TeXgefühl

German has several words for which there is no English equivalent, and so we've adopted them into our language. Of these, perhaps the most famous is Schadenfreude (literally, something like "harm-joy"), which means "pleasure taken at the misfortune of others".

Another good one is Ohrworm. Literally "ear worm", it refers to a catchy song that you just can't get out of your head.

My colleague Jean-Paul Allouche introduced me to another some time ago: Sprachgefühl. Literally, "language feeling", this word refers to a native speaker's intuitive understanding of the subtleties of his own language. When a French speaker says, "We now prove this by recurrence on n", Jean-Paul looks at me and mouths the word "Sprachgefühl", because he knows that the speaker should have said induction, not recurrence. Similarly, French speakers often say couple instead of pair, and speak about notations instead of notation. (Notation is usually a mass noun in English and hence rarely appears in the plural in mathematics and computer science research -- unless the paper is written by a non-native speaker!) French speakers also often say something like "We denote by |x| the length of the word x", when a native speaker would probably say something like "We let |x| denote the length of the word x".

Based on this, I've coined a new word: TeXgefühl. This means "the intuitive understanding of what is proper usage in the mathematical typesetting language TeX". (There is also the related word, LateXgefühl.) Neither word appears in a Google search, so I really do appear to be the first to say them online.

Both TeX and LaTeX have some subtleties which beginners find difficult to master. These include constructs that improve the appearance of the manuscript, like knowing to put "\ " after any lower-case letter followed by a period that does not end a sentence, as in "Dr.\ Smith"; if you don't do this, tex inserts too much space between "Dr." and "Smith". Another example of TeXgefühl is knowing to use the proper kind of dots in a mathematical expression -- you should write "x_1,   x_2,   \ldots,   x_n" but "x_1   x_2   \cdots   x_n". The subtleties also include knowing that both TeX and LaTeX have reasonably good algorithms for deciding on spacing, so that manuscripts should not be littered everywhere with "\noindent" and \bigskip", and that there is no need to put "\par" or "\\" at the end of every paragraph.

If you have LaTeXgefühl, you know not to hard-code references to theorems, lemmas, etc.. Instead, you use labels inside theorem environments to store the name of the theorem, and then you refer to to the theorem by saying something like Theorem~\ref{thm1}. (The twiddle after "Theorem" is another example of TeXGefühl.)

Those with TeXgefühl know that single-letter functions are always in the italic font, using something like $f(x)$, but that multi-letter functions, such as sin and cos, are nearly always in the roman font, and should be specified using the built-in expressions \sin and \cos. (For some reason, many people also forget this for \gcd.) They know that left-quotes in TeX are different from right-quotes, so that you should write ``quoted expression'' instead of "quoted expression". And they know that page ranges should be specified with two hyphens, like "237--246".

It's hard to attain Sprachgefühl in a foreign language - I will probably never get there in French or German. But with a little work, nearly everyone can attain it in TeX.