Running Head: PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST
THEOREM
Pierre de Fermat and The Worlds Battle Against His Last Theorem
Mayra Verde
El Paso Community College
Author Note
This paper was prepared for Pre-Calculus Math 1314, Honors Program
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
Pierre De Fermat and the Worlds Battle Against His Last Theorem
Mathematics has a reputation for being boring, lacking passion, romance, drama, and
mystery. Nobody wants to hear or read a story about the majority of people’s worst subject. Yet,
here is a story of great mystery, passion, rivalry, love, suicide attempts, and even cross dressing.
In fact, this story is so interesting even the Simpsons took interest. They saw what every other
mathematician saw in this story; this great mystery which took over 350 years, several attempts by
some of the greatest minds, including Homer Simpson, and finally the love and passion of a man
to finally solve it. Fermat’s Last Theorem perplexed everyone for centuries, and the man behind it
was such a mischievous mathematician that even after death he continued to tantalize the world
with one of the greatest math problems. Pierre Fermat’s story and the one that follows after his
death resemble a fairy tale that includes a little bit of everything from drama and love to that of a
dream come true.
This story begins in the 1600’s; August 17, 1601 to be exact, in the mathematical land of
France. Now, Pierre wasn’t poor, he didn’t live in a shoe, and although he did have 3 siblings,
none of them enslaved him or tore his outfit before the great ball. He was just the son of a wealthy
Frenchman. Although little is known of his early childhood or where he went to school, everyone
can probably imagine that a man this smart and mischievous probably spent his childhood days
doing just that until it was time to head to college, where he would make great mathematical
discoveries and earn a law degree (O’Conner & Robertson, 1996).
It is hard to believe that a man with only a law degree would eventually become one of the
greatest mathematicians of all time. But Fermat was no ordinary man; he was well versed in
different languages to include Latin and Greek. The knowledge of these languages would greatly
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
assist Fermat in his love for restoring ancient texts. While attending the University in Bordeaux he
restored a copy of Apollonius’s Plane loci (O’Conner & Robertson, 1996). Perhaps inspired by
Apollonius work he develops important advances in maxima and minima of functions (O’Conner
& Robertson, 1996). After Bordeaux Fermat moved to Orleans where he earned his degree in law,
he practices until he becomes a judge, eventually joining parliament. Due to strict conduct
restrictions, Fermat kept to himself and instead of partying, he would solve math problems as a
hobby after work.
While in school, Fermat made friends with several mathematicians, whom he would
correspond with over the years. Fermat was a genius and enjoyed corresponding with his peers by
sending them math problems he had solved and asking them to solve them. Many couldn’t, not
with the mathematical techniques of their time, and so they would ask him to explain his methods.
Most of the time he didn’t divulge his methods; however, when he would, his techniques were not
understood and were seen just as another effort to tease them. During this time his reputation grows
as a mathematician. Including his teasing math problems with no explanations that frustrate the
mathematical community so much that great philosopher “Rene Descartes calls Fermat ‘a
braggart’ and the English mathematician John Wallis calls him ‘that damned Frenchman”
(O’Conner & Robertson, 1996).
By the 1630’s Fermat’s reputation had grown. Mathematicians would send him papers to
review and it is because of this that he becomes involved in a serious mathematical dispute with
Descartes. Both had independently and through different methods developed analytical geometry,
but their dispute was over refraction and their theories on it. In 1637, Fermat submerged in
correspondence with other mathematicians, ignores a copy of Descartes’ work that was sent to him
by Beaugrand (O’Conner & Robertson, 1996). He is asked again to give an opinion on La
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
Dioptrique, and he does, “describing it as groping about in the shadows.” (O’Conner & Robertson,
1996). His opinion and later his reasoning infuriate Descartes, and thus their great battle over
refraction begins. They correspond back and forth, bring in other mathematicians to side with, and
eventually a mediator to name the winner. It was like The Thrill in Manila of the 17th century,
Muhammad Ali as Fermat and Joe Frazier as Descartes. In case you don’t know who won that
fight, there is a reason why there is a mall in Manila called the Ali Mall. Unfortunately, Descartes
proves to be a sore loser and writes a letter to Marsenne, saying not true, he wasn’t wrong, he
didn’t get his butt kicked, and “Fermat is inadequate as a mathematician and a thinker.” (O’Conner
& Robertson, 1996). Descartes was well respected and his word versus that of Fermat proved more
powerful; thus, he accomplishes in tainting Fermat’s reputation.
In the second half of his life, Pierre de Fermat for various reasons, isolates himself, and
studies Number Theory where he focuses on the relationship between whole numbers, their
patterns, and how they relate to each other (O’Conner & Robertson, 1996). Although we can
actually thank Fermat and not Newton, for the endless years of Calculus we have to take, or for
being able to calculate our chances at winning the lottery, we don’t really see or use Number
Theory. Yet, his last theorem perplexed us for centuries, so why or how did his last theorem
become so famous, if we don’t apply it anywhere? First, let’s look at his last theorem to better
understand why it was so demanding. Everyone knows Pythagoras Theorem, which states that
𝑎2 + 𝑏 2 = 𝑐 2 all the time. Fermat noticed that if you change the power to other positive numbers
greater than two, there exist no solution in the equation 𝑎𝑛 + 𝑏 𝑛 ≠ 𝑐 𝑛 . When he solved this
problem, he wrote “I have discovered a truly remarkable proof which this margin is too small to
contain” in his book Diophantus's Arithmetic, yet there was no proof anywhere (O’Conner &
Robertson, 1996). How is it then that it was so difficult to prove that 𝑎𝑛 + 𝑏 𝑛 ≠ 𝑐 𝑛 ? Isn’t is
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
enough to plug in a few numbers and that’s it ? Not really, mathematicians have to have absolutely,
undeniably, error proof evidence that is always true for any number you plug in. In an equation
with an infinite number of values, how do you prove that one number in that infinite could make
the equation false.
Many of his theories were not known until after his death in 1665, when his son published
his father’s book Diophantus's Arithmetic with his notes in the margins in 1671 (O’Conner &
Robertson, 1996). The book contained many theories but no proof was provided, just his claim
that he could prove it. Because of his lack of proof, the mathematical community rushed to try and
prove all his theories, and as they did, many more advances and discoveries were made in
mathematics. Every single one of his theories were proven, except for one which became known
as Fermat’s Last Theorem.
Hence the quest began to find the proof. Many were intrigued and in love with it. Sophie
Germain was a French mathematician, who unfortunately was born a woman. In France, in the
18th century, all you could do as a woman was sit there and look pretty. Yet she was one of the
greatest minds that France ever produced. She was such a brilliant mathematician that she was one
of the few to have developed theories as to how to solve Fermat’s Last Theorem, but because she
was a woman she had to do it in disguise. Sophie was so in love with math, especially Fermat’s
Last Theorem, that she assumed the identity of a man, Monsieur Le Blanc, dressed as him to attend
school and be able to practice math.
Then, there is the passionate but depressed man, Paul Wolfskehl, who, story has it, planned
to commit suicide as a result of a heartbreak, but was saved by Fermat’s Last Theorem. While
waiting on the hour he had set to commit suicide, he decided to take a look at Fermat’s Last
Theorem; hours went by and before he knew it, the time had passed (Barner, 1997). Renewed by
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
a sense of purpose to prove it, he decided to not commit suicide. Later, he would set up a fund, a
prize, for whomever could prove Fermat’s Last Theorem (Barner, 1997).
Simon Singh (2013), introduces us to how Homer Simpson took a swing at Fermat’s Last
Theorem during the episode “The Wizard of Green Terrace”. In this episode he decides to become
a scientist and Homer disproves Fermat’s Theorem with the equation 398712 + 436512 =
447212 . What’s baffling is that if you plug the numbers into a calculator, it’s actually true, but
Fermat says this is impossible. If some of the greatest mathematical minds attempted to prove it,
but none succeeded, how did Homer Simpson do it? The truth is he didn’t. In a 10 digit calculator
it is true, but if you were to plug into a calculator with the capacity for more digits, then it would
show that after 10 digits it becomes false; thus, Fermat’s Last Theorem fights back.
When Princeton professor Andrew Wiles was 10 years old, he came across the theorem,
intrigued and puzzled like everyone else before him, attempted to solve it but like everyone else
failed (Singh, 2013). It became his passion, love, and dream to prove Fermat’s Last Theorem. For
years he didn’t make any advances to solving it. That is until 1994, after 7 years of isolation,
working in secret, he finally proves it. His lifelong dream finally comes true. Simon Singh (2013)
tells us that “there is a saying in mathematics; that a problem worthy of attack, proves its worth by
fighting back”. Fermat’s Last Theorem fought back like Joe Frazier on that legendary match; it
fought back for over 300 years until it met its match with Andrew Wiles.
PIERRE DE FERMAT AND THE WORLDS BATTLE AGAINST HIS LAST THEOREM
References
Barner, K. (1997, November 1). Paul Wolfskehl and the Wolfskehl Prize. Retrieved November
11, 2014, from http://www.ams.org/notices/199710/barner.pdf
O'Conner, J., & Robertson, E. (1996, December 1). Biographies: Pierre de Fermat. Retrieved
November 2, 2014, from http://www-history.mcs.standrews.ac.uk/Biographies/Fermat.html
Singh, S. (2013, September 24). Fermat's Last Theorem - Numberphile [Video file]. Retrieved
from http://www.youtube.com/watch?v=qiNcEguuFSA
Singh, S. (2013, September 29). Homer Simpson vs Pierre de Fermat - Numberphile [Video
file]. Retrieved from http://www.youtube.com/watch?v=ReOQ300AcSU
Singh, S. (1997, October 26). Math's Hidden Woman. Retrieved November 5, 2014, from
http://www.pbs.org/wgbh/nova/physics/sophie-germain.html
Singh, S. (n.d.). Who was Fermat? Retrieved November 2, 2014, from
http://simonsingh.net/books/fermats-last-theorem/who-was-fermat/