""" The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only allowed to use words that are four letters long or shorter.
...
This [research] goes on for several years, and finally you write a thesis about how if you turn a vacuum cleaner upside-down and submerge the top end in water, you can make bubbles!
Your thesis committee is unsure of how this could ever be useful, but it seems pretty cool and bubbles are pretty, so they think that maybe something useful could come out of it eventually. Maybe.
And, indeed, you are lucky! After a hundred years or so, your idea (along with a bunch of other ideas) leads to the development of aquarium air pumps, an essential tool in the rapidly growing field of research on artificial goldfish habitats. Yay! """
- [1.] https://www.quora.com/What-do-grad-students-in-math-do-all-d...