/sci/ - Science & Math

Which frontiers of mathematics would probably be the most useful for us to make progress in in order to improve our science and technology?

for example, say the government wanted to try and streamline and optimise mathematics research so that more research were being done into the areas that would probably be most useful for science and technology, which areas of mathematics would be given more funding?

would most of the funding go to analysis?
how much funding would go to algebraic geometry or number theory?
What reasoning or evidence would be used to try and judge how 'rich' a field of mathematics is in terms of how much benefit it will provide to science and technology?