The means used to express mathematical ideas on paper or other visual medium.
Our MathematicalNotation has come a long way in only a few centuries. This footnote from a history of probability is instructive:
"To illustrate the difficulties... [A] multplication sum is written as follows:-
4.p.R6 4.m.R6 Productum 16.m.6 10.
or, as might now be written, :-
(4 + sqrt(6)) (4 - sqrt(6)) = 16 - 6 = 10.
We do not realise our own good fortune.
F.N. David Gods, Games and Gambling
There are still many missing and cumbersome constructs in modern math notation. See http://www.jsoftware.com/books/help/camn/camn.htm for an excellent paper on the subject. -- JimRussellIverson has proposed quite a few new notations beyond those mentioned in that paper, and Knuth has exploited the flexibility he has with TeX to begin using some of those notations in his books and papers (beginning, I think, with Concrete Mathematics) in an attempt to popularize them. -- GlennVanderburg
P.H. Nidditch introduced several formal languages which are easy to type. See LowKeystrokeFormalLanguages.
See also MathWikiEzMathMathMlCategoryMath