Algebra

Reading the comments to this article. There's more than one comment with the sentiment "I cannot recall the last time I used algebra!"

If you've ever been in a situation where you had to try to calculate something without having all the information, you've used algebra. Shopping without knowing the prices. Deciding what to spend your tax return on before you get it. Figuring out how big a home loan you can afford.

Let's say you're organising an event, and you want to get an idea of how much profit you're going to make. You know what your expenses are, and what the ticket price is, but you don't know how many people are going to turn up. What do you do? I'm a mathematician, and I'll tell you what I do: I work out a pessimistic estimate, and an optimistic estimate, and keep those two numbers around. I know that the real ticket sales will be somewhere in between, and now I have a rough idea of what's possible, and what's likely. I don't work out the precise linear relationship between ticket sales and profit.

You don't need to write any of this stuff on paper in order for you do be doing things mathematically. Of course if you do, you can get much more accurate results. But most of the time we don't need more accurate results, we just guesstimate. But it's still mathematical thinking.