lot to root for back in the sixteenth century). Ferrari, naturally, felt that his
own brilliance was responsible for his victory. At this point, the story of
the search for a solution by radicals to polynomial equations pauses for
two centuries, awaiting the arrival of the final characters in this drama.
The travails suffered by many of the major characters in this drama are
the stuff of which miniseries are made. Cardano’s wife died young, his
elder son Giambattista was executed for murder, and his other son was
imprisoned for criminal activities. Cardano himself was thrown in jail for
heresy (not a good era in which to be a heretic), but he was later pardoned.
Cardano’s epitaph might well be the last line of his Ars Magna: “Written
in five years, it may last thousands.”^8 Ludovico Ferrari died from poison,
which many historians believe was administered by his sister.
The Insolubility of the Quintic
The general cubic had been solved by reducing it to a depressed cubic, and
the quartic had been solved by reducing it to a cubic—but the solutions to
each polynomial of higher degree were becoming ever more involved and
complicated. It appeared that the future of solving the general quintic—
the polynomial of degree five—was going to follow the same path: find the
transformation that reduced it to a quartic, and then use Ferrari’s formula.
This seemed a rather dreary prospect. Perhaps that’s why more than two
centuries passed, and though mathematics made considerable advances,
most were in calculus and related areas. Trying to find the general solu-
tion to the quintic was no longer a top priority of the mathematical com-
munity— calculus was newer and a whole lot sexier.
As sometimes happens in both mathematics and science, the tools avail-
able to the community are simply inadequate for solving certain prob-
lems, and the mathematical or scientific community hits the wall. New
and different techniques are required—although often the community
simply doesn’t realize it until those techniques actually make an appear-
ance. Such was the case with the solution of the quintic. The resolution of
this problem did not occur until the turn of the nineteenth century, when
three brilliant mathematicians broke new ground with a totally different
approach, one which was to forever alter the direction of mathematics.
Paolo Ruffini
For nearly 250 years after Cardano and Ferrari had solved the quartic,
mathematicians had tried to crack the mystery of the quintic. Some of
the great names of mathematics foundered on the shoals of this problem,The Hope Diamond of Mathematics 89