Mathematics arises from many different kinds of problems. At first these were found in
commerce,
land measurement,
architecture and later
astronomy;
today, all sciences suggest problems studied by mathematicians, and
many problems arise within mathematics itself. For example, the
physicist Richard Feynman invented the
path integral formulation of
quantum mechanics using a combination of mathematical reasoning and physical insight, and today's
string theory, a still-developing scientific theory which attempts to unify the four
fundamental forces of nature, continues to inspire new mathematics.
[32]
Some mathematics is only relevant in the area that inspired it, and is
applied to solve further problems in that area. But often mathematics
inspired by one area proves useful in many areas, and joins the general
stock of mathematical concepts. A distinction is often made between
pure mathematics and
applied mathematics. However pure mathematics topics often turn out to have applications, e.g.
number theory in
cryptography. This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what
Eugene Wigner has called "
the unreasonable effectiveness of mathematics".
[33]
As in most areas of study, the explosion of knowledge in the scientific
age has led to specialization: there are now hundreds of specialized
areas in mathematics and the latest
Mathematics Subject Classification runs to 46 pages.
[34]
Several areas of applied mathematics have merged with related
traditions outside of mathematics and become disciplines in their own
right, including
statistics,
operations research, and
computer science.
For those who are mathematically inclined, there is often a definite
aesthetic aspect to much of mathematics. Many mathematicians talk about
the
elegance of mathematics, its intrinsic
aesthetics and inner
beauty.
Simplicity and generality are valued. There is beauty in a simple and elegant
proof, such as
Euclid's proof that there are infinitely many
prime numbers, and in an elegant
numerical method that speeds calculation, such as the
fast Fourier transform.
G.H. Hardy in
A Mathematician's Apology
expressed the belief that these aesthetic considerations are, in
themselves, sufficient to justify the study of pure mathematics. He
identified criteria such as significance, unexpectedness, inevitability,
and economy as factors that contribute to a mathematical aesthetic.
[35] Mathematicians often strive to find proofs that are particularly elegant, proofs from "The Book" of God according to
Paul Erdős.
[36][37] The popularity of
recreational mathematics is another sign of the pleasure many find in solving mathematical questions.
Sumber:http://en.wikipedia.org/
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