क्यों हज़ारो सालो तक algebra से डरते रहे mathematician | fear of symbol | era of Muslim mathematician
Algebra has been part of mathematics since records began nearly 4,000 years ago, but not always in the symbolic form we learn today. In fact, for most of those four millennia it was written entirely in words and numerals — although works such as Euclid’s famous 300 B.C.E. textbook "Elements" also included geometric diagrams, to help prove such things as Pythagoras's theorem, and to show how to expand squares that we would write today as (a+b)^2. So "algebra" was communicated in cumbersome word problems or increasingly complicated diagrams — although geometry did have its advantages. For instance, it's the easiest way to prove Pythagoras's theorem. In figure 1.1, I've given an algebraic adaptation of such a proof, although the ancients simply rearranged the diagram to show visually that the shaded area is equal to the sum of the areas of the squares on the adjacent sides of the triangle — a pretty clever approach!
It took a long time for algebra to emerge from arithmetic and geometry as a separate subject. It didn't even get its name until medieval times, and that was thanks to the ninth-century Persian mathematician Muhammed ibn-Mūsā (al-)Khwārizmī… He studied at Caliph al-Ma’mūn’s pioneering Baghdad-based university, or "House of Wisdom," when the great Arabic translation movement was at its height: Greek, Indian, and other ancient manuscripts were being collected from all corners of the burgeoning Islamic empire and translated into Arabic.
Imperialism is rarely ethical and often violent, but it can ultimately lead to cultural cross-fertilization, and in this case the visionary translation movement was so important that by the 12th century, Europeans were learning Arabic in order to translate these manuscripts into Latin — including Ptolemy’s "Almagest" and Euclid’s "Elements," along with new Arabic works such as those of al-Khwārizmī. The name "algebra” famously comes from the first word in the title of his book "Al-Jabr wa’l muqābalah" — which means something like "The Compendious Book on Calculation by Completion and Balancing."
Judging from the problems al-Khwārizmī included, an example of what he meant by "Completion" is "completing the square," the method you might have learned in school to solve quadratic equations...
Al-Khwārizmī didn't write equations in the symbolic form we use today, either. In fact, to modern eyes his book is more arithmetical than algebraic, and one of its important impacts in Europe, when it was translated into Latin, was the popularization of the Hindu-Arabic decimal system of numeration that eventually evolved into our modern one.
Yet Al-Khwārizmī is often called the "father of algebra." He may have used words rather than symbols, and the problems he included may have been simple — his purpose, he tells us, was to teach students how to solve basic problems in "cases of inheritance, legacies, partitions, lawsuits and trade, and in all their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other objects of various sorts and kinds are concerned."
But he systematically set out word-form linear and quadratic equations, with algorithmic methods for solving them — that is, for finding the "unknown numbers," our modern x's and y's. In fact, the English word "algorithm” — meaning a set of rules for performing a calculation or other operation — comes from "algorismi,” an early Latinized attempt at Al-Khwārizmī.
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क्यों हज़ारो सालो तक algebra से डरते रहे mathematician | fear of symbol | era of Muslim mathematician
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