The earliest development of mathematics is closely tied to the development of counting and numbers. For thousands of years before there was a system for writing numbers, ancient people used a variety of methods to either estimate or guess at the amounts of things they dealt with in their daily lives. At some point, they began to invent ways of keeping a tally of their possessions, such as livestock or sacks of grain. The simple methods for doing this varied widely from one part of the world to another, from civilization to civilization, but inevitably they led to the development of numbers. The first we know about came from Sumeria (around the area now known as Iraq) about 3000 B.C. Number systems also varied from one area to another, just as the early Sumerian system was very different from what we use today, but even their early attempts to improve how they worked with quantities helped prepare the way for the development of one of the most important uses for numbers, mathematics.
The Sumerians, Babylonians and, the ancient Egyptians were the first mathematicians and, not by coincidence, the first highly skilled scientists. They took the use of numbers beyond the everyday basic tasks of counting or keeping track of flocks and grain, to trading with "bills of sale" instead of direct bartering for goods and services, and solving the practical problems of agriculture, building, and astronomy. At first, in some areas of the world, such as Greece, the use of mathematics, like many advanced skills developed by early civilizations, was only taught to the wealthy or powerful, but it eventually became clear that, in many was, civilization itself could benefit so much from the knowledge of mathematics that its use needed to be available to more than just the elite. The ability to create an accurate calendar in order to predict the seasonal cycles was vital to survival. As civilizations grew, whole economies based on trade and more complicated building practices also demanded the use of fairly advanced mathematics. The more complex their lives became, the more important were their abilities to use mathematics. The ability to do calculations had to grow with these needs.
About 3000 B.C., in China, the first abacus was invented and became the first "adding machine," allowing simple arithmetic calculations to be performed without the use of objects or fingers. About 1000 years later, the Babylonians used multiplication tables so by that time the first branch of mathematics, arithmetic, was being used. addition and subtraction had been used in many different ways for much longer, and multiplication had been carried out very early as well by combining symbolic representations of numbers called hyroglyphs. But the use of actual multiplication tables was a true advancement. The Babylonians had chosen to use the cycle of the moon's phases as the basic unit of their calendar. This means they had to use fractions in order to arrange the number of lunar cycles within a year. About 1675 B.C., the oldest mathematical record was written by a scribe named Ahmes. Among other things, this document, called the Rhind papyrus, tells how to use fractions to divide daily food rations. It is clear, then, that by 1600 years B.C., arithmetic was being used for a number of practical purposes.
As these very basic aspects of mathematics came to be commonly used, other methods also began to benefit the people through the use of basic geometry. Literally the Greek word for "earth measuring," geometry was used in about 240 B.C. to actually measure the circumference of the earth with amazing accuracy. The astronomer who performed this feat was a Greek named Eratosthenes of Cyrene. Greece produced a number of great mathematical minds, including the philosopher and mathematician Pythagoras (c. 580-500 B.C.). He is famous for the theorem which carries his name to this day. It states that the sum of the squares of two sides of a right triangle is equal to the square of the third side. This seemingly simple concept and others developed during the centuries to come would advance mathematics into the future. But long before the time or Pythagoras, geometry was used in many ways. Perhaps the most famous and accurate use from the ancient world was the determination of the angles and heights of the sides for the pyramids of Egypt. The sides of the Great Pyramid are the same to within one inch and the angles to within a fraction of a degree. This took not only very accurate measurements, but also an accurate understanding of geometry.
Through astronomy and other sciences, mathematics began, very early to help people better understand their world and the universe. Complicated calculations had to be made in order to predict the motion of the sun and moon. Out of necessity, mathematics continued to develop because it was needed in order to survive, but also to increase understanding of the physical world. In about 330 B.C., the Greek mathematician, Euclid of Alexandria published his ideas on geometry and number theory in which he collected the works of others including Pythagoras, recording, for the first time the basic rules of mathematics as they were known until that time. Geometry students used Euclid's book as their mathematics text for more than 2000 years and his ideas still influence mathematicians today. Various aspects of arithmetic, algebra, geometry and trigonometry continued to be applied as to matters of daily life, commerce, architecture, and the sciences both old and new throughout this time, with ever greater complexity and accuracy. But in the 17th century, the first really dramatic addition to mathematics would come. Devised independently by two mathematicians, Gottfried Wilhelm Leibniz in Germany, and Isaac Newton in England, calculus provided new techniques for dealing with very small changes in distance, area, or times. This new form of mathematics allowed for the determination of areas and volumes of complex shapes, among other things. With calculus, scientists now strive to understand, calculate and create models for virtually everything both large and small, from the tiniest sub-atomic particle to the universe as a whole.
This is the complete article, containing 1,014 words
(approx. 3 pages at 300 words per page).
