"There is no question about what arithmetic is for
or why it is supported. Society cannot proceed
without it. Addition, subtraction, multiplication,
division, percentages: though not all citizens can
deal fluently with all of them, we make the
assumption that they can when necessary.
Those who cannot are sometimes at a disadvantage.
Algebra, though, is another matter."
— Underwood Dudley in the Notices of the
American Mathematical Society, May 2010:
"What Is Mathematics For?"
A less nuanced remark from the American
Mathematical Society (AMS) today—
"The answer to the recent Op-Ed piece
in The New York Times entitled
'Is Algebra Necessary?'
is resoundingly YES!"
— Eric Friedlander, AMS president
* A review of philosophical terminology—
"The distinction between necessary truth
and contingent truth is a version of Leibniz 's
distinction between truths of reason and truths
of fact. A necessary truth must be true and
could not be false, whatever way the world is.
It is true in itself. A contingent truth, on the other
hand, depends upon the empirical world and might
have been false had the world been different."