Mathematics is a way of describing relationships
between numbers and other measurable quantities. Mathematics can express simple
equations as well as interactions among the smallest particles and the farthest
objects in the known universe. Mathematics allows scientists to communicate
ideas using universally accepted terminology. It is truly the language of
science.

We benefit from the results of
mathematical research every day. The fiber-optic network carrying our telephone
conversations was designed with the help of mathematics. Our computers are the
result of millions of hours of mathematical analysis. Weather prediction, the
design of fuel-efficient automobiles and airplanes, traffic control, and
medical imaging all depend upon mathematical analysis.

For the most part, mathematics remains
behind the scenes. We use the end results without really thinking about the
complexity underlying the technology in our lives. But the phenomenal advances
in technology over the last 100 years parallel the rise of mathematics as an
independent scientific discipline.

Until the 17th century, arithmetic, algebra, and geometry were the only mathematical disciplines, and mathematics was virtually indistinguishable from science and philosophy. Developed by the ancient Greeks, these systems for investigating the world were preserved by Islamic scholars and passed on by Christian monks during the Middle Ages. Mathematics finally became a field in its own right with the development of calculus by English mathematician Isaac Newton and German philosopher and mathematician Gottfried Wilhelm Leibniz during the 17th century and the creation of rigorous mathematical analysis during the 18th century by French mathematician Augustin Louis Cauchy and his contemporaries. Until the late 19th century, however, mathematics was used mainly by physicists, chemists, and engineers.

At the end of the 1800s, scientific researchers began probing the limits of observation, investigating the parts of the atom and the nature of light. Scientists discovered the electron in 1897. They had learned that light consisted of electromagnetic waves in the 1860s, but physicist Albert Einstein showed in 1905 that light could also behave as particles. These discoveries, along with inquiries into the wavelike nature of matter, led in turn to the rise of theoretical physics and to the creation of complex mathematical models that demonstrated physical laws. Einstein mathematically demonstrated the equivalence of mass and energy, summarized by the famous equation

*E=mc*in his special theory of relativity in 1905. Later, Einstein’s general theory of relativity (1915) extended special relativity to accelerated systems and showed gravity to be an effect of acceleration. These mathematical models marked the creation of modern physics. Their success in predicting new physical phenomena, such as black holes and antimatter, led to an explosion of mathematical analysis. Areas in pure mathematics—that is, theory as opposed to applied, or practical, mathematics—became particularly active.

^{2},
A similar explosion of activity began in
applied mathematics after the invention of the electronic computer, the ENIAC
(Electronic Numerical Integrator and Calculator), in 1946. Initially built to
calculate the trajectory of artillery shells, ENIAC was later used for nuclear
weapons research, weather prediction, and wind-tunnel design. Computers aided
the development of efficient numerical methods for solving complex mathematical
systems.

Without mathematics to describe physical
phenomena, we might be living in a world with beautiful art, literature, and
philosophy, but no technology. Even the medical advances of the last 50 years
might not have occurred. Science and technology, in their turn, have provided
many of the problems that motivated progress in mathematics. Such problems
include the behavior of weather systems, the motion of subatomic particles, and
the creation of speedier and smaller computers that can perform multiple tasks
simultaneously.

(Encarta Encyclopedia)