In my opinion, math is the most beautiful of any "traditional school subject," but the thing is schools are set up in a way that encourages teaching math as a bunch of formulas to memorize. And real math is seldom about memorization. I heard a friend describe math as "the most useful game humanity has ever created" and I have to say I agree with that. Math is like a game, it's a playground where you try to extrapolate truths from a set of rules. I will now spend the rest of this post explaining parts of math that are ignored in schools but are super interesting to me. My explanations don't use any technical math terms, but some of the videos linked will require some thinking.

1.) fractals: You might have heard of these before. Essentially, they're shapes that no matter how much you zoom into them, they're still rough. They never end up looking straight like a polygon or curved like a... curve. Some of my favorite are the Mandelbrot set, the burning ship fractal, and the Sierpinski triangle. All of these are mathematical objects that have infinite complexity but are governed by relatively simple rules. The Sierpinski triangle is just putting triangles in triangles, and the other two use something called "complex numbers" which sounds very obtuse, but can actually be explained in under 30 minutes. But these fractals are even crazier: we often think of shapes in terms of how many dimensions they have. A line is 1D, a square is 2D, a cube is 3D, etc. But by a certain definition, fractals have a fractional dimension. So. for example, that Sierpinski triangle is about 1.585 dimensional. See this video for details

2.) Chaos theory: ever heard of the term "the butterfly effect?" This actually originated from a field of math called chaos theory, which studies systems that are sensitive to initial conditions. One example of a system they study is called the Lorentz Attractor, which is a simplification of the laws that govern the weather. What I love about the Lorentz attractor, is that when you "solve" it with a computer, it draws out paths that look like these beautiful butterfly wings. Let me make that clear: a couple of mathematical equations draw out something that looks as beautiful as that. There isn't human intervention in that drawing, that's just what the equations draw. There's also the Chaos Game which uses probability to draw things. When you run the chaos game on certain initial conditions, you get this absurdly accurate drawing of a fern. Again, none of this is done by a human, all of these works of art are made entirely by solving mathematical equations. If you find that out and don't want to learn more, you're crazy

3.) Unexpected results: Let's take a second to play a game of pool. We'll knock one pool ball (ball one) into another (ball two), and count how many times they collide with each other or the wall. Then, let's change the mass of one of the balls and see how that affects the collision count. Tell me if you notice a pattern

Mass of ball 1    Mass of ball 2      Collision #
1kg               1kg                 3
100kg             1kg                 31
10000kg           1kg                 314
1000000kg         1kg                 3141
100000000kg       1kg                 31415
10000000000kg     1kg                 314159
1000000000000kg   1kg                 3141592

Now you might not notice it, because it's not something you'd expect, but when you increase the mass by 100x, the collision count adds another digit of pi. Again, hitting some balls against each other writes out the digits of pi. I find that crazy. Pi is normally about circles: I don't see a circle. And pi is counting something. When was the last time you saw it do that? In the words of the legendary math educator Grant Sanderson "If you have a soul you need to know why!"

I could name more instances of math being beautiful, but I think these three should be sufficient for a silly Reddit post. However, even if I didn't completely change your view of math, I hope you understand why people like me love it.