Princeton Science Library: An Imaginary Tale

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Complex numbers, particularly the square root of minus one (i), have a rich history filled with adventure and intrigue. In this exploration, the author delves into the 2000-year journey of this elusive number, recounting the mathematical challenges that led to its discovery and the colorful figures who sought to understand it. The tale begins in 1878 when two brothers unearthed a mathematical papyrus in the Valley of Kings, revealing the earliest known instance of a negative square root. This document contained a specific example of calculating the volume of a truncated square pyramid, hinting at the necessity of i. Earlier, in the first century, Heron of Alexandria encountered i but mismanaged the calculations. Medieval mathematicians, grappling with negative numbers, dismissed their square roots as nonsense. By Descartes' time, the concept of "imaginary numbers" began to gain theoretical traction, sparking intense debates. Ultimately, i found acceptance and application in complex analysis and theoretical physics during the Napoleonic era. The narrative is rich with historical anecdotes and mathematical insights, illustrating the significance of complex numbers in solving key problems, such as Kepler's laws of planetary motion and AC electrical circuits, making it a captivating read for both general and scholarly audiences.