The American and Japanese Perspectives
Elementary forms of mathematics have probably been with man throughout his evolution. As human societies advanced, so too did mathematics. From the 1500s to the present, a long lineage of mathematicians have revolutionized the field. These men were often of European origin. Only in the last century has the United States and Japan emerged as dominant mathematical forces. At present, either of these nations could lead the field into the future.
The first systems of numeration were invented by the Greeks and the Romans (Struik, 1987, p. 80 81). Later, the Western merchant, Leonardo of Pisa, introduced the Hindu Arabic system of numeration into Western Europe. Europeans came to accept these ten symbols gradually. For many centuries, the Greek system of numeration remained popular. Computation was usually performed on the ancient abacus. Roman numerals were then used to register the result. Resistance to Hindu Arabic numerals resulted from the fact that they made the ledgers difficult to read. Throughout the Middle Ages, Roman numerals can be found in merchants' ledgers. As trade increased, interest in mathematics increased also. Initially, this interest was a matter of practical necessity. Arithmetic and algebra were taught outside the universities by self made, Rechenmeisters ("reckon masters," arithmeticians). This knowledge was needed primarily for bookkeeping and navigation (Struik, 1987, p. 81).
It was also during this period, however, that speculative mathematics was investigated by scholastic philosophers. These men combined the study of Plato and Aristotle with meditations on the nature of God, the nature motion, the continuum, and infinity.
For example, St. Thomas Aquinas postulated that every continuum was potentially divisible ad infinitum (Struik, 1987, p. 82). He thought that only points were indivisible, and that a point generated a lin...