


Complex numbers, initially termed "imaginary," were not conceived as we study them today. Above all, they were introduced as tools for solving polynomial equations—and tackling the mathematical challenges that raged across Renaissance Europe.




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Until the end of the 18th century, algebra was essentially about solving algebraic equations. That chapter in the history of algebra closed with the work of Abel and Galois. Before them, what questions occupied mathematicians? What problems could they hope to solve?

The standard identities studied in middle school (and now at the start of high school…) can prove very useful in finding the solutions to certain equations, including quadratics. The trick is knowing where these mysterious identities are hiding!

Following his work on solving fourth-degree equations, Lagrange turned to the fifth-degree case. It was not until Abel that these equations were shown not to be solvable by radicals. Galois would provide a necessary and sufficient condition for an equation of any degree to be so solvable. In doing so, he founded group theory.

Arithmetic and geometry, the two traditional branches of elementary mathematics, come together in nomograms. But what exactly does this term, evidently derived from Greek, mean? What are nomograms used for, and how are they designed?
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