Mathematics, 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 disigned 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 airplane, traffic control, and madical 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, arithmatic, algebra, and geometry were the only mathematical disciplines, and mathematics was virtually indistinguishable from science and philosophy. Developed by the acient greeks, these systems for investigating the world were preserved by islamic scholars and passed on by crhistian 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 conteporaries. Until the late 19th century, however, mathematics was used mainly by physicists, chemists, and engineer.
At the end of the 1800s, scientific researches began probing the limits of observations, investigating the parts of the atom and the nature of light. Scientist discovered the electron in 1897. They had learned that light consisted of electromagnetic waves in 1860s, but physicist Albert Einstein showed in 1905 that light could also behave as particles. These discoveries, along with inquiries into the wave like nature of matter, led in turn in 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=mc2, 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 accelaration. These mathematical models marked the creation of modern physics. Their succes 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.
A similar explosion of activity began in applied mathematics after the invention of the electronic computer, the ENIAC (Elecronic 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 system.
Without mathematics to describe physical phenomena, we might be living a world with beautiful art, literature, and philosophy, but no technology. Even the medical advance of the last 50 years might not have ocurred. Science and technology, in their turn, have provided many of the problems that motivated progress in the mathematics. Such problems include the behavior of weather system, the motion of subatomic particles, and the creation of speedier and smaller computers that can perfrom multiple tasks simultaneously.
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