most recent 30 from http://mathoverflow.net 2013-05-19T07:51:35Z http://mathoverflow.net/feeds/question/64071 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64071/what-does-the-term-yoga-mean-in-mathematics Sridhar Ramesh 2011-05-06T00:59:34Z 2011-05-06T02:28:27Z

<p>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?</p>

http://mathoverflow.net/questions/64071/what-does-the-term-yoga-mean-in-mathematics/64073#64073 Todd Trimble 2011-05-06T01:23:14Z 2011-05-06T01:23:14Z

<p>I sometimes have used the word myself, without ever having sat down and asked myself what do I mean by that exactly. I've used it roughly to mean a coherent body of techniques; I'm not sure if I can amplify much further. "The yoga of adjunctions and mates", "the yoga of the Yoneda lemma and its correlates", and you will find a bunch more scattered around the nLab ("the yoga of 'generalized the' ") if you use the search function. To me, a "yoga" is not quite as formalized (or pretentious) as a "calculus", but it's somewhat in that vein. </p>

http://mathoverflow.net/questions/64071/what-does-the-term-yoga-mean-in-mathematics/64076#64076 Allen Knutson 2011-05-06T01:55:22Z 2011-05-06T01:55:22Z

<p>"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. </p> <p>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".')</p>

http://mathoverflow.net/questions/64071/what-does-the-term-yoga-mean-in-mathematics/64078#64078 Dan Petersen 2011-05-06T02:28:27Z 2011-05-06T02:28:27Z

<p>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.</p> <p>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.)</p>