by George
A. W. Boehm
Never
before have so many people applied such abstract mathematics to so great a
variety of problems. To meet the demands of industry, technology, and other
sciences, mathematicians have had to invent new branches of mathematics and
expand old ones. They have built a superstructure of fresh ideas that people
trained in the classical branches of the subject would hardly recognise as
mathematics at all.
Applied
mathematicians have been grappling successfully with the world's problems at a
time, curiously enough, when pure mathematicians seem almost to have lost touch
with the real world. Mathematics has always been abstract, but pure
mathematicians are pushing abstraction to new limits. To them mathematics is an
art they pursue for art's sake, and they don't much care whether it will ever
have any practical use.
Yet the
very abstractness of mathematics makes it useful. By applying its concepts to
worldly problems the mathematician can often brush away the obscuring details
and reveal simple patterns. Celestial mechanics, for example, enables
astronomers to calculate the positions of the planets at any time in the past
or future and to predict the comings and goings of comets. Now this ancient and
abstruse branch of mathematics has suddenly become impressively practical for
calculating orbits of earth satellites.
Even
mathematical puzzles may have important applications. Mathematicians are still
trying to find a general rule for calculating the number of ways a particle can
travel from one corner of a rectangular net to another corner without
Now that
they have electronic computers, mathematicians are solving problems they would
not have dared tackle a few years ago. In a matter of minutes they can get an
answer that previously would have required months or even years of calculation.
In designing computers and programming them to carry out instructions,
furthermore, mathematicians have had to develop new techniques. While computers
have as yet contributed little to pure mathematical theory, they have been used
to test certain relationships among numbers. It now seems possible that a
computer some day will discover and prove a brand-new mathematical theorem.
(from The New World of Mathematics, Faber and Faber, London, 1959)
Taken from: http://www.uefap.com/reading/exercise/tewufs/tewufs15.htm
Taken from: http://www.uefap.com/reading/exercise/tewufs/tewufs15.htm
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