hear any predictions on future developments in mathematics.