I want to study math and I prefer to type on a computer. I tried learning Latex (a mathematical typesetting language) to see if it’s a good replacement for pencil and paper. It is. One can memorize latex, bang out equations and show steps just like with pencil and paper - especially in Obsidian which has first class Latex support.

Here’s an example equation to solve for x like one would see in algebra class.

$$(x + 2)(x - 1) = 4$$

Multiplying these two binomials using foil gives me

$$x^2 + x - 2 = 4$$

I’m a bit rusty but that’s okay. Latex should be able to handle mistakes. That equation becomes

$$x^2 + x = 6$$

$$x\cdot(x + 1)=6$$

$$x+1=\frac{6}{x}$$

$$1=\frac{6}{x}-x$$

Whoops! That doesn’t feel right. But since this is latex, I can try again and even type equations on my phone. This is wonderful. This is the joy people experience when studying math. Let’s try again.

$$x^2=6-x$$

$$x=\frac{6}{x}-1$$

Back where I started :( I’ll try another approach from the beginning.

$$(x+2)(x-1)=4$$

$$x+2=\frac{4}{x-1}$$

Not great. A google-fu for a hint reveals I forgot the quadratic formula. The new approach will be to rewrite the equation as follows and use the quadratic formula to solve it.

$$x^2 + x - 6=0$$

The quadratic formula is

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Whereas

$$a=1$$

$$b=1$$

$$c=-6$$

Which becomes

$$x=\frac{-1\pm\sqrt{1^2-4\cdot1\cdot-6}}{2\cdot1}$$

$$x=\frac{-1\pm\sqrt{25}}{2}$$

$$x=\frac{-1\pm5}{2}$$

Which leaves

$$x=-3$$

And

$$x=2$$

That was fun and I wrote this on my phone waiting for an oil change at Valvoline in Obsidian. Latex is now a part of my learning toolkit going forward. I’m excited! :)