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(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}

EDIT on 14th August 2018: Originally I sold this software on a website, but I recently made it open-source.

For Mac users I wrote an app to do precisely this, called SpeakLaTeX. It works with Dragon for Mac v6 although it's possible v5 may work too. There is a demonstration video:

https://www.youtube.com/watch?v=ay1LyHgUIjY

The customisation interface is designed for people who want full control over what comes out onto the page. You can expand or change the default commands freely.

For more details, see https://github.com/danielmartin0/SpeakLaTeX and the download link is at https://github.com/danielmartin0/SpeakLaTeX/releases.

At Michigan State University we us MathTalk and Scientific Notebook to dictate equations. http://www.mathtalk.com/

Dragon Naturally Speaking also has the ability to create macros that may be useful for commonly used LATEX strings.

I haven't used this yet, so I can't comment on how well it works, but voicecode extends Dragon Dictate and looks like it could handle this.

So far it's Mac only with Windows/Linux coming soon.

See this YouTube video for an example of voicecode in action. That example is coding in Ruby but the process looks transferable.

It sounds a bit crazy but it's a spoken language in it's own right for coding by voice, so it looks like it should support all of the symbols needed to construct LaTeX equations effectively by voice commands.

This post is now mostly out of date, so just see Mike Roberts' post about mathfly. There might be a little more vocab here than it is in mathfly https://gist.github.com/alexboche/cbad0f7b5ddf1e178b0edcf5a2beb601
and here's another demo https://www.youtube.com/watch?v=z-iHvPmjcas

Further to Alex's post about caster, this functionality has now been released as Mathfly, with full documentation and example videos on the Github page. It is built on top of Dragon Professional Individual and uses Natlink to load its grammars. The LaTeX module is enabled by saying "enable latex" and provides a wide range of commands for inserting LaTeX syntax.

For example, saying "begin equation" will insert:

begin{equation}
end{equation}

and "symbol fraction" will produce:

frac{}{}

Commands can be changed and new commands added on the fly very easily, making this (in my opinion) an incredibly natural and intuitive way to dictate LaTeX. There are also grammars for dictating into WYSIWYG editors like LyX and Scientific Notebook which eliminates the need to learn LaTeX syntax.

For a full list of commands, check out the documentation for the LaTeX module.