Math without pencil and paper For someone who is physically unable to use a pencil and paper, what would be the best way to do math?
In my case, I have only a little movement in my fingers. I can move a computer mouse and press the left button. Currently I do very little math and when I do I use MS Office but this is a very slow way of doing it and will break my thinking process.
EDIT:
Thank you for the answers. I have a lot to try. I won't accept an answer since it's dependent on the disability but thank you all.
 A: I'm all in favor of assistive devices, but consider your feet.  As someone who struggles to overcome their own disabilities I can tell you that the simplest workarounds are the most reliable.
A: Wolfram Mathematica is nice. It pretty prints all the math by default and the input format (after adjusting the keybindings a little) is much more "direct" than latex (i.e. entering "3^4" gets you $3^4$). Aside from the easy input, you also get the whole suite of computer algebra functions and symbolic manipulation.
A: I'm very ignorant on the topic, however I would use a programming language probably. Something like Python would be good. Or also Matlab, which is probably easier and you'll find maybe more documentation about Matlab rather than Python, regarding Maths.
With Python you can do any mathematical computation, at least any you may need from elementary school to university and maybe further to research.
I suppose that you can use one of those keyboards which are displayed on the monitor and you only have to click the letters, in this way you can program. You could write your own programs that you could run in the future, saving time.
Apart from that I have no idea to be honest
A: Check out Efofex. In particular, Efofex Equation was designed to type equations without breaking the thought process. Most of the symbols can be entered with single keys or shift and a key (you can use sticky keys if necessary), and there's a fairly complete graphical entry system for everything except basic operators (+, -, *, /, =). If you need it for school, check out their empower program. Their customer service is uncommonly good, too. 
A: It's very individual what works, and I don't think maths is very different from a lot of other subjects in presenting challenges for (partially) disabled people.
Your level/what you want to do probably also matters, the rest of my answer is somewhat geared towards a high level, but it might be useable in any case (I have no experience with your kind of situation).
Some people prefer scribling away on paper, others prefer lying on a bed/couch with their eyes closed and just thinking about stuff. Both approaches requires that you afterwards write up your results nicely. 
A thing that sometimes works for me is "scribling" in the air, but just moving my hands+fingers gives me another sense of  things, even though you have limited movement of your fingers, the movement of your hands might give you something.
.Henrik
A: Voice input takes much load off the keyboard. Google search by voice is possible, as it converts spoken matter directly to text. Even individual letters can be spoken into. Mouse left click can be sparingly used to make corrections for documents. About math symbols I do not know, but believe may be possible after some trial.
I produced the following:

a x squared + bx + c = 0

when I spoke to/into Google search microphone:
$$ a x^2 + bx + c =0 $$
EDIT 1:
Encouraged by your response, may I go on with a suggestion.
All characters on a standard keyboard have an ASCII code but not all their corresponding voice inputs (with standard spoken English) translate to math symbols e.g.,

back slash, caret or power, greater than, curly opening bracket, square closing bracket, exclamation and interrogation marks

do not automatically print symbolically as:

( \ , ^ , > , {  ,  ]  , !  , ?  , )

So a coding exercise for someone here or in Google Company likely implementable with an optional Voice MathSymbol Switch/Selector from keyboard appears to be an urgent need. This can be directly embedded as Latex input format.
Voice input $\rightarrow$  Math symbolic equation output. It may be doable.
This may help not only Jeroen but even the vast majority of us more luckily endowed :) ..
EDIT 2 :
Just googled MathTalk.com  Dragon Naturally Speaking in  Anna Kirkpatrick's moving answer here. This can symbolically  convert polynomials, powers, trig, fractions, Greek characters and what have you with adequate speed.
MathTalk
A: You might be interested in watching Using Python to Code by Voice.
A: I'm not sure what devices might be able to fit a stylus to your fingers (even a modified one that can accomodate your strength and range of motion), but have you considered using a device like
(writing tablet)? 
Also I'm wondering if anything software-based has predictive symbols for math similar to Windows 7 'math input' panel. 
A: I am a graduate student in a mathematical field with a chronic injury to my hands. I have recently been using Mathfly to dictate LaTeX math by voice. Please see mathfly.org for instructions on how to install and use it as well as demonstration videos and the chat room. It is free and open source, and well documented.
Unlike mathtalk, mathfly allows continuous command recognition (ccr) which means that you don't have to pause between commands. Mathfly is also completely customizable.
A: A long time ago I worked supporting disabled students using computers and this is a problem we often had.   Also my writing is impossible to read, so I was allowed to use a computer to do exams, including maths courses at university,  my wife has Cerebral Palsy and likewise used a computer while doing her university maths degree.
There are two separate problems to solve, do not mix them up!

Firstly the disabled person has to be able to “type” on the computer (and use the mouse), for this there are lots of custom hardware and software solutions, including speech input.    (Let’s just say that Stephen Hawking can’t use speech input, so don’t assume that speech input is the answer for everyone.)    An assessment by an expert needs to be done so as to advice on the best options.   In the UK contact The Access Centre at Hereward Collage or Abilitynet, in the USA try the Trace Centre at University of Wisconsin-Madison.
However this is often a solved problem, as the student will have been using a computer at school, also at least 50% of our clients could use a standard keyboard with no modifications, other then maybe enabling “Sticky Keys”.

Then software is needed to allow “maths” to be done. 
This is different than allowing maths to be presented in a nice way.   Image learning to solve your first equations using Latex notation!   When “doing maths” by pen/paper, people do not work “left to right”, they build up equations in all sorts of order, therefore the software that is used has to be flexible.
For a long time ChiWriter was the chosen package for disable university students dong maths degrees, as it did not force a person to input an equation in a given order.     It is no longer on the market, and must have been replaced with something better!    Sorry I am nearly 20 years out of date on what is the best software to use. 
A: (Background: I have a chronic pain condition, and it is extremely painful for me to do any sort of repetitive fine motor activity, including writing and typing.  I earned an undergraduate degree in math with quite little handwriting, and I'm currently a graduate student.)
Unfortunately, I've never been able to find any one solution or approach to replace the work that many people do with pencil and paper, but there are lots of partial solutions that work for different situations and types of mathematics.  Here are some of the ones that I use and which, based on your description, might be applicable.


*

*Getting really proficient at mental math.  I think you've already done a lot of this, so all I'm going to say is that I can do a lot more math in my head than I would've believed was possible pre-disability.  It just takes a lot of practice.  Of course, it doesn't work for everything; some calculations just require remembering too many things at once.

*Speech-to-text.  If you have clear speech, then a speech-to-text system is potentially very helpful.  (I use Dragon NaturallySpeaking.)  Maybe you already use one for general writing and computer use.  If so, then you have almost certainly noticed that they are not designed for mathematics (or, for that matter, computer science), so some additional software is necessary in order to do math. 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, I can dictate a plain text file containing this NatLaTeX source.  I then use in 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!).
The big advantage to a dictation system like this is that you get to go through the process of formally presenting your work, which is really helpful for checking understanding and practicing proof writing.  Disadvantages include a steep learning curve and not being able to see your work (typeset, at least) in real time.  You also have very limited choices in text editors because Dragon will only "play nice" with a couple of them.

*Programming languages and computer algebra systems.  When you actually need to do calculations, plot functions, etc., it is hard to beat a good computer algebra system.  There are lots of choices out there, and I think the choice of which one to use ultimately comes down to personal preference and perhaps compatibility with whatever assistive technology you use.  Of course, you still face the problem of how to handle getting input to that computer algebra system.  Typing with one finger on an on-screen keyboard sounds rather slow and tedious.  Here are a few alternatives you might want to look into.


*

*If you have head and neck movement, a head pointer is one option.  I sometimes use one that actually marketed as a gaming device called TrackIR.  (Gaming peripherals are much less expensive than assistive technology peripherals!)  You can use this to type on an on-screen keyboard or to interact with the input panels found in many computer algebra systems.  For mouse click, you could use a switch with your finger or a dwell/hover click.

*Eye tracking is a technology that has recently become much more affordable due to relatively new consumer-level devices marketed for gaming applications.  Just a couple months ago, I got an Tobii EyeX eye tracker, and it has been great!  I use it with a simple mouse emulation script and Dasher to write code in Sage.  Dasher is really cool, by the way, and quite good for text entry with low-precision input devices like eye trackers.  It's also much faster than most on-screen keyboards.  Just as a warning, the EyeX is not intended as an assistive device so you do have to do a some software configuration in order to make it do what you want it to do.  But you're studying computer science, so I don't think that should be a problem for you.  (FreePIE, OptiKey, and Dasher are all good pieces of free software to look up and consider for use with the EyeX.)
The big advantage to computer algebra systems is that you can do all of the numerical calculations and tedious symbolic manipulations without needing to ever write down a single number.  The disadvantage is that hiding all of the details can sometimes hinder your conceptual understanding.
Those are the main strategies I use.  I hope something here can help you out, too.
EDIT: 
There has been a request for some examples of what NatLaTex can do, so here are a couple of different examples pulled files on my hard drive. 
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}
A: If I were unable to use my hands, I personally would attempt to use a sophisticated voice to text interface like Dragon Naturally Speaking http://www.nuance.com/dragon/index.htm, which includes addons that specifically permit you to voice-type into IE or Firefox. Why would that capability be particularly useful? Because the second portion of my strategy would be to then go to https://sagecell.sagemath.org/ and use that (Sage) free alternative to Maple, Mathematica, Matlab and the like. Sage is a full symbolic math processor with beautiful graphics output and, if you are saving your abstract math work or sharing it with other, you can save the work you are doing only in pdf form or output LaTex and the like to get high quality mathematics documents.
Now, I should emphasize that I have not implemented the solution I envision (thankfully not requiring it), so I am glibly describing a process of software installation and learning curve/troubleshooting that will be challenging. That being said, I believe this approach would accomplish your goal of hands-free math work in a visual symbolic and numeric calculation environment.
A: You mentioned that you use MS Office and that this is slow.
The other answers have already said good things, but here is maybe a strange suggestion: Learn LaTeX. Install a nice plain text editor and a version of LaTeX. Yes, LaTeX code can be a bit intimidating, but with time it is not that hard to read. The nice thing about it is that you are able to share what you have written with someone else (the PDF file). It is fairly easy to edit. This, of course, might not be the best idea for actually doing mathematics.
Just a thought.
A: You may want to use SymPy, "a Python library for symbolic mathematics". If you use SymPy Live, you don't even need to install anything in your machine.
For example, suppose you want to expand $(x+y)^9$ without computing the binomial coefficients manually. Using SymPy Live, we get
>>> x, y = symbols('x y')
>>> expand((x+y)**9)
 9      8         7  2       6  3        5  4        4  5       3  6       2  7        8    9
x  + 9*x *y + 36*x *y  + 84*x *y  + 126*x *y  + 126*x *y  + 84*x *y  + 36*x *y  + 9*x*y  + y 

Or, perhaps you want the 7th order truncation of the Maclaurin series for $\tan$
>>> x = symbols('x') 
>>> tan(x).series(x,0,8)
     3      5       7        
    x    2⋅x    17⋅x      ⎛ 8⎞
x + ── + ──── + ───── + O⎝x ⎠
    3     15     315         

A: Though not impaired, I recently began working with Accessibility, so my computer and I can communication audibly.  Was very challenging at first, but re-running the "improve" process helps, plus this week I found a note and downloaded WSRMacros, for Windows Speech Recognition.
Essentially I use it to make boilerplates ahead of time, set one up so I'd say, for instance, "quadratic" and it might output Ax^2 + Bx + C, which appears fairly useless, except that you can then turn around and by voice "select A" and replace it, repeat for B and C.  Tedious, but each new macro adds more functionality, and the symbols are integrated into the macro, rather than somehow spoken into the equation for each instance.  Maybe you can combine this with the other ideas above, like using Google voice to get a good basic equation on your clipboard.
Also, MathML is interesting, it's like writing webpages in HTML, but with specific math tags.
These are free and/or open source tools, or included with Windows.

