New Books In Mathematics

From 1667 to 1676, a pivotal controversy played out among several mathematical luminaries of the time, partly in the proceedings of the Royal Society but partly in private correspondence. The controversy concerned whether an infamous problem of Ancient Greek geometry, the quadrature of the central conic sections (better known as squaring the circle), could be solved using the classical tools of straightedge and compass. While its impossibility would not be rigorously proven for two more centuries, the theoretical and philosophical implications of these attempts to settle the issue were constitutive of the contemporaneous development of calculus. Dr. Davide Crippa's book The Impossibility of Squaring the Circle in the 17th Century (Birkhäuser, 2019) is a deep dive into this little-covered episode in the modern European history of mathematics. He examines the advances of Gregory and Leibniz in full mathematical detail, clarifying in current notation and elegant figures the steps and missteps of their constructi