This is science in a nutshell (as well as math, in the event you don't think of it as science).

A lot of cancer-fighting treatments don't come from directed research looking for a cure, but rather from pure research gathered in natural studies. So don't write off silly-sounding investigation into, say, the motility of sea urchin sperm.

It's another arena where politicians suck, too. There was a funded study on dog micturition (urination) that I can easily imagine a US politician shouting at the cameras, "We're wasting three thousand dollars on dog pee!", because it's a great soundbite for outrage. In reality the study looked at the fact that all puppies pee sitting down, but curs stand up, which means something changes the instinct. Turns out that neurons in the spinal cords of male dogs physically rearrange themselves to do this. Groundbreaking research can be challenging to fund, in part because it often isn't directed at a solution to a problem in advance. Sometimes we just have to learn more about nature.