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.