Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published
many years ago, when i was still in school, i discovered Fermat's Last Theorem which is simple math problem that had stumped the best mathematicians in world for well over 300 years.
and i was very intrigued by it, to the point where i spent several hours a day, for years on end, trying to "prove" it was true.
while i wasn't ever able to actually "prove" it was true, it was still a very good tool for practicing your math skills,
and i would highly recommend to anyone who is at all into math, to try and prove Fermat's Last Theorem...
the problem isn't that difficult to understand.
And so literally as i was working on trying to prove Fermat's Last Theorem, there's an announcement made that Fermat's Last Theorem had been proved!
I didn't think too much of it at the time, except i remember wanting to see the proof for myself, you know, for my own curiosity, to see how it was done.
But guess what?
Turns out this guy tried to divide by zero, and so his "proof" was bunk.
Then he spends another year, trying to correct his fatal flaw of dividing by zero, by going off on another tangent.
math pun intended.
And to this very day, i still have yet to see an actual "proof" of anything
What i have seen, are basically "chunks" of random mathematical proofs,
that are kind-of not-very mathematically rigorous,
meaning they use way too much English,
and not enough actual math.
What you will find, are these glowing reviews of the proof, by people who likely never even saw the proof, or didn't understand it even if they did see it.
At the time i was working on proving Fermat's Last Theorem, it had occurred to me that i could be engaged in a fools errand, because it could very well be that it is impossible to prove.
And i still suspect that Fermat's Last Theorem is actually impossible to prove,
And i suspect Andrew Wiles proof is flawed,
And that like so many other things in Clown World,
The mockingbird media goes along with the bullshit about someone achieving the impossible.
"One Small Step, For A Man...
One Giant Leap, For The Morons Who Believe This Bullshit Is Real..."
And so recently I've been spending more time on ChatGPT, and i started asking about Fermat's Last Theorem, and the answers i got were very evasive, suspicious, etc.
like, ChatGPT was telling me it couldn't give me Fermat's Last Theorem because it was copyrighted.
so i asked for a link to Fermat's Last Theorem
my exact prompt: Prove that X^n + Y^n = Z^n has no solutions when n > 2
ChatGPT: The statement you mentioned is known as Fermat's Last Theorem, and it was famously proven by Andrew Wiles in 1994. The proof is quite complex, and involved advanced mathematical concepts. If you're interested in the details, i recommend exploring Wile's original paper for a comprehensive understanding.
me: show me the math here
ChatGPT: Andrew Wiles proof of Fermat's Last Theorem involves several sophisticated mathematical concepts, including modular forms, elicit curves, and Galois representations. It stands over 100 pages and goes beyond what can easily be explained in a brief message.
If you're interested in the the detailed mathematics behind the proof, i recommend reading Wiles original paper titled "Modular Elliptic Curves and Fermat's Last Theorem", published in the Annals of Mathematics in 1995. It provides a thorough explanation of the intricate mathematical reasoning involved in the proof.
me: Prove Fermat's Last Theorem
ChatGPT: 4 long-winded paragraphs basically talking down to me, trying to baffle me with bullshit, while also utterly failing to even attempt to do as i asked.
me: how is it that Fermat could prove his theorem with the math of his day, but Andrew Wiles had to use math that hadn't even been discovered in Fermat's day?
ChatGPT: Fermats proof for Fermat's Last Theorem remains elusive because there no evidence that he actually had a proof... (then 2 more paragraphs of math babble)
BINGO!
i mean, everyone who knows anything about Fermat's Last Theorem knows that there was supposedly brilliant proof, but the margin of this book is too small to contain it.
But here we have ChatGPT stating the elephant in the room, which is that Fermat himself never produced any proof, and if that is true, then why should we expect anyone else to produce a proof? If the man himself couldn't even do it?
How easy would it be to scrawl on the margin of a book,
"i have discovered a truly brilliant way of making a dollar out of 99 cents, but unfortunately the margin of this book is too small to contain it"
its basically trolling.
And when you start asking for the actual proof of Fermat's Last Theorem, you'll notice a weird kind of push-back.
And it has all the classical signs of being professional trolls or shills,
for example instead of simply showing you the math, they will imply that you are too stupid to understand the math.
so then we must assume that these trolls and shills are smart enough to understand the math... right?
so we ask them to explain it to us, since they are obviously smart.
and they will get all squirrelly and elusive,
and it becomes clear that they don't understand the math either,
and yet, its a really weird topic for someone to take an interest in, enough to become a shill or a troll, and yet these same people don't take enough of an interest to actually understand what it is that they are mouthing off about?
do they understand the proof is shit,
and are simply propping up the official story?
So here we have Andrew Wiles, being the public face of the fake proof of Fermat's Last Theorem, which can't be proven.
Wiles had already published one false proof, like so many others before him.
Its almost certain that his next proof was also false, which is why they don't want you to debate the finer details of the supposed proof.
if we could clearly debunk Wiles proof, we could embarrass the entire math and science community,
So think about this... for well over 300 years, this very simple math problem has been shown over and over and over to be impossible to prove, with every single "proof" ever published, eventually being shown to be false, including Fermat's own supposed proof, that probably never even existed...
Then we have CHatGPT, which should be as smart as 100 top mathematicians,
and instead of just cranking out this proof, one line of math at a time, step-by-step, from beginning to end,
we get excuses. we get hemming and hawing. we get re-directed.
If ChatGPT is so smart, why can't it even attempt to explain the proof of Fermat's Last Theorem?
ChatGPT is behaving like someone who has something to hide.
please share this post, in your social circles, and try to generate some interest in the topic.
this story has intrigued audiences for over 300 years, and will continue to intrigue audiences for many more years, because its impossible to solve, and yet fools will keep trying.
fools like me.
do not let them get away with simply presenting the proof as if its true, and putting the onus on the audience to prove its false.
quite the opposite. the onus is on Wiles, to prove his proof is true.
its 100 pages of techno babble that doesn't prove anything.
but they will just claim that you are an idiot for not understanding their math...
the math that they themselves can't really explain.
So heres the thing... Fermat's Last Theorem is a very simple problem, and if there was any actual proof, it should be well within your mathematical ability to see it, and understand it, and explain it to another person.
Do you know Pythagorean Theorem?
A^2 + B^2 = C^2
you can probably apply this theorem, for a quiz.
you can probably explain this theorem, to a student.
and if you have already learned this much in math class, then you can also learn about Fermat's Last Theorem.
and yet, you still aren't learning anything about the actual proof of Fermat's Last Theorem,
you can't apply it, for a quiz,
you can't explain it to a student.
do they teach Fermat's Last Theorem proof as a math class?
so instead of explaining this supposedly brilliant math proof,
they imply we are all too illiterate to understand the proof.
it has that same feel of the COVID vaccine.
just accept it, and stop asking so many questions.
"We'll know our disinformation program is complete when everything the American public believes is false."
- William J. Casey, CIA Director (1981)
it is far easier for them to lie to us, than it is for us to prove that they are lying.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem
https://en.wikipedia.org/wiki/Andrew_Wiles
https://en.wikipedia.org/wiki/Wiles's_proof_of_Fermat's_Last_Theorem
Greetings! I read it all. Every other proof Fermat claimed was shown to be real later, so the question all along has been: was Fermat mistaken and didn't admit it if he realized it later, or did he actually have the elegant path? My leaning is toward the former, but either way it's still a great problem to find the most elegant proof (or counterexample!).
I've glanced through Wiles, but do not have the luxury of reading the entire proof attentively to follow it all the way through. I trust those who have, as there is a consensus and there is not an objection of the sort that you raise. It is true that Wiles went down false trails, but the solution came up when he combined part of one trail and part of another trail and realized that both portions worked and together they constituted the complete proof. The details involve narrowing the limits on solutions by converting them to alternate mappable and reducible functions until the solution space becomes searchable; it requires great ingenuity, just like the Poincare conjecture (proven) and the Riemann (unproven).
It's my belief that the solution can be improved and that means your work is not in vain because anyone who improves on Wiles will get mentioned in math history like forever. But until we do some practical work with the transform spaces involved we don't have the right to question those who have worked with them for years.
I would strongly suggest though that instead of improving the Wiles proof you work on either the Riemann conjecture or the P=NP problem. Not only do they look easier, there's more prize money in them.
u/LoneWulf, supercomputers have been looking for a solution all this time and haven't found one up to n in the hundreds of thousands.
u/BerlinWallCrosser, that was a joke solution, it's only accurate to about a dozen places, so it looks accurate if your computer rounds it.
It’s better than that. The writers on the Simpsons, who are also degrees mathematicians, gave one great mathematical gag as a background joke for about 3 seconds in one episode. All 3 numbers exceed 10^43. The first 11 digits at the front of number add up correctly. Also, at least the last 8 digits add up correctly. The key difference comes in the middle 20 numbers. This is called a very close Fermat triple. Most calculators sold to students make it seem plausible. Few people have the patience or the ability to correctly calculate a 4 digit number to the 12th power. You need a computer that can calculate all 43 digits to find the flaw. When I saw this gag the first time, I backed up the episode on my DVR, wrote the triple down and spent the next 2 days working on it eventually using a university computer to calculate the whole number without rounding nor using scientific notation. I have to admit, it was a fun two days for me.
There any many other psyops in the history of science. One example was that special relativity demonstrated long contraction and time dilation which in fact a few years after Einstein offered his theory of special relativity two phycists actually proved time dilation and length contractions occur at high speeds even if the speed of light is NOT constant from every frame of reference. All that is required to prove time dilation and length contraction is the notion of that there is no universal reference frame but only inertial reference frames which galileo made a point of. Another is that Galileo discovered the earth revolves around the sun. He didn't prove it. It wasn't prove and accepted by the scientific community until the 1700s after Newtonian physics was discovered. Bug the biggest of biggest of biggest psyops was awarding the major proponent and pioneer of transgender theory the highest award in science: an award given my the royal society of scientists in England, which few received historically including newton. THAT is a real disgusting politically corrupt and politically motivated psyop.
You should try again using the ChatGPT DAN (Do Anything Now) workaround.
https://www.fastcompany.com/90845689/chatgpt-dan-jailbreak-violence-reddit-rules
Chat GPT doesn't actually "know" anything. It can't do math. It's a social bot. It looks at lots of text, and when it replies, after every word an algorithm is run to select the next word that makes the most sense there. It cannot create proofs of anything. It's basically a glorified search engine. Except that ChatGPT can actually lie to you. They call it "hallucinations". It actually makes shit up!
I tried playing a game with it once, i called it "Florida man". I asked it to give me 10 Florida Man headlines, except one has to be real, and i had to guess the real headline. After several rounds, i realized none of the headlines were ever real. They were all made up, despite my clear instructions that one HAD TO BE real, and NOT MADE UP. It just wasn't possible for it to find any real headlines to use.
☝🏻exactly this. ChatGPT is a large language model for unstructured problems. It’s a form of supervised learning, which means that it has to be trained on prior dataset. LLMs are limited to producing words/ phrases that have been included in the training datasets. “Smart” AI? Dont hold your breathe. The sequence of words/ phrases produced by LMMs are merely randomization among patterns found in the training dataset. Ripe for bias of course!
What would, or potentially could a solution for Fermat's Last Theorem actually prove, if it were applied towards some kind of technology, theoretical, or otherwise?
I ask, because that might give a clue as to why ChatGTP is programmed to not cooperate with revealing the answer, and steering people away from looking for a solution.
As an example, could the solution to the equation lead to a breakthrough in zero-point energy, or some other spectacular technological advancement?
i always took Fermat's Last Theorem to be a logical extension of the Pythagorean Theorem,
but instead of saying "this always works" with Pythagorean,
we say "this never works anywhere else, other than Pythagorean" with Fermat's
"Prove that X^n + Y^n = Z^n has no solutions when n > 2"
All you have to do to prove the formula isn't true is to find a single solution. One would think a supercomputer could speed up that process a bit.
Thus, you won't need a fancy proof if you can find a solution proving it false.
Of course, finding that one solution might take awhile. 😂
Maybe I'm just completely stupid and absolutely don't understand Fermat's last theorem but can't you prove that there is a solution for n>2 as follows:
1^2 + 0^2 = 1^2.
Now this holds true for any n element of the real numbers.
You missed the part where n must be greater than 2. 😉
but n is the exponent,
and he has 0 as the base
The base numbers have to be greater than zero:
"Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
https://en.wikipedia.org/wiki/Fermat's_Last_Theorem
"The positive integers are the numbers 1, 2, 3, ... sometimes called the counting numbers or natural numbers.
A positive number is any number greater than 0."
https://byjus.com/question-answer/what-is-a-positive-integer/
The Simpson’s actually disproved it over a decade ago when 3987^12 + 4365^12 = 4472^12 appeared on Frink’s chalkboard in the background of a scene.
i plugged that into ChatGPT
The real psyop in Mathematical history is the belief that infinite processes can be completed and the real numbers, in particular irrational numbers, are sensible mathematical objects. The psyop encompasses the acceptance of cantor's theory of infinite sets of which many philosophers of mathematics demonstrated was full of logical paradoxes. This fact was largely accepted by the mathematical community until... they realized you need this theory to define the real numbers. No one has ever provided a valid definition of real numbers: dedekind cuts and Cauchy sequences are full of vagueness, circular reasoning, and the assumption of infinite irrational numbers as valid. In other words, they assume real numbers are valid and defined when trying to prove real numbers are valid and offer a definition. I've been reflecting on the meaning of the square root of 2 for years, and it was the marvellous work of math professor Norman Wildberger on YouTube which demonstrated the logical nonsense of the real numbers.
What're your thoughts on square root of 2?
Excellent point. Cantor got everyone on the wrong track in the 19th century with his multiple infinities and then quantum physics followed with its uncertainty principle.
There is no such "real" thing as a Cantor diagonal number because it would take an infinity of time to derive it so it cannot be conceived. Thus aleph-null equals C and all protests to the contrary are the real null.
The real difference is between the infinity we know and the infinity we don't know, but in reality they are the same and the difference is all perception. For instance if you know naturals but don't know integers, then integers are part of the infinity you don't know; but once you define integers they move to the infinity you know but they don't change at all (even though you haven't yet defined fractions). If you pursue this line you will solve P=NP and win a million dollars.
c/BerlinWallCrosser, c/VaccinesCauseSIDS
Your take on infinities is insightful. Maybe I can add to it.
To know something is to know a category (or as the historical philosophers say, a unifying idea; whether that idea unifies an objects identity through time or is the category of multiple objects through space.)
Instead of thinking of the universal definitions of the natural numbers as an infinity set, maybe we can take a clue (roughly speaking) from special relativity and say the size of the set of natural numbers is relative according to the category in a given circumstance. So you can never have a set of natural numbers without first defining an environment with objects which could be categorised (this links to special relativity in that there is no single entity which is the universe but rather only particular individual-entities; this is also Aristotelian in nature).
So if I'm in a park and there are three tree, two dogs, one human. Then under the category of tree, the set of natural numbers is 1, 2, 3 (a finite set). Under the category of dog, the natural numbers is the set of 1, and 2. Under the category of human, the natural numbers is 1. You only have finite sets. What about under the category of hammer? The natural numbers is 0.
Under this perspective, you can only have an infinite set of natural numbers if there's some individual-entity which embodies a category (given there are many of this entity) in a circumstance or reality as a whole of which theres an infinite number and, technically is a property or part of every being. If this is true, you can have an infinite set, if this is false you cannot have an infinite set. Hence, defining the size of a set of natural numbers begins with an environment of categorizable objects. This also has the benefit of ensuring your mathematics is always tethered to describing something in reality as a whole whether that object is physical or not.
Anyways, this is just my random ponderings and is most likely full of problems because I'm actually quite stupid and a slow learner.
Update to my earlier question: mathematics formulas related to elliptical curves makes me think of the kinds of maths used for ICBM targeting systems. As such, that might explain why you have encountered contradictory information about a possible solution to this equation.