While on your bi-weekly excursion to your local grocer, you notice that there is a new species of mushroom in stock. You've never seen it before, and you're not sure how to prepare it or what exactly it will taste like, but something about it's aroma appeals to you. You place it in your cart an continue on your way.
You run to Target for some personal items, and as you scurry around a child screaming in the center of an aisle, your eyes fall on a birthday card with a curious drawing. You open it, read, and chuckle. Though no one close to you has an upcoming birthday, you buy it and save for an appropriate occasion.
Realizing that your couch desperately needs to be either reupholstered or thrown away, you embark on a trip to the fabric discount store. You find the shade of red that you are looking for, but you also find a bolt of green that you can't resist. It's a real bargain, and it finds it's way home with you.
What do all of these stories have in common? Well, for starters, I know people who regularly do these things, and I'll bet you do, too. People who buy a dress without having anywhere to wear it or squirrel away the styrofoam packing from a computer purchase. These aren't packrats that I'm portraying. They don't save everything indiscriminately. Rather, these are people whose life experience allows them to judge the potential usefulness of a brand new item with reasonable accuracy. They are experienced cooks with a new ingredient, accomplished seamsters with a new cloth, and stylish socialites with closets full of perfect ensembles.
These characters are to their area of expertise what mathematicians are to mathematics. Why do these spmetimes bespectacled bookworms play around with formulas and numbers and patterns, seemingly without purpose? Why do they care about things that don't relate to the "real world?" They play for the same reason we all play. Because it's fun. They care because the shelf life of a piece of mathematics is a whole lot longer than a mushroom. It is not uncommon for a discovery to collect dust for centuries before someone makes a connection or draws a comparison, and suddenly that dusty function springs to life, providing just the thing needed to complete the recipe.
I can't cook. I wouldn't know a porcini from a shitake. But I love to eat, and I appreciate the experienced chefs who are willing to try new ingredients and new combinations. Nor will I ever gain fame as a mathematician, but I still love what it is they do. And you should, too.