## Taming the Unknown: |

What is algebra? For some, it is an abstract language of x’s and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era.
" "This original and high-quality book is a significant contribution to the history of mathematics. It will be useful to scholars doing research in the history of mathematics, as well as to a broader readership that includes mathematics teachers, advanced undergraduate or graduate students, and mathematicians." "This fine survey of the history of algebra is clearly and engagingly written. It will become the standard reference on this topic by virtue of its scholarship, coverage, and readability."
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