diamonds, but not forestall tragedy. Her firstborn son died at age nine in
a car crash, her daughter committed suicide when she was twenty-five,
and her husband was declared insane and lived out his life in a mental
institution.
The Hope left a swath of misfortune in its wake—but this pales in com-
parison to the sufferings of the major players in the search for the solu-
tion to polynomial equations of ever-higher degree.
A Mathematician’s Job Interview
Mathematics students are told of the mathematician who applied for a job
with a corporation. When asked what he could do, the mathematician re-
plied that he solved problems. The interviewer took him to a room in which
a fire was blazing. There was a table on which rested a bucket of water, and
the mathematician was instructed to put out the fire. The mathematician
grabbed the bucket, dumped water on the fire, and extinguished it. He
then turned to the interviewer and asked, “Do I get the job?”
“You’ll have to take the advanced test,” replied the interviewer. The
mathematician was taken to another room in which a fire was blazing.
There was a table, under which rested a bucket of water, and the mathe-
matician was instructed to put out the fire. The mathematician grabbed
the bucket—and placed it on top of the table. Why on Earth, students
want to know, would he do that? Because mathematicians like to reduce a
new problem to one they’ve previously solved.
Progress in mathematics is often cumulative, with previous results
being used to derive ever deeper and more complex results. Such is the
story of the search for the solutions of polynomial equations, such as
ax^3 bx^2 cxd0, which is the general polynomial equation of degree 3.
Polynomials are the only functions that we can calculate,^2 because they
involve only addition, subtraction, multiplication, and division. With rare
exceptions, when we calculate a value such as a logarithm or the sine of an
angle (for example, by using a calculator), the logarithm or sine is approxi-
mated by a polynomial, and it is this approximate value that is calculated.
Early Results: Solutions of Linear and Quadratic Equations
The story of the search for the solution to polynomial equations starts
tamely enough in ancient Egypt, whose mathematicians were sufficiently
adept to solve linear equations. An example of one such is the equation
7 xx19, which nowadays is comfortably solved by sixth-graders, who
would add the terms on the left to obtain 8x19, and then divide both
82 How Math Explains the World