(This is an edited version of an answer I posted on Math Stack Exchange. The original question was about doing math without handwriting due to disability. link.)
(Context: I have a chronic pain condition and typing is very painful.)
I use a system based on NatLaTeX to dictate all of my formal mathematics, including anything in that I'm going to turn in for my coursework. Basically, NatLaTeX defines a speakable form of many common LaTeX commands, including everything you need for most mathematical expressions. Using a custom vocabulary in Dragon NaturallySpeaking, I can dictate a plain text file containing this NatLaTeX source. I then use scripts from the NatLaTeX project to transform my dictated text into actual LaTeX source, which I can then compile into nicely typeset mathematics using a standard LaTeX compiler. (Actually, I use a batch file to automate the process.) Just as a note, I have made several modifications to NatLaTeX in order to optimize it for mathematics (the original author was a physicist) and to adjust for changes in LaTeX. Feel free to contact me if you want a copy of the modified scripts. I do eventually intend to post them somewhere online, but I need to spend some time updating the documentation first (and that's really hard to justify spending time on it while I'm preparing for comprehensive exams!).
Advantages to NatLaTeX include flexibility and speed (no need to pause between "commands," unlike some other systems). Disadvantages include a steep learning curve and not being able to see your work (typeset or in LaTeX source) in real time. NatLaTeX is more verbose than LaTeX, so it's harder to read, but it can be edited using the built-in commands in Dragon, because everything is speakable.
You also don't get the advantages of using a nice text editor that does syntax highlighting etc., because Dragon only has "full text control" (which is necessary for easy editing by voice) in a couple of editors. I've actually written a good bit of NatLaTeX in MS Notepad for this reason. DtPad is a better, but still not great, option.
Here are a few examples to show how NatLaTeX works.
Discrete Math Example:
NatLaTeX Input (dictated with Dragon)
Given a poset "(P, precedes)", a collection of linear extensions" {calligraphy R }
equals left curly brace precedes sub one, precedes sub two, low dots, precedes sub
k right curly brace" is called a ``realizer'' of "P" if "precedes equals
intersection of sub {i equals one } to the k precedes sub k", where each relation
"precedes sub i" is interpreted as a set of ordered pairs and "intersection of"
is set intersection. Equivalently, "{calligraphy R }" is a realizer of "P" if, for
all "p, q in P", "p precedes q" if and only if "p precedes sub i q" for all "one
less than or equal to i less than or equal to k".
LaTeX Output
Given a poset \( ( P , \prec )\), a collection of linear extensions \(
{ \mathcal R } = \{ \prec_1 , \prec_2 , \ldots , \prec_k \}\) is called
a ``realizer'' of \( P\) if \( \prec = \bigcap_{ i = 1 }^k \prec_k\),
where each relation \( \prec_i\) is interpreted as a set of ordered
pairs and \( \bigcap\) is set intersection. Equivalently, \( { \mathcal
R }\) is a realizer of \( P\) if, for all \( p , q \in P\), \( p \prec
q\) if and only if \( p \prec_i q\) for all \( 1 \leq i \leq k\).
Analysis Example:
NatLaTeX Input (dictated with Dragon)
begin theorem [Monotone Convergence Theorem]
Let "left curly brace f sub n right curly brace sub {n equals one } to the infinity"
be a sequence of nonnegative measurable functions with "f sub one less than or
equal to f sub two less than or equal to low dots less than or equal to f sub n less
than or equal to f sub {n +1 } less than or equal to low dots" and "limit of sub n
f sub n equals f" (pointwise). Then, "f" is measurable and
@begin{equation}
limit of sub {n right arrow infinity } integral f sub n d Greek mu equals integral
limit of sub {n right arrow infinity } f sub n d Greek mu equals integral f d Greek mu
@end{equation}
end theorem
LaTeX Output
\begin{theorem}[Monotone Convergence Theorem]
Let \( \{ f_n \}_{ n = 1 }^\infty\) be a sequence of nonnegative
measurable functions with \( f_1 \leq f_2 \leq \ldots \leq f_n \leq f_{ n
+ 1 } \leq \ldots\) and \( \lim_n f_n = f \) (pointwise). Then, \( f \) is
measurable and
\begin{equation}
\lim_{ n \rightarrow \infty } \int f_n d \mu = \int \lim_{ n
\rightarrow \infty } f_n d \mu = \int f d \mu
\end{equation}
\end{theorem}
TeXForm[WolframAlpha["square root of one over twenty times x minus y", "PodCells"][[1]]]yields\sqrt{\frac{1}{20} x-y}. How cool. – alfC Aug 24 '14 at 06:07