Although mathematicians frequently use specialist software in direct teaching of mathematics, as a means of delivery e-learning technologies have so far been less widely used. We (mathematicians) insist that teaching methods should be subject-specific and content-driven, not delivery-driven. We oppose generic approaches to teaching, including excessively generalist, content-free, one-size-fits-all promotion of information and communications technology. This stance is fully expressed, for example, in the recent Teaching Position Statement from the London Mathematical Society (2010) and is supported by a recent report from the National Union of Students (2010, 5): "Not every area of study needed or was compatible with e-learning, and so to assume it would grant blanket advantages was not accurate". This paper is an attempt to explain mathematicians' selectivity in use of information and communications technology and its guiding principles. The paper is addressed to our non-mathematician colleagues and is not intended to be a survey of the existing software and courseware for mathematics teaching--the corpus of existing solutions is enormous and its discussion inevitably involves hardcore mathematics. (Contains 4 notes and 5 figures.)