Algebra is better known as the most jaded subject in our curriculum. The subject usually represents mathematical ideas and techniques involving symbols rather than numbers. It began with finding the solutions of an equation. Algebra has a beauty in its own strange and abstract way. The most fascinating thing is that the language of algebra has mottled significantly across the history of all civilizations. In the initial stages after its apparent day of birth, it evolved with the idea of theory of equations. In fact the word "algebra" originated from the Arabic word al-jabr, which initiated from the treatise, written in the year 830, by a medieval Persian mathematician, Muhammad ibn Musa al-Khwarizmi. The treatise provided systematic solution of linear and quadratic equations. Algebraic expressions appeared in three different stages starting from Rhetorical algebra (where equations were written in full sentences) to Syncopated algebra and finally to Symbolic algebra. Since its inception this branch of mathematics has bristled in its ways with several stages of development, from geometric stage, Static equation-solving stage, Dynamic function stage and finally Abstract stage. Several noteworthy observations were made by Babylonians, Egyptians, Greek, Chinese, Indian and Persian mathematicians to cultivate Algebra in their own approach. I feel sometimes, how enriched is the flavor of mathematics, starting its journey centuries behind mathematics has evolved each day. As Einstein had once insisted, that mathematics is “a product of human thought that is independent of experience”. Being an abstract discipline algebra has always elucidated the natural world in its own powerful way. The Babylonian system of Mathematics had used sexagecimal (base 60) number system which in modern days gives us the origin of 60 seconds per minute, 60 minutes per hour or, 360 degrees in a circle. Babylonian algebra has traces of use of quadratic and cubic equations and is believed to be more progressive than Egyptian algebra, who dealt with only linear equations. In contrast to them, Greeks were not considered to be Algebraists. This conclusion is totally mistaken since Greeks created a branch called geometric algebra. This is yet another innovation where the algebraic terms were exemplified by sides of geometric entities. For example, lines had letters allied with them. Greeks found a new course in the path of algebra where to find solutions of equations they used ‘application of areas’. Algebra thus has its roots in the period of Plato, Euclid and Pythagoras. We have a very petite knowledge about life of a Greek mathematician named Thymaridas, although he had unparalleled contributions to Algebra. He was a Pythagorean and a number theorist. He had named a prime number rectilinear as it had a one-dimensional representation only, whereas non-primes such as 12 turn out to be rectangles of sides 4 and 3 using geometric algebra. He also had observed ‘one’ as a 'limiting quantity' or a 'limit of fewness'. "Bloom of Thymaridas" or, "flower of Thymaridas", is a notable rule perceived by Thymaridas which states that: “If the sum of n quantities be given, and also the sum of every pair containing a particular quantity, then this particular quantity is equal to 1/(n - 2) of the difference between the sums of these pairs and the first given sum.” The reason of sharing these lesser known facts is to make everyone reading this discover the diverse topographies of algebra, which has contributions from different civilizations and different cultures.
Article by:
Dr. Rituparna Ghosh
Assistant Professor,
Department of Mathematics,
Heritage Institute of Technology, Kolkata.
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