Ever heard of octonions ? They're not a new kind of vegetable, but are part of a high dimensional algebra, which is disturbingly fascinating. While reading the introduction, I got the disturbing sense that the author was just making stuff up and seeing if he could get away with it.
But I guess that's the technical definition of "research in mathematics". Truly, it is: the researcher sits or paces, possibly muttering, and then writes. The basic idea is that you come up with an idea and see just how far you can stretch it before it breaks or passes the Hooke's Law limit.
It is important also to stay away from the Hooke's law limit on one's own mind. More coffee and other mind-altering substances have been consumed in the pursuit of mathematics than in all of sysadminnery, it seems...
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