Fastest way to type in math formulas out of the box?

I love using the built-in Equation Editor in Word 2007. Alt + = brings up the editor, then you type this:

(a+b)^n=\sum_(k=0)^n (n\atop k)a^k b^(n-k)

This will produce the following:

It doesn't get much easier than that.

There is also an entire paper (PDF) about using plaintext to type up formulas.

Even today, it's hard to beat (La)TeX's math notation. For comparison purposes, Nathan's Word 2007 example can be typeset using the code

$ (a+b)^n=\sum_{k=0}^n {n \choose k} a^k b^{n-k} $

to produce the output

From this example, the only noticable difference is that Word uses () both to typeset parentheses and to enclose blocks for typesetting, whereas (La)TeX reserves {} for enclosing blocks (and uses \{ and \} to typeset curly braces).

The killer feature of (La)TeX, though, is the fact that you can write your own macros, and therefore define your own shortcuts, for mathematical (and nonmathematical) content. As far as I know, Word 2007's equation editor does not have this capability.

The fastest (La)TeX shortcuts for you will depend on your usage patterns; some of the more standardized ones that I use are the \ce{} macro (provided by the mhchem package) for typesetting chemical formulae and the \SI{value}{unit} (provided by the siunitx package) for typesetting units and values, but they probably would not be very useful for people who rarely use chemical formulae or physical units in their documents.

While looking for a faster way to enter differential equations, I found that you can actually add autocorrect for math so instead of typing \partial_x I can type \px (I chose that because it is a common one).

This means I can enter equation about 10x faster. I can even program in longer equations using this method. This is very exciting. This also makes it work better for note taking, as this could be entered almost as quickly as doing it by hand but neater.

I did this testing inside OneNote 2013. I then opened up Word and it actually had my customizations, but when I tried it it seemed to work a little differently. I might work as well, but I don't need to use it there so I didn't spend any more time on it. This is the fastest possible way of entering equations that I know of, because it is completely customizable and you can gear it to what you commonly use. Once I have a decent library I can actually enter equations faster than I can by hand.

Hopefully this picture comes through with some of the Math AutoCorrect that I defined below: