Edit made on November 23, 2008 by DerekCouzens at 20:33:03
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A recurring theme in mathematics is that sometimes
different things have something in common. Finding
that something and then studying it in isolation,
in the abstract, can then teach us something about
If you see what I mean.
A case in point is an area of mathematics called
Group Theory. There are many cases where we have
a collection of things, along with some way of
them. them in specific way are classified as groups. Examples are numbers (which we
can add or subtract) and rotations (which we can
combine by doing one after the other).
Galois did a lot with group theory, to the point
where there's a sub-topic call Galois Theory.