# Why is Math so Hard?

Let me start by saying something that will come as a shock to many: it isn't. As a caveat, this is coming from a person who, while tutoring a student at the university, was greeted by one of the math professors who offered me a "recreational" linear algebra test. My response? "Cool! Thanks!" But

on a more normal level, yes, math is easier and language, and we're talking by two years old. Think about it. Even before electronics, there were

mechanical computers that could add, subtract, multiply, and divide. Yet it's only been recently that computers got any good and understanding or producing speech, and they're still not as good at it as humans. Language is much more difficult problem.

Here's another example. You're in a room, and need to find the shortest path from one corner on the floor to the opposite corner on the ceiling. You can determine that by applying variational calculus to a path length to minimize the functional.... "Wait!" you interrupt. "It's just a straight line

from one to the other!" You're right. Congratulations, you just did variational calculus ... in your head. Essentially, that is what you did. So if math is really not so hard, why do so many people think it is? Let's take a look at some of the reasons.

### 1. People tell you it's hard

Look at all the movies and comics. Math is something that whiz kids and scientists do, like the students in *Real Genius* do in between building megawatt lasers. Math is an art form they use to make something look complicated, even if it actually isn't. Take the image here. If you look

closely, you'll see it's gibberish, not even real math. It's something AI generated, but it looks complicated, doesn't it? That's the point. Math has

become the symbol for something complicated. You start to believe it, everyone around you believes it, which only convinces you that you were right to

believe it. It's a con. Think of math more like a jigsaw or crossword puzzle, or solving the challenges in a video game. That's a much more accurate and productive way to look at it.

### 2. Some math teachers aren't really math people

To become a teacher, you go to college and get a degree in education, do your practicum, and get certified as a teacher. Some may take an extra class or two on how to teach math, or maybe really want to be an art teacher, but they already have an art teacher, so they get stuck teaching math. A person that isn't really into math isn't likely to pass on much enthusiasm to the students.

### 3. Schools often don't teach math that well

And this sometimes goes for college, too, but it's usually better there. All too often, they teach math as a set of rules, something to memorize, instead helping students see what it's all really about. Image if you tried to solve jigsaw puzzles by memorizing every possible rule, like "A piece with half a moon and an S-shaped curve on the left probably goes next to a piece with the other half of the moon and an S-shaped curve on the right." Of course you don't do that! So why approach math that way. Instead, you see the big picture, and figure out how to put the pieces of the puzzle together. Math is all about finding patterns. Take Fibonacci numbers, which are related to Lucas numbers, the Golden ratio, and logarithmic spirals. They're all connected. They're also all over nature, from pine cones, to snail shells, to sunflowers, to galaxies. Why do you suppose that is? What is the great pattern throughout the universe that brings all those things together. It's like a mystery, isn't it? It's not really about rules and memorization at all.

Another aspect of this is that we often teach math as something abstract, separate from reality. We learn things like the Pythagorean theorem about right triangles *c ^{2}=a^{2}+b^{2}*, but so what. Did Pythagoras pluck that out of a tree? Actually, it's pretty easy to show in a picture why that's true, then it's like the light comes on ... "Oh...." The reason a lot of people hate word problems is because we do teach math in the abstract, so when it comes to applying it to the real world, which is actually why we are learning it, students get lost.

### 4. Math builds on previous knowledge you might have missed

If you're going to do differential equations, you'll obviously need to know what differentials are. Those come from calculus, and for that you need limits. For limits, you need algebra, and for that you need arithmetic. Most of those are skills most people will never have any use for, but it illustrates a point. You can't build on a foundation that you don't have. And I don't mean just learning the methods; I mean really getting into it and understanding what you're doing. Those limits often use division, and it sure helps if, in addition to just being able to work the problems, you have a good idea in your head what it's really doing. If you're stuck somewhere, you might have to go back and see if you've missed anything.

### 5. You have a learning disability that gets in the way

It's always possible that for you, math really is hard, and that doesn't mean you can fall back on this as a excuse. People with ADHD often have trouble focusing, and not just on math. It can be anything. Other times, they can have trouble *not* focusing, and it's hard to get their attention off something. Also, there is a condition called dyscalculia. It's a neurological condition like dyslexia, only it affects numbers instead of words, and it can make math extremely difficult. And there's autism. Any of these conditions, or others, need professional care to address, and for most people, they're not the problem.

### 6. You just don't like math

There's always this possibility. As far as hamburgers, go for me, few things beat a mushroom and Swiss cheese burger. Unfortunately, my son Ryan can't handle mushrooms, so, that's that. It's hard for me to imagine, but I accept it as the truth. Likewise, there's no law that says you have to like math. But please, please, PLEASE don't use that as an excuse just because you find something difficult. Once you get it figured out, you might find you like it. That sort of change in perspective happens all the time.

When I was younger, I used to explore caves, deep, dark, mysterious. There's nothing like that feeling of discovering a new passage, exploring it, wondering where that crack or that crawlway goes. The drive to push on can be overwhelming. Math can be like that with the right attitude. Take pi (π). Anyone in high school knows it's the ratio of a circle's circumference to its diameter, but there's a lot more to it than that. It shows up in radio waves, zebras' stripes, sub-atomic physics, the momentum of light. Good grief, it's all over the universe.

Also interesting is that there are dozens if not hundreds of ways to calculate it, and pretty much all of them involve adding, multiplying, dividing, or something, an infinite number of terms. Browse through the Wikipedia article for some of them. One has to wonder how you can possibly calculate an infinite number of terms finally ending in an infinite nesting of square roots. One has to wonder how all those different formulas, that look nothing like each other, can possibly give the same result.

Come on, now. Aren't you the least bit curious?