I find it incredibly disappointing that so many people in the general public seem to regard people who use mathematics in their profession as “number-crunchers”. Each time I hear someone say it, I die a little on the inside (even though I know they mean it in a good way). It’s as if the only notion of mathematics that these people have is that one does arithmetic. In my mind, it’s like saying that all a photographer does is take photographs or that a businessperson only makes calls all day for deals. It’s a narrow-minded view of any of those disciplines, and it gets a lot of it wrong.
First of all, our minds are brilliant things. The human mind has come up with descriptions of the universe that are much more accurate than any other story we’ve ever told about the universe. Therefore, why would we want to waste our time on performing a bunch of calculations using our minds or by inputting them into a calculator? The answer is that we don’t. We use computers for this because they are both better than us at it, and we can then use our minds for something else. Number-crunching may have once been what a lot of scientists do, but now we’ve got computers for the job.
(Of course, we still do have to statistically analyze data, but the point I’m trying to make is that a lot of the heavy lifting has now been shifted to computers.)
Second, this view of mathematics fails to see how much of an art form it is. Yes, I said it. Go out to any artist, and I’m sure they’ll soon start telling you about how a blank canvas is often paralyzing, and making art becomes much easier when there are constraints involved. Does that remind you of something? Oh yeah, that’s virtually the job of the engineer.
Moreover, mathematics at its purest is just that: logical implications following from certain constraints. Notice that I didn’t say anything about numbers or formulas. While these do have their place within mathematics, they are only there because of their utility.
So why do so many people seem to believe mathematics is just number-crunching? The answer is fairly obvious: elementary and secondary education. There are two things at play here: necessity, and algorithms.
Mathematics is not optional when you are in elementary or secondary school. You take it every year, without any say. In secondary school you are usually introduced to optional courses. These include things like fine arts, drama, dancing, fitness, wood and metal working, and so on. Notice that none of these “options” are mathematics. Why? Because you’re still forced to take the mathematics course, year after year. This is fine for those who enjoy mathematics (as I do), but it can be incredibly frustrating for those who don’t. Then, when students either enter the workforce or pursue more education, most of them won’t get to have any more mathematics education, only having learned the basics. Therefore, they will only see mathematics as remembering how to do very “set up” problems and knowing which formula to use.
This brings us to the other issue: the curriculum. Unfortunately, the curriculum isn’t exactly made to stimulate interest in the students with respect to mathematics. Instead, it’s mostly about knowing how to use different formulas and to recognize that this kind of question will lead to this kind of answer. It’s basically a lot of plug-and-play, which is why I’m not surprised that many people see mathematics as simply performing an algorithm or “number-crunching”.
The only solution I can see is to radically change the curriculum for elementary and secondary education. At the moment, I don’t think many students are ever excited to go to mathematics class, which is a shame because a lot of the ideas are wonderful and interesting. I know that mathematics has the content to interest young student, but the onus is on those who design curriculum to do so in a way that brings this