Julie Freeman, age 14, of Gastonia, N.C., for her question:
HOW DID ALGEBRA BEGIN?
A number stands for the size of a set of things in arithmetic. But in algebra letters can be used. In working out an algebra problem, a letter may often be replaced by more than one number. First a student must learn how algebra uses letters for numbers. Then the student must learn how algebra makes statements about numbers.
Algebra is one of the most important branches of mathematics. Problems can be solved with algebra that cannot be solved by arithmetic alone.
Thousands of years ago the Chinese, Persians and people in India used algebra. First definite evidence appears in the writings of an Eygptian mathematician named Ahmens who lived about 1700 B.C.
As time went by, the Greeks contributed to the development of algebra. Diophantus was a Greek mathematician who lived in 200 A. D., and he is often called the father of algebra. He was the first person to use quadratic equations and symbols for unknown quantities.
Many contributions to the study of algebra came from the Arabs. They first used negative and positive signs and developed fractions, much as they are used today.
During the 800s the Arabs introduced the zero from India, and this is considered to be one of the greatest advances in the history of mathematics.
A teacher of mathematics in Baghdad between 813 and 833 named A1 Khowarizmi collected and improved the advances in algebra of previous Arab and Hindu scholars. The Arabic word algebra, which means reduction in the sense of solving an equation, comes from the title of his work. Also writing on the subject of algebra was the Persian astronomer poet Omar Khayyam.
During the Middle Ages there wasn't much progress in the development of algebra. But by the 1500s most scholars studied algebra since they believed it to be the symbolic language of mathematics.
Many have contributed to the later development of algebra. Recent direction of algebra has been toward more abstract extension of many of the discoveries throughout mathematics, where earlier work had been centered on the solution of equations as a matter of theory.
"Variable" is a symbol in algebra, usually a letter, that can be replaced by one or more numerical values. ''Expression'' is a certain number or variable, or numbers and variables, combined by operations such as addition, subtraction, multiplication or division. "Absolute value" is the size shown by a number, whether the number is positive or negative.