DARPA has put out a list of 23 challenge problems in pure and applied mathematics. Some of them are specific, such as number 19:

SETTLE THE RIEMANN HYPOTHESIS

The Holy Grail of number theory.

Some are vague, such as number 3:

CAPTURE AND HARNESS STOCHASTICITY IN NATURE

Address Mumford’s call for new mathematics for the 21st century.

Via Peter Woit.