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Introduction
T
he mathematical sciences are part of everyday life. Modern
communication, transportation, science, engineering, technol-
ogy, medicine, manufacturing, security, and finance all depend
on the mathematical sciences, which consist of mathematics, statistics,
operations research, and theoretical computer science. In addition,
there are very mathematical people working in theoretical areas of
most fields of science and engineering who also contribute to the
mathematical sciences. There is a healthy continuum between research
in the mathematical sciences, which may or may not be pursued with
an application in mind, and the range of applications to which math-
ematical science advances contribute. To function well in a technologi-
cally advanced society, every educated person should be familiar with
multiple aspects of the mathematical sciences.
Although the mathematical sciences are pervasive, they are often invoked without
an explicit awareness of their presence. For example, in the everyday operation of
making a cell phone call, the mathematical sciences are essential in every step: We
enter numbers in the decimal system, which are converted into sequences of bits (zeros
and ones); next comes conversion to an electromagnetic signal; after an available
receiver is located, the signal is transmitted and (finally) converted into the sound of
our voice. Wireless technology uses techniques called “error correcting codes,” “linear
in the 21st Century
The Mathematical Sciences
1
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and nonlinear filtering,” “hypothesis testing,”
“spatial multiplexing,” “statistical waveform
or parameter estimation,” and these are built
on tools of the mathematical sciences, such as
matrix analysis, linear algebra, algebra, random
matrices, graphical models, and so on.
More generally, the mathematical sciences
contribute to modern life whenever data must
be analyzed or when computational modeling
and simulation is used to enable design and
analysis of systems or exploration of “what-if”
scenarios. The emergence of truly massive
data sets across most fields of science and
engineering, and in business, government,
and national security, increases the need
for new tools from the mathematical sciences. Because the mathematical sciences
are independent of a particular scientific context, they can facilitate the translation of
advances from one discipline to another.
The mathematical sciences provide a
language—numbers, symbols, graphs, and
diagrams—for expressing ideas in everyday life as
well as in science, engineering, medicine, business,
and the arts. Mathematical symbols, which are
more universal than Chinese, English, or Arabic,
allow communication across communities with
completely dissimilar spoken and written languages.
The stories told here describe a number of
recent advances made possible by research in the
mathematical sciences.
FUELING
innovation and discovery
2
