What is mathematics?

Mathematics is often defined as the study of quantity, magnitude, and relations of numbers or symbols. It embraces the subjects of arithmetic, geometry, algebra, calculus, probability, statistics, and many other special areas of research.

There are two major divisions of mathematics: pure and applied. Pure mathematics investigates the subject solely for its theoretical interest. Applied mathematics develops tools and techniques for solving specific problems of business and engineering or for highly theoretical applications in the sciences.

Mathematics is pervasive throughout modern life. Baking acake or building a house involves the use of numbers, geometry, measures, and space. The design of precision instruments, the development of new technologies, and advanced computers all use more technical mathematics.

Mathematics is the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and abstraction of its subject matter.

Ancient history
Mathematics first arose from the practical need to measure time and to count. Thus, the history of mathematics begins with the origins of numbers and recognition of the dimensions and properties of space and time. The earliest continuous records of mathematical activity that have survived in written form are from the 2nd millennium BC. The Egyptian pyramids reveal evidence of a fundamental knowledge of surveying and geometry as early as 2900 BC.

The Greeks were the first to develop a truly mathematical spirit. They were interested not only in the applications of mathematics but in its philosophical significance, which was especially appreciated by Plato. They developed the idea of using mathematical formulas to prove the validity of a proposition. Aristotle, engaged in the theoretical study of logic, the analysis of correct reasoning. No previous mathematics had dealt with abstract entities or the idea of a mathematical proof.

Middle Ages
Indian mathematicians were especially skilled in arithmetic, methods of calculation, algebra, and trigonometry. Aryabhata calculated pi to a very accurate value of 3.1416. Because Indian mathematicians were not concerned with such theoretical problems as irrational numbers, they were able to make great strides in algebra. Their decimal place-valued number system, including zero, was especially suited for easy calculation. Indian mathematicians, however, lacked interest in a sense of proof. Most of their results were presented simply as useful techniques. One of the greatest scientific minds of Islam was called al-jabr who became known as algebra. Consequently, the numbers familiar to most people are still referred to as Arabic numerals.