Viewpoint: Yes, mathematics should be pursued for its own sake, as doing so will eventually present practical benefits to society. Viewpoint: No, mathematics should first be pursued by everyone for its societal utility, with the mathematically gifted...

Mathematics/Mathematical Ability Study of numbers and their operations. Skill with mathematics is as important as literacy for daily living. Mathematics are used daily—to keep score in sports, to calculate the amount of change due when making a...

During the nineteenth century advances in mathematics pointed toward a universe not necessarily limited to three dimensions and not necessarily absolute in time and space. By developing new mathematical models and precise formulas with enormous...

In the years after 1450 European mathematics flourished, yet during the previous 850 years almost all mathematical developments occurred in other parts of the world. In Medieval Europe the religious and philosophical works of the ancient Greeks and...

During the classical period of mathematics in the ancient world, many fundamental branches of mathematics originated and were developed to a remarkable degree. However, due to various catastrophes, much of this ancient mathematical learning was lost,...

1900-1949 Abstraction and generalization have often been useful elements of the mathematician's toolkit. They gained in prominence in the nineteenth century and became perhaps the most distinguishing features of mathematics during the period...

The basic notions of number and magnitude can be seen in markings on cave walls and primitive tools. However, it took many thousands of years for the first use of quantities to evolve into the abstract concept of numbers as we use them today. The...

Following on the resounding successes of the preceding century, eighteenth-century mathematics not only continued to break important new ground, but also paused to consolidate the gains made by Isaac Newton (1642-1727) and Gottfried Leibniz (1646-1716)...

As the eighteenth century drew to a close, mathematics was in a state of rapid change. New areas of mathematics remained wide open to research, while older, established areas of mathematics were finding new applications. Advances in analytic geometry,...

Over the centuries, people have thought of mathematics, and have defined it, in many different ways. Mathematics is constantly developing, and yet the mathematics of 2,000 years ago in Greece and of 4,000 years ago in Babylonia would look familiar to a...

The invention and ideas of many mathematicians and scientists led to the development of the computer, which today is used for mathematical teaching purposes in the kindergarten to college level classrooms. With its ability to process vast amounts of...

While solving problems and constructing proofs, mathematicians use many different approaches. A common technique for proving a statement is by contradiction. In this approach, it is supposed that the converse of the statement, or its opposite, is true....

Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary...