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Fermat’s Last Theorem: Solving the World’s Most Difficult Math Problem

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Notes scribbled into the margin of an ancient mathematical text would eventually be known by the math community as Fermat’s Last Theorem, one of the most famous problems in the history of mathematics. The seemingly simple, but terribly complex math statement has captured the minds and imaginations of some of the greatest mathematicians of our day, but may have been lost forever if it weren’t for its compelling nature and the mystery surrounding its author.

17th century mathematician, Pierre de Fermat, is often considered to be the father of modern calculus, with other notable contributions to analytic geometry and probability. Aside from his list of accomplishments, Fermat is arguably most remembered for the mathematical notes he scribbled in Latin into the margin of his copy of Arithmetica by Greek mathematician, Diophantus.

The full text of Fermat’s statement has been translated to: “It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”

Perhaps the greatest draw to Fermat’s Last Theorem is that the proof he claimed to have was never found among his documents. His notes regarding the theorem were published posthumously by his son thirty years after his death, which sent out a public challenge to mathematicians worldwide to solve what Guinness Book of World Records named “most difficult mathematical problem.”

In summary, Fermat’s Last Theorem states that no three positive integers satisfy the equation an + bn = cn  for any integer value of n greater than two.

The problem stood for 358 years, even leading Dr. Paul Wolfskehl, of Darmstadt to famously bequeath 100,000 German marks (equivalent to $1 million today) for proof of Fermat’s theorem in his will.

It wasn’t until a mathematician obsessed with solving Fermat’s theorem, that the world’s hardest math problem finally met its match.

Andrew Wiles first met Fermat at age ten and made it his life’s work of proving his theorem. In June of 1993, Wiles presented his proof to the public at a conference at Cambridge, but it was later discovered that his proof contained a flaw in one area.

Wiles' Proof of Fermat's Last Theorem As with all math problems, mistakes happen, but Wiles did not let that deter him and the brilliant mathematician tried and failed for over a year to repair his proof. According to Wiles, he finally fixed the problem with help from his former student, Richard Taylor, while on the verge of giving up.

For his efforts, Wiles has received numerous math awards and worldwide recognition, including the Abel Prize,  Wolfskehl’s Prize, and was knighted by the British Empire in 1999.

The story of Fermat’s Last Theorem is a lesson to math students everywhere. Never give up, even when trying to answer the hardest math problem in the world!

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Homer's Last Theorem

In an episode of The Simpsons titled, “The Wizard of Evergreen Terrace,” Homer appeared to solve Fermat’s Last Theorem, which sent the mathematics world into a frenzy. Upon first glance, it looks like Homer’s answer is correct, but the numbers only add up while using a simple calculator. The math prank was to pay homage to Pierre de Fermat and Andrew Wiles and sneak some mathematics into another episode, something the show does quite often actually.

Since its debut in 1989, The Simpsons has frequently paid homage to the many wonders of the mathematical world from the often unnoticed “freeze-frame gags” such chalkboard scribbles to almost entire episodes devoted to math. Not surprisingly, many of the writers and producers of The Simpsons are also mathematical heavyweights, including several PhDs and ivy league graduates with extensive math backgrounds.

The regularity of math references throughout the show’s long history has been an ongoing topic of discussion within the math community and is the subject of a recent book by popular science author and mathematician, Simon Singh, titled, “The Simpsons and Their Mathematical Secrets,” which Singh goes into extensive detail on Homer’s Last Theorem and many others.

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