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--> '''Farnsworth''' "Meanwhile, as long as you're dead, be a sport and poke around the afterlife for me. See if you can find Fermat and get him to say whether he was just jerking us around."

to:

--> '''Farnsworth''' '''Farnsworth:''' "Meanwhile, as long as you're dead, be a sport and poke around the afterlife for me. See if you can find Fermat and get him to say whether he was just jerking us around."


** [[AC:Farnsworth:]] [-Meanwhile, as long as you're dead, be a sport and poke around the afterlife for me. See if you can find Fermat and get him to say whether he was just jerking us around.-]

to:

** [[AC:Farnsworth:]] [-Meanwhile, --> '''Farnsworth''' "Meanwhile, as long as you're dead, be a sport and poke around the afterlife for me. See if you can find Fermat and get him to say whether he was just jerking us around.-]
"


** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Here the fallacy is less transparent, but it is still simple to disprove, without need for a super powerful calculator: 3987 and 4365 are multiples of 3, and so so is the result of raising each to the 12th (or any) power, as is their sum. But 4472 is not divisible by 3, so neither is the stated result.[[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]

to:

** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Here the fallacy is less transparent, but it is still simple to disprove, without need for a super powerful calculator: 3987 and 4365 are multiples of 3, and so so is the result of raising each to the 12th (or any) power, as is their sum. But 4472 is not divisible by 3, so neither is the stated result.[[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]


* ''WesternAnimation/TheSimpsons'': The creators have on two occasions inserted apparent counterexamples to Fermat's theorem as a background InJoke:
** In [[Recap/TheSimpsonsS7E6TreehouseOfHorrorVI the Halloween episode which aired in 1995]], a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection it is clear why this cannot hold: raising any integer ''n'' to any power produces a number of the same parity as ''n'', and summing an even number and an odd number gives an odd number, but the number on the right of the equation is clearly even.
** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]

to:

* ''WesternAnimation/TheSimpsons'': The creators have on two occasions inserted apparent counterexamples to Fermat's theorem as a background InJoke:
InJoke. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers:
** In [[Recap/TheSimpsonsS7E6TreehouseOfHorrorVI the Halloween episode which aired in 1995]], a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection it is clear why this cannot hold: raising any integer ''n'' to any power produces a number of the same parity as ''n'', and summing an even number and an odd number gives an odd number, but the number on to the right of the equation equals sign is clearly even.
** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: counterexample: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting Here the fallacy is less transparent, but it is still simple to verify these equations on disprove, without need for a pocket calculator would find that they super powerful calculator: 3987 and 4365 are apparently true, but that multiples of 3, and so so is because pocket calculators are the result of raising each to the 12th (or any) power, as is their sum. But 4472 is not precise enough for such astronomically large numbers.divisible by 3, so neither is the stated result.[[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]


** In ''[[Series/StarTrekDeepSpaceNine Deep Space Nine]]'', Jadzia says that one of Dax's earlier hosts had the most original approach to Fermat's last theorem "since Wiles 300 years ago". This may be an attempted HandWave for the TNG example, by showing that people are still working on the problem in the ''Star Trek'' universe even though it's been solved, perhaps forever trying to find progressively simpler and more elegant ways of proving it, possibly to determine how Fermat might have solved it without the whole fields of mathematics developed later that Wiles's proof relied on. However, in TNG Picard did say "for 800 years people have been trying to solve it", which strongly suggests that there had been no successful attempts at that point.

to:

** In ''[[Series/StarTrekDeepSpaceNine Deep Space Nine]]'', Jadzia says that one of Dax's earlier hosts had the most original approach to Fermat's last theorem "since Wiles 300 years ago". This may be an attempted HandWave for the TNG example, by showing that people are still working on the problem in the ''Star Trek'' universe even though it's been solved, perhaps forever trying to find progressively simpler and more elegant ways of proving it, possibly to determine how Fermat might have solved it without the whole fields branches of mathematics developed later that Wiles's proof relied on. However, in TNG Picard did say "for 800 years people have been trying to solve it", which strongly suggests that there had been no successful attempts at that point.


** In ''Series/StarTrekTheNextGeneration'', Picard spends some time trying to prove Fermat's last theorem. He says he finds it humbling that an 800-year-old problem, first posed by a French mathematician without a computer, still eludes solution. (The episode in question was broadcast [[ScienceMarchesOn five years before Wiles' proof was released]].)
** In ''Series/StarTrekDeepSpaceNine'', Jadzia says that one of Dax's earlier hosts had the most original approach to Fermat's last theorem "since Wiles 300 years ago". This may be an attempted HandWave for the TNG example, by showing that people are still working on the problem in the ''Franchise/StarTrek'' universe even though it's been solved. (Another interpretation might be that the characters are still trying to find a short proof that Fermat might have come up with, without the whole fields of mathematics developed later that the Wiles proof relied on.)

to:

** In ''Series/StarTrekTheNextGeneration'', ''[[Series/StarTrekTheNextGeneration The Next Generation]]'' (TNG), Picard spends some time trying to prove Fermat's last theorem. He says he finds it humbling that an 800-year-old problem, first posed by a lone French mathematician without a computer, still eludes solution. (The episode in question Rather embarrassingly, the episode, which was broadcast at a time when the problem had remained unsolved for over 350 years, would become [[ScienceMarchesOn out of date only five years before Wiles' later when Wiles's proof was released]].)
released]].
** In ''Series/StarTrekDeepSpaceNine'', ''[[Series/StarTrekDeepSpaceNine Deep Space Nine]]'', Jadzia says that one of Dax's earlier hosts had the most original approach to Fermat's last theorem "since Wiles 300 years ago". This may be an attempted HandWave for the TNG example, by showing that people are still working on the problem in the ''Franchise/StarTrek'' ''Star Trek'' universe even though it's been solved. (Another interpretation might be that the characters are still solved, perhaps forever trying to find a short proof that progressively simpler and more elegant ways of proving it, possibly to determine how Fermat might have come up with, solved it without the whole fields of mathematics developed later that the Wiles Wiles's proof relied on.)on. However, in TNG Picard did say "for 800 years people have been trying to solve it", which strongly suggests that there had been no successful attempts at that point.


* ''WesternAnimation/TheSimpsons'': The creators have on two occasions inserted supposed counterexamples to Fermat's theorem as a background InJoke:

to:

* ''WesternAnimation/TheSimpsons'': The creators have on two occasions inserted supposed apparent counterexamples to Fermat's theorem as a background InJoke:


** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4. [[/note]][[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]

to:

** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4. [[/note]][[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]


** In [[Recap/TheSimpsonsS7E6TreehouseOfHorrorVI the Halloween episode which aired in 1995]], a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection it is clear why this cannot hold: raising any integer ''n'' to any power produces a number of the same parity as ''n'', and when you sum an even number and an odd number you get an odd number, but the number on the right of the equation is clearly even.
** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]][[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]

to:

** In [[Recap/TheSimpsonsS7E6TreehouseOfHorrorVI the Halloween episode which aired in 1995]], a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection it is clear why this cannot hold: raising any integer ''n'' to any power produces a number of the same parity as ''n'', and when you sum summing an even number and an odd number you get gives an odd number, but the number on the right of the equation is clearly even.
** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An episode from a few years later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) 4. [[/note]][[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of EasterEggs like this.[[/note]]


* ''WesternAnimation/TheSimpsons'' has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this, an episode from a few years later more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.

to:

* ''WesternAnimation/TheSimpsons'' has ''WesternAnimation/TheSimpsons'': The creators have on two occasions included inserted supposed counterexamples to Fermat's theorem as a background in-joke. In InJoke:
**In [[Recap/TheSimpsonsS7E6TreehouseOfHorrorVI
the Halloween episode which aired in 1995, 1995]], a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see it is clear why this cannot hold: raising any integer ''n'' to any power produces a number of the same parity as ''n'', and when you sum an even number raised to any power gives an even number, and an odd number raised to any power gives you get an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right of the equation is clearly even. Perhaps because of this, an even.
** [[Recap/TheSimpsonsS10E2TheWizardOfEvergreenTerrace An
episode from a few years later later]] more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] [[/note]][[note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs EasterEggs like this.[[/note]]


* ''WesternAnimation/TheSimpsons'' has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this an episode from a few years later more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.

to:

* ''WesternAnimation/TheSimpsons'' has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this this, an episode from a few years later more prominently features another apparent counterexample where the fallacy is far less transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.


* ''WesternAnimation/TheSimpsons'' has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this a few years later an episode showed another apparent counterexample where the fallacy is far less transparent; a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.

to:

* ''WesternAnimation/TheSimpsons'' has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this an episode from a few years later an episode showed more prominently features another apparent counterexample where the fallacy is far less transparent; transparent: a blackboard Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.


* ''WesternAnimation/TheSimpsons'' have on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. A few years later an episode showed a blackboard displaying the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]]

to:

* ''WesternAnimation/TheSimpsons'' have has on two occasions included supposed counterexamples to Fermat's theorem as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. A With a little reflection anyone can see why this cannot hold: an even number raised to any power gives an even number, and an odd number raised to any power gives an odd number, and an even number plus an odd number gives an odd number, so the result must be odd, but the number on the right is clearly even. Perhaps because of this a few years later an episode showed another apparent counterexample where the fallacy is far less transparent; a blackboard displaying Homer is writing on displays the equation 3987^12 + 4365^12 = 4472^12. Anyone attempting to verify these equations on a pocket calculator would find that they are apparently true, but that is because pocket calculators are not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]] A surprising proportion of ''Simpsons'' writers have mathematical backgrounds. The book ''The Simpsons And Their Mathematical Secrets'' details more examples of Easter Eggs like this.


* ''WesternAnimation/TheSimpsons'' pulled a prank that supposedly 'proved' that Fermat's theorem was false. One episode showed a blackboard in the background that showed the equation 3987^12 + 4365^12 = 4472^12, which would prove Fermat false. The statement is false, but calculators register it as true because the numbers are so large. [[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]]

to:

* ''WesternAnimation/TheSimpsons'' pulled a prank that supposedly 'proved' that have on two occasions included supposed counterexamples to Fermat's theorem was false. One as a background in-joke. In the Halloween episode which aired in 1995, a few months after Wiles published his proof, the equation 1782^12 + 1841^12 = 1922^12 can be seen in the Third Dimension. A few years later an episode showed a blackboard in the background that showed displaying the equation 3987^12 + 4365^12 = 4472^12, which 4472^12. Anyone attempting to verify these equations on a pocket calculator would prove Fermat false. The statement is false, find that they are apparently true, but that is because pocket calculators register it as true because the numbers are so large. not precise enough for such astronomically large numbers.[[note]] (You are a mathematician if you disprove it in your head in five seconds with arithmetic modulo 4.) [[/note]][[/note]]


In fact, it's almost certain that Fermat himself didn't really have a proof. Wiles' proof certainly would have been inaccessible to Fermat; it relies on mathematical concepts which weren't developed until after the Second World War. Romantically, one might imagine that Fermat had come up with some simple proof that has since eluded everyone else. In reality it's far more likely that he was mistaken, especially since later in life he went to the effort of working out a proof for a certain special case (that no fourth power can be written as the sum of two fourth powers)[[note]]Though he could still have had a general proof for all odd numbers or odd primes, since proving the case for all odd numbers/primes and 4 would prove Fermat's last theorem for all cases[[/note]]. In fact, 19th-century mathematician Gabriel Lamé had a flawed proof attempt that could have been much like Fermat's -- the idea is just about practicable for a brilliant 17th century mathematician, whereas the flaw in it is a rather subtle technical matter that escaped just about everyone even in the 19th century.

to:

In fact, it's almost certain that Fermat himself didn't really have a proof. Wiles' proof certainly would have been inaccessible to Fermat; it relies on mathematical concepts which weren't developed until after the Second World War. Romantically, one might imagine that Fermat had come up with some simple proof that has since eluded everyone else. In reality it's far more likely that he was mistaken, especially since later in life he went to the effort of working out a proof for a certain special case (that no fourth power can be written as the sum of two fourth powers)[[note]]Though he could still have had a general proof for all odd numbers or odd primes, since proving the case for all odd numbers/primes and 4 would prove Fermat's last theorem for all cases[[/note]]. In fact, 19th-century mathematician Gabriel Lamé had a flawed proof attempt that could have been much like Fermat's -- the idea is just about practicable for a brilliant 17th century 17th-century mathematician, whereas the flaw in it is a rather subtle technical matter that escaped just about everyone even in the 19th century.

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