Nathan Larson, age 13, of Cleveland, Ohio, for his question:
WHEN DID WE DEVELOP MATHEMATICS?
Prehistoric man was the first to practice mathematics. Before the time of recorded history prehistoric peoples had learned to count such things as the animals in their herds. At first they probably used their fingers or pebbles to keep track of small numbers.
As time passed, prehistoric people most likely learned to use the length of their hands and arms and other standards of measure.
By the year 3000 B.C., the peoples of ancient China, Egypt and Babylonia had already developed a practical system of mathematics. They used written symbols to stand for numbers and they knew the simple arithmetic operations.
The ancients also developed a practical geometry that was helpful in engineering and agriculture. The Egyptians, as an example, knew how to survey their fields and to make the intricate measurements necessary to build huge pyramids.
Between 600 and 300 B.C., the Greeks took the next great step in mathematics. They inherited a large part of their mathematical knowledge from the Babylonians and Egyptians. But they became the first to separate mathematics from practical problems.
The Greeks separated geometry from practical applications and made it into an abstract exploration of space. They based this study of points, lines and figures, such as triangles and circles, on logical reasoning rather than on facts found in nature.
In about 200 B.C., Archimedes, the leading mathematician of ancient times, devised processes that foreshadowed those of integral calculus and also made contributions to physics. The Greek astronomer Ptolemy in about A.D. 150 developed trigonometry and the Greek mathematician named Piophantuis earned the title of the father of algebra in A.D. 275 when he worked on numbers in equations.
The ancient Romans built impressive buildings, but showed little interest in pure mathematics.
After the fall of Rome in A.D. 476, Europe saw no new developments in mathematics for hundreds of years. But the Arabs preserved the mathematical tradition of the Greeks and Romans.
Mathematicians in India developed zero and the decimal number system. Then, after A.D. 700, the Arabs adopted these inventions from the Indians and used the new numbers in their mathematics. The Arabs also preserved and translated many of the great works of Greek mathematicians.
After 1100, Europeans started to borrow the mathematics of the Arab world. European merchants started to use the decimal number system and European scholars began to study Arab works on algebra and geometry.
The Renaissance produced many great advances in mathematics. The exploration of new lands and continents called for better mathematics for navigation. The growth of business demanded better mathematics for banking and finance. The invention of printing brought the appearance of hundreds of popular arithmetic books.