# Better Handwritten Math with LaTeX

2022-09-04

Argument: LaTeX improves your handwritten math.

Put more precisely: If you are a first-year undergrad in science or engineering, practicing LaTeX is beneficial for your handwritten math.

I began learning LaTeX in high school for mostly trivial tasks. In university however, my calculus professor awarded a 10% bonus to whichever group submitted their assignment in LaTeX. Unless circumstances forbid, I would be responsible for formatting my own and my teammates' handwriting into LaTeX, and secure the bonus even if I was ignorant math-wise.

In the summer semester the same professor taught us linear algebra and multivariable calculus, and the bonus remained in effect. Meanwhile, as an experiment, I kept my linear algebra notes in LaTeX.

Any LaTeX user knows there are two styles for math script: inline and
display. To use these two options wisely is part of what makes a document
"beautiful". For example, if I had an equation that looks like ```
x
= expression = another expression
```

, I will consider:

- How many equal signs are in there?
- If I wrote it inline, how wide will it be?

and, most importantly,

- Will I need to label individual steps?

This is a case where display is way better than inline:

LaTeX is helpful here because you can always try again if you messed up. I learned to avoid overfull hboxes, and formed many other typesetting habits this way. I underwent the transition from quick & dirty scribbling to structured logical statements (compared to whatever shit math I was doing before).

The magical thing is, **these habits aren't constrained to the keyboard;
they will flow from your pentip also.**

Later this semester we had a midterm exam, where we had to write on paper. I knew, with a little conscious thought, where or how large something should be even without LaTeX. It was as if I was compiling a LaTeX document from my head, except it was more like JIT interpreting. I would remember to:

- Leave a margin
- Align equations by equal sign
- Label equations
- Make parentheses large enough
- Draw a tombstone after a finished proof
- Write the real set in
`mathbb`

style

Most of these are trivial, yes, but I believe they contributed to an answer sheet that at least went easier on the eye. There were significantly fewer scribbles and awkward linebreaks than I usually had in high school.

Why is it so?

Hypothesis: Donald Knuth, Leslie Lamport, and the folks who made amsmath were all virtually swimming in academia. They expected a math paper to look a certain way, and when they designed the (La)TeX ecosystem they made it the default. As such, when you are using LaTeX, you are basically reusing a template made by top scholars. And when you write LaTeX, you go their way by default. The error messages are super unintuitive, but if you don't get any, you can be pretty sure you're doing things right.

Conclusion: LaTeX is not only a typesetting program for digital documents; it helps you preprocess your mathemetical thoughts before you commit it to any medium. If you practice LaTeX as a first-year undergrad, you will find handwriting math easier and prettier on the first try.