1. When was Algebra invented?

    2. The first algebra problems were word problems and there were no general procedures for solving them. Around 250 CE a Greek, Diophantus, showed the importance of defining one unknown quantity in terms of other unknowns. About 600 years later, a Persian mathematician, Al-Khwarizmi, described procedures for solving a problem by simplifying it until the answer was self evident.

    In the early days, algebra problems and their solutions were expressed in ordinary language. In Europe, people did their calculations using Roman numerals and the abacus well in to the 13th Century. Many of the notations, procedures, and tools we use in algebra today were first developed in Europe during the 17th and 18th Centuries.

  2. Was algebra invented all at once or in stages?

    Modern algebra was not invented all at once. Modern algebra is a synthesis of inventions in notation, procedure, tools, and theory that accumulated over a 1500 year period, beginning in 250 CE or earlier.

    The notations used in algebra–such as variables, the equals sign, the negative sign, exponents, fractions, function notation, coordinate planes, graphs, equations, and matricies–were all invented by specific people known to history. Much of this notation was invented in the 17th and 18th Centuries as mathematicians tried to make their ideas clear to each other and to their students.

  3. Was Algebra invented for its beauty or to help people solve practical problems?

    Many of the best mathematicians wanted to put algebra and other mathematics into the hands or ordinary people. These mathematicians understood that the economy required workers who could perform mathematical tasks without having first engaged in a deep and careful study of mathematics. Even today, students’ introduction to algebra emphasizes notation and procedures and makes unembarrassed use of calculation aids such as tables, slide rules, and calculators.

    The insight that equations could be graphed on a coordinate plane, due ot the 17th Century mathematician Pierre de Fermat, gave scientists and engineers a powerful tool for understanding a wide range of physical phenomena. As evidenced by the publication of many textbooks on Algebra during the early days of the Industrial Revolution, algebra was being used as a language for communicating and applying newly discovered physical principles to a vast range of inventions.

  4. What is the connection between Algebra and Geometry?

    In the 17th and 18th Centuries, many mathematicians, including Descartes, thought Algebra was ugly compare to Geometry. They did not think an Algebra problem was properly solved until it could be represented and solved using Geometry. Descartes, for example, described in great detail who quadratic equations could be solved using geometric figures constructed with ruler and compass. In time, Algebra came to be understood as a field of mathematics which was as important and as rigorous as geometry. Now, in an introduction to geometry course, students are taught to use algebra as an important tool to help in the understanding of geometric ideas.

  5. Is it cheating to use tools such as calculators to solve Algebra problems?

    6. Many of the advances in algebra have been the result of the best mathematicians creating notations, procedures, and tools that would make it possible for people to perform mathematical tasks as part of their work even though they did not have a deep understanding of why the math they are using works.

    Algebraic equations have been an important way of expressing scientific and engineering principles that workers need to apply when designing and building the machines, structures, and industrial processes needed by our civilization. It is important that many people can do the calculations required to apply those equations. So no, it is not cheating to use tools such as calculators. The timeline featured on this website lists over fifteen hundred years of work done with the intent of putting powerful mathematics in the hands of ordinary people who need to use it to get things done.

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