I use a separate Twitter account for work purposes to create as much of a professional barrier as possible within the social platform. A few students follow this account, but I have consistently refused to follow students accounts. This is mainly due to the students' inability to separate private and public forums - which would end up filling my (your) timelines with who's fallen out with who, or what sauce they had on their burgers that evening.
I use my account to follow people of interest within the field and also those within the wider spectrum that may have benefit when looking for inspiration outside my subject.
Some good examples of maths specific people to follow...
Mark McCourt @EmathsUK
Chairman, Teacher Development Trust; CEO, Beluga Learning; Former Senior Director, Tribal; Director, NCETM; School Leader; Inspector; AST
Marcus du Sautoy @MarcusduSautoy
Simonyi Professor for the Public Understanding of Science and Professor of Mathematics
Algebra Fact @AlgebraFact
One fact per day M-F from algebra and number theory by @JohnDCook. Other daily math tweets: @TopologyFact, @ProbFact and @AnalysisFact.
There are plenty more like this last one.
As I've already said it is easy to find people around the subject area that may also be of interest...
CERN Verified account @CERN
CERN, the European Organization for Nuclear Research, is the biggest particle physics laboratory in the world.
Royal Institution @ri_science
The Ri connects people with the world of science through events, education, and the world-famous Christmas Lectures. Watch Ri videos here: http://www.richannel.org
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