Simplification is Calculation
My thesis: Algebra was invented in many steps over many centuries, with each step helping people who had not been educated in mathematics perform mathematical tasks as part of their work.
The great Persian mathematician Al-Khwarizmi wrote a book, “The Compendious Book on Calculation by Completion and Balancing” which showed readers a general way of analyzing and solving mathematical problems. In this book Al-Khwarizmi introduced the world to methods for simplifying and solving equations. One of his methods was to force a negative term to become positive by moving it to the other side of the equality. In the cartoon above, the teacher forced the term -4x to become positive by moving it from the left to the right-hand side of the equation. Al-Khwarizmi termed this forcing operation al-ğabr, a word we now mispronounce as algebra.
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