The Evolution of Math

Introduction

Mathematics, study of relationships amidst amounts, magnitudes, and properties and of ordered procedures by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, if of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, although, mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions. This latter outlook encompasses mathematical or symbolic reasoning, the science of using symbols to supply an exact idea of logical deduction and inference based on definitions, axioms, postulates, and rules for blending and transforming primitive elements into more convoluted relations and theorems.(This short survey of the history of mathematics traces the evolution of mathematical ideas and concepts, starting in prehistory. Indeed, mathematics is nearly as vintage as humanity itself; clues of a sense of geometry and interest in geometric pattern has been discovered in the designs of prehistoric pottery and textiles and in cave paintings.(Monastyrsky, 87) Primitive counting systems were almost certainly based on using the fingers of one or both hands, as evidenced by the predominance of the numbers 5 and 10 as the bases for most number systems today.

Ancient Mathematics

The earliest records of advanced, organized mathematics date back to the ancient Mesopotamian homeland of Babylonia and to Egypt of the 3rd millennium BC. There mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry and with no trace of later mathematical concepts such as axioms or proofs.(Ziman,45)

The soonest Egyptian texts, composed about 1800 BC, disclose a decimal numeration scheme with distinct symbols for the successive powers of 10 (1, 10, 100, and so forth), just as in the scheme utilised by the Romans. Numbers were represented by composing down the symbol for 1, 10, 100, and so on as many times as the unit was in a granted number. For example, the symbol for 1 was in writing five times to represent the number 5, the symbol for 10 was in writing six times to represent the number 60, and the symbol for 100 was in writing three times to represent the number 300. Together, these symbols comprised the number 365. Addition was finished by totaling separately the units--10s, 100s, and so forth--in the numbers to be added. Multiplication was based on successive doublings, and division was based on the inverse of this process.(Monastyrsky, 87)

Greek Mathematics

The Greeks adopted components of numbers from both the Babylonians and the Egyptians. The new component in Greek mathematics, although, was the creation of an abstract mathematics based on a logical structure of definitions, axioms, and proofs.(Pappas, 22) According to later Greek accounts, this development began in the 6th 100 years BC with Thales of Miletus and Pythagoras of Sámos, the latter a religious leader who taught the importance of studying numbers in alignment to understand the world. Some of his disciples made ...