From Cardano’s great art to Lagrange’s reflections: filling a gap in the history of algebra | Reviews

Review in Ann. Sci.“This must be the first book describing exactly, in detail and nearly completely, the development of algebra in this period in more than two centuries. I learned much, especially many details and illuminating connections. The book is a must-read for researchers interested in the history of mathematics and for mathematicians dealing with algebra.” — Ulrich Reich (Bretten)
Review in Bull. Lond. Math. Soc.“The aim of the book is not to examine this slow and halting progress with the hindsight of modern understanding, but rather to try to get into the minds of the mathematicians of the sixteenth to the eighteenth centuries and try to look at the progress they made using the tools and notation then available. This is an ambitious, yet very valuable, approach. It is ambitious because the reader has to throw away the way they think about mathematics and try to appreciate a very different style of mathematical thought. It is valuable because this approach, more than any other, leads to a deeper understanding of how mathematics develops.” — Edmund F. Robertson (St. Andrews)
Review in MAA Reviews“The gap in Stedall’s title is [...] the period between the solution of the cubic and quartic equations (the time of Cardano, in the middle of the 16th century) and the first work to make a serious contribution to understanding why the quintic was resisting solution (Lagrange’s Reflections, late in the 18th century). Stedall shows us what was going on in between, paying attention in particular to the themes that led to Lagrange’s ideas.” — Fernando Q. Gouvêa (Waterville, ME)
Review in Math. Semesterber. (in German)
Review in MathSciNet“This 200-page book covers over 200 years of mathematicians seeking solutions to algebraic equations. It begins with Cardano and ends after Lagrange. Included are the following: (I) From Cardano to Newton: 1545 to 1707; (1) From Cardano to Viète; (2) From Viète to Descartes; (3) From Descartes to Newton. (II) From Newton to Lagrange: 1707 to 1771; (4) Discerning the nature of roots; (5) Roots as sums of radicals; (6) Functions of the roots; (7) Elimination; (8) The degree of a resolvent; (9) Numerical solution; (10) The insights of Lagrange; (11) The outsiders. (III) After Lagrange; (12) Dissemination and new directions. This is a difficult book. Stedall’s explanations of newly discovered solutions to equations are quite terse and beginners can get lost. The reader should bring some knowledge of history before studying the book. However, Professor Stedall writes with a sense of humor, so the book is not boring.” — Donald Cook
Review in zbMATH“The pivots of [Stedall’s] argument are four figures who, each in his own moment of history, rounded off and completed what had been done until then and at the same time opened the field for new development: Cardano himself, Viète, Newton, and Lagrange. Between these, the contributions of a large numbers of other contributors to the understanding of algebra and equation theory are discussed, some major (including Harriot, Descartes, Leibniz, Euler and Bézout) and many minor but still significant in one way or the other. Stedall challenges (p. ix) ‘the view that mathematics somehow progresses only by means of ‘great and significant works’ and “substantial changes”’ – a view that she takes to explain that not only general histories of mathematics but also works explicitly dealing with the history of algebra tend to jump directly from Descartes to Lagrange.” — Jens Høyrup (Roskilde)