A project log for The Mathboard

A side keyboard for scientists and engineers

magne-lauritzenMagne Lauritzen 07/05/2022 at 10:180 Comments

This log entry relates to the motivation behind creating the mathematical keyboard.

When you want to type mathematical equations on a computer, you have a set of options.

The TL;DR is:

In each case, the mathematical keyboard will save the user time by reducing the amount of memorization, clicking, or copypasting, by simply having the codes, symbols, and operators available with a single keystroke.

Typing in LaTeX

Of the three, typing in LaTeX is the most flexible and has long been the standard in many scientific fields like mathematics and physics. The downside to LaTeX is that it requires you to memorize LaTeX codes. Often these codes are logical, like `\alpha` to get α, or `\plusminus` to get ±. Other times they can be a bit more obscure, like `\ngtr` for ≯ . And when you get into limits, sup/subscripts, and advanced formatting it quickly gets messy. Let's look at what's needed to type the Fourier Transform definition:

The LaTeX code for this equation looks as follows:

\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,dx,\quad \forall\ \xi \in \mathbb R

 If you have never written equations in LaTeX this can seem daunting. Many new users of LaTeX spend a good chunk of their time looking up the codes for the symbols they need, and how to make sure they appear in the way they want them to. You'll usually see undergraduate and graduate students alike with LaTeX cheat sheets covering the walls of their study area. A keyboard that automatically writes the correct  codes for commonly used symbols and operators might save them some time.

Typing in an equations editor

Typing in the Microsoft Office or Apache Open Office equations editor has the benefit of much of the same flexibility as LaTeX, but with the need for copious amount of clicking around in menus. Typing the Fourier Transform definition in the Word equations editor took me 46 mouse clicks in 5 different menus, and that's the best case after some practice. All this time spent clicking around and looking for the correct symbols in different menus could be reduced by the mathematical keyboard.

Typing in plaintext

The Unicode standard defines a large set of mathematical symbols, and it is therefore possible to type simple equations alongside the regular text. This is very useful when you just want to, for example, remind the reader that σ = ±2.2 or that ε ∈ ℂ . You can even define slightly more advanced equations, but there is a limit due to the lack of Unicode support for superscript, subscript, and much more. But if we try to write the Fourier Transform in plaintext we get:

f̂(ξ) = ∫_(-∞)^∞ f(x)e^(-i2πξx) dx, ∀ ξ∈R 

 Doesn't look too great, but it works. The downside to typing in plaintext is that almost none of the symbols are available to you on a typical keyboard layout. When did you last see a keyboard with an integral sign on it? You will either need to copypaste every symbol from a source like Wikipedia, or memorize their 4-character Unicodes. For example, typing in Alt+222B gives you ∫. But this also requires you have a keyboard with a numpad, which isn't that common anymore. A mathematical keyboard would be hugely useful when you want to type plaintext equations.