This morning I ran across a list of 23 math problems compiled by DARPA. I assume their choice of exactly 23 problems was meant to be an allusion to Hilbert’s famous list of 23 math problems from 1900.
Some of Hilbert’s problems were a little broad, but most had crisp mathematical statements. DARPA’s list is the opposite: a few of the questions have a crisp statement, but most are very broad. Hilbert’s problems were pure. DARPA’s problems are applied.
One of the questions that stood out to me concerns computational duality.
Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
I think it’s safe to say the answer is “yes” because it already has been done to some degree, though the question remains as to how much more can be done.