Latin, Renatus Cartesius); he was the first to publish a work explaining how to use
coordinates for finding points in space. Around the same time, Pierre de Fermat devel-
oped the same idea independently (see below). Both Descartes’s and Fermat’s ideas
would lead to what is now known as Cartesian coordinates.
Descartes is also considered by some to be the founder of analytical geometry. He
contributed to the ideas involved in negative roots and exponent notation, explained
the phenomenon of rainbows and the formation of clouds, and even dabbled in psy-
chology.Who was Pierre de Fermat?
French mathematician Pierre de Fermat (1601–1665) made many contributions to
early methods leading to differential calculus; he was also considered by some to be
the founder of modern number theory (see “Math Basics”) and did much to establish
coordinate geometry, eventually leading to Cartesian coordinates. He supposedly
proved a theorem eventually called “Fermat’s Last Theorem.” It states that the equa-
tion xnynznhas no non-zero integer solutions for x, y,and zwhen nis greater
than 2. But there is no proof of Fermat’s “proof,” making most mathematicians skepti-
cal about his supposed discovery.Was Fermat’s last theoremfinally solved?
Just before the end of the 19th century, German industrialist and amateur mathemati-
cian Paul Wolfskehl, on the brink of suicide, began to explore a book on Fermat’s Last
Theorem. Enchanted with the numbers, he forgot about dying and instead believed
that mathematics had saved him. To repay such a debt, he left 100,000 marks (about
$2 million in today’s money) to the Göttingen Academy of Science as a prize to anyone
who could publish the complete proof of Fermat’s Last Theorem. Announced in 1906
after Wolfskehl’s death, thousands of incorrect proofs were turned in, but no true
proof was offered.
But people kept trying—and failing. Fermat’s Last Theorem was finally solved in
1994 by English mathematician Andrew John Wiles (1953–). Wiles was offered the
Wolfskehl prize in 1997. By that time, the original $2 million had been affected by not
only hyperinflation but also the devaluation of the mark, reducing its value to
$50,000. But for Wiles, it didn’t matter; his proving the Last Theorem had been a
childhood dream.
It is interesting to note that some mathematicians do not believe Wiles uncovered
the true proof of Fermat’s Last Theorem. Instead, because many of the mathematical
techniques used by Wiles were developed within recent decades (some even by Wiles
himself), Wiles’s proof—although a masterpiece of mathematics—could not possibly
be the same as Fermat’s. Still other mathematicians wonder about Fermat’s words in
26 claiming that he had found a proof. Was it really a proven or flawed proof he was talk-