The Importance Of Math

A lot of math grad school is reading books and papers and trying to understand what's going on. The difficulty is that reading math is not like reading a mystery thriller, and it's not even like reading a history book or a New York Times article.

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.

What can you say?

"It is a tool that does suck up dust to make what you walk on in a home tidy."

That's certainly better than nothing, but it doesn't tell you everything you might want to know about a vacuum cleaner. Can you use a vacuum cleaner to clean bookshelves? Can you use a vacuum cleaner to clean a cat? Can you use a vacuum cleaner to clean the outdoors?

The authors of the papers and books are trying to communicate what they've understood as best they can under these restrictions, and it's certainly better than nothing, but if you're going to have to work with vacuum cleaners, you need to know much more.

Fortunately, math has an incredibly powerful tool that helps bridge the gap. Namely, when we come up with concepts, we also come up with very explicit symbols and notation, along with logical rules for manipulating them. It's a bit like being handed the technical specifications and diagrams for building a vacuum cleaner out of parts.

The upside is that now you (in theory) can know 100% unambiguously what a vacuum cleaner can or cannot do. The downside is that you still have no clue what the pieces are for or why they are arranged the way they are, except for the...

... middle of paper ...

...and and tell you that vacuuming the outdoors is unlikely to be very useful. Something about how a vacuum cleaner is too small to handle the outdoors and that we already know about other tools that are much better equipped for cleaning streets and such.

This 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!

source