David S. Richeson's book Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019) is the fascinating story of the 2000 year quest to solve four of the most perplexing problems of antiquity: squaring the circle, duplicating the cube, trisecting the angle, and constructing regular polygons. The eventual conclusion was that all four of these problems could not be solved under the conditions laid out millennia ago. But it's also an engaging tale of some of the greatest mathematicians, and some not-so-well known ones, who met the challenge and moved mathematics forward in ways that the Greek geometers could never have envisioned. Even if you never read a single proof through to its conclusion, you'll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school.
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David S. Richeson, "Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity" (Princeton UP, 2019) | New Books in Mathematics podcast - Listen or read transcript on Metacast
