"MTBoS" (variant, "MTBOS") is an acronym for "Math Twitter Blogosphere" and is used by some mathematics educators on Twitter use to describe their community. The term is often used as a hashtag on Twitter ("#MTBoS") in order to make tweets of the community more visible and searchable.
History of "MTBoS" Acronym
"Blogosphere" has a history that predates math educators' adaption of the term. it was coined as early as 1999, re-coined in 2002, and widely used by writers and the media to describe the interconnected network of blogs on the internet (https://en.wikipedia.org/wiki/Blogosphere).
The term "twitterblogosphere" was used as early as 2010 to describe an emerging online community of math educators (https://twitter.com/jybuell/status/19270779491). Other variants included "blogotwitterversphere" (http://samjshah.com/2010/06/30/blogotwitterversphere/).
"Mathblogosphere" (https://twitter.com/nik_d_maths/status/271309095515070465) and "Math Twitter Blogosphere" (https://twitter.com/j_lanier/status/227965292150669312) were in use by 2012. Other variants included "Math Blogotwittosphere" (http://blogs.edweek.org/edweek/edtechresearcher/2012/07/the_math_blogotwittosphere_is_the_best_blogotwittosphere.html).
The first use of the acronym was in 2013 by Christopher Danielson:
I do wonder how collective wisdom of mtbos could be brought to this larger audience. Answer may just be time.