How Math Explains the World.pdf

table to the top of the table—these equations reduce to a quadratic! Solv-
ing 3stC for t in terms of s yields tC/3s, and substituting this into
t^3
s^3 D results in the equation

C^3 /(27s^3 )
s^3 D

Multiplying through by s^3 and collecting all the terms on one side gives

s^6 Ds^3 
(C^3 /27) 0

This equation is quadratic in s^3 , for it can be written

(s^3 )^2 Ds^3 
(C^3 /27) 0

Using the quadratic formula, we obtain two possible solutions for s^3 , but
if the cube root of either is taken and t computed from the formula
tC/3s, the quantity s
t will be the same and will solve the original de-
pressed cubic.
It doesn’t seem so difficult when it is neatly presented in a textbook, but
when you have only a month and your future is at stake, it’s a lot tougher. In
a desperate race against time, an exhausted (no wonder) Tartaglia managed
to find an ingenious geometrical approach to the problem, which yielded
the solution just before the period allowed for the challenge expired. He
solved all of Fior’s problems, easily winning the contest. Tartaglia mag-
nanimously did not require Fior to pay for losing the bet—in this case, he
had bet thirty sumptuous feasts—but this may have been small consola-
tion for Fior, who faded into obscurity as Tartaglia’s fame increased.

Cardano and Ferrari—Scaling the Summit

One person to learn of Tartaglia’s success was Girolamo Cardano, cer-
tainly one of the most unusual individuals ever to appear on the mathe-
matical scene. Cardano was brilliant but bedeviled—aff licted with a
number of infirmities, including hemorrhoids, ruptures, insomnia, and
impotence. Compounding these physical problems was an assortment of
psychological ones. He had acrophobia, an uncontrollable fear of mad
dogs, and may not have been a masochist, but had formed the habit of
inf licting physical pain upon himself because it was so pleasant when he
stopped. We know all this because Cardano, who would have been a sta-
ple of late-night talk shows had such existed in the sixteenth century,
wrote an extensive autobiography in which no details, no matter how inti-
mate, seem to have been spared.
Cardano was fascinated by Tartaglia’s victory, and wrote several letters
imploring Tartaglia to tell him the secret of his success. Tartaglia re-

86 How Math Explains the World