TITLE: What does the term "yoga" mean in mathematics?
QUESTION [37 upvotes]: Just exactly what the title says; often, in mathematics, particularly in the vicinity of Grothendieck, I see reference to "the yoga of...". What exactly does the term "yoga" mean in these contexts?

REPLY [38 votes]: I've taken "yoga" to mean a part of the body of mathematics which does not consist of many actual theorems or results -- or in fact could not be formalized as just a few theorems -- but rather a collection of principles and techniques that one needs to wrap one's head around completely, after which one will be able to use them almost effortlessly.
As an example, I would say that there is a yoga of generating functions in combinatorics. (Perhaps this is the simplest example of a yoga.)

REPLY [13 votes]: "Yoga" and "yoke" (as in of oxen) are derived from the same
Indo-European root, meaning a linkage. Of course "linkage", and
"relation", and "connection", and "join", all have mathematical meanings 
already, so one must go further afield to talk about two mathematical 
concepts being yoked to one another. 
When I have seen the word used
by mathematicians (esp. Bott), it is usually in exactly this way -- the yoga of X and Y,
not of X.
(As such I must disagree with the comment
`of course it has nothing to do with any proper meaning of the word "yoga".')