Every so often, the Pentagon's blue sky research arm gets slammed, for funding investigations that are a little too down-to-Earth. Then Darpa turns around, and sponsors a new project to "develop a mathematical theory to build a functional model of the brain."

It's one of 23 "mathematical challenges" issued today by the agency. In addition to cooking up a theory that predicts how to make a mock-brain, Darpa is looking for mathematicians to:

Finally solve the 150 year-old Riemann Hypothesis, the "Holy Grail of number theory."

"Develop the high-dimensional mathematics needed to accurately model and predict behavior" in biology and human interactions.

Figure out the "fundamental laws of biology."

Full proposals in response to Darpa's math challenges are due in a year. So you've got time, to put on your thinking caps.