Part IV — Chapter 10
Cardano & Renaissance Algebra
The dramatic race to solve the cubic — secrets, betrayals, and breakthroughs
10.1 The Cubic Problem
Scipione del Ferro secretly discovered a method for solving depressed cubics around 1515. When Tartaglia independently found the solution, a public mathematical contest ensued. Gerolamo Cardano (1501–1576) then published the cubic formula in his landmark Ars Magna (1545), along with Ferrari's solution to the quartic equation.
10.2 Complex Numbers Emerge
Cardano's formula sometimes required taking square roots of negative numbers. Rafael Bombelli (1526–1572) boldly developed rules for manipulating these “impossible” quantities, laying the groundwork for complex numbers — the first appearance of numbers that seemed meaningless yet produced correct results.