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

in a November talk at the Simons Center, as reported by Peter Woit.

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.