Who originated Cartesian coordinates?
Cartesian coordinates are a way of finding the location of a point using distances from
perpendicular axes. (For more information about coordinates, see “Geometry and
Trigonometry.”) The first steps toward such a coordinate system were suggested by
French philosopher, mathematician, and scientist René Descartes (1596–1650; in 25
HISTORY OF MATHEMATICS
What was the scandal between mathematicians
working on cubic and quartic equations?T
he early work on cubic equations was a tale of telling secrets, all taking place
in Italy. No sooner had Antonio Maria Fiore (1526?–?)—considered a mediocre
mathematician by scholars—received the secret of solving the cubic equation
from Scipione del Ferro than he was spreading the rumor of its solution. A self-
taught Italian mathematical genius known as Niccoló Tartaglia (1500–1557?;
nicknamed “the stutterer”) was already discovering how to solve many kinds of
cubic equations. Not to be outdone, Tartaglia pushed himself to solve the equa-
tion x^3 mx^2 n, bragging about it when he had accomplished the task.Fiore was outraged, which proved to be a fortuitous event for the study of
cubic (and eventually quartic) equations. Demanding a public contest between
himself and Tartaglia, the mathematicians were to give each other 30 problems
with 40 to 50 days in which to solve them. Each problem solved earned a small
prize, but the winner would be the one to solve the most problems. In the space
of two hours, Tartaglia solved all Fiore’s problems, all of which were based on
x^3 mx^2 n. Eight days before the end of the contest, Tartaglia had found the
general method for solving all types of cubic equations, while Fiore had solved
none of Tartaglia’s problems.But the story does not end there. Around 1539, Italian physician and mathe-
matician Girolamo Cardano (1501–1576; known in English as Jerome Cardan)
stepped into the picture. Impressed with Tartaglia’s abilities, Cardano asked him
to visit. He also convinced Tartaglia to divulge his secret solution of the cubic
equation, with Cardano promising not to tell until Tartaglia published his results.Apparently, keeping secrets was not a common practice in Italy at this time,
and Cardano beat Tartaglia to publication. Cardano eventually encouraged his
student Luigi (Ludovico) Ferrari (1522–?) to work on solving the quartic equa-
tion, or the general polynomial equation of the fourth degree. Ferrari did just
that, and in 1545 Cardano published his Latin treatise on algebra, Ars Magna
(The Great Art), which included a combination of Tartaglia’s and Ferrari’s works
in cubic and quartic equations.