The theme of the blog, Math Island, is not meant to imply all the areas of mathematics stand alone but more in line with the message from John Donne’s poem:
No man is an island,
Entire of itself,
Every man is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less.
As well as if a promontory were.
As well as if a manor of thy friend’s
Or of thine own were:
Any man’s death diminishes me,
Because I am involved in mankind,
And therefore never send to know for whom the bell tolls;
It tolls for thee.
There are of course today many fields of study of mathematics and none really stand alone for very long. The number of fields of mathematics keeps increasing with more specialization but there is overlap of the areas and dependencies on other fields of study. The classification used by AMS, Mathematics Subject Classification, has 98 major categories (broken down into over 5,000 sub categories of study) in the 2010 version.
Many times when I start to work on a math problem, puzzle or a new topic of interest I end up visiting many different fields (islands) of mathematics. For example, I really enjoy working on ‘math magic’ which amaze the audience but behind the trick is mathematics. There is a really neat card trick using 5 cards drawn at random from a standard deck and place on a table by the magician’s assistance with all but one card face up (credit given to W. Fitch Cheney). The magician then announces the value and suit of the hidden card. The mathematics behind the trick covers combinatorics, lexicographical ordering, modular arithmetic, lateral thinking and others.
This is just one example of an adventure one can have visiting many of the islands (fields) of mathematics while collecting something of interest from each one.