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Mathematics consists essentially of :
a) proving the obvious
b) proving the not so obvious
c) proving the obviously untrue
For example, it took mathematicians until the 1800'ies to
prove that 1+1=2 and not before the late 1970 were they
confident of proving that any map requires no more
than four colors to make it look nice, a fact known by
cartographers for centuries.
There are many not-so-obvious things which can be proved true
too. Like the fact that for any group of 23 people, there is
an even chance two or more of them share birthdays. (With
groups of twins this becomes almost certain. Not quite certain
as you will of course point out: they might all have been born
either side of midnight).
Mathematicians are also fond of proving things which are obviously
false, like all straight lines being curved, and an engaged telephone
being just as likely to be free if you ring again immediately after,
as if you wait twenty minutes.
-- R. Ainsley in Bluff your way in Maths, 1988
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