View Full Version : Did anyone ever thought that the Fermat's Last Theorem was a joke?

Crowbar of Irony +3

10-30-2005, 04:42 AM

My friend and I were discussing Fermat's Last Theorem the other day, about how Fermat wrote in the margin of a book that "I have discoverd a truly remarkable proof of this thoerem which this margin is too small to contain". My friend was suggesting perhaps Fermat actually meant this to be a joke...

Had anyone else thought the same way too?

Capt. Ridley's Shooting Party

10-30-2005, 04:45 AM

Yes. IIRC, Fermat was known for winding people up. Either that, or he'd thought he'd discovered a proof when he really hadn't.

Crowbar of Irony +3

10-30-2005, 04:49 AM

Yes. IIRC, Fermat was known for winding people up. Either that, or he'd thought he'd discovered a proof when he really hadn't.

Great gosh, then why on earth did people still spend so much time working on it, given Fermat's reputation?

Capt. Ridley's Shooting Party

10-30-2005, 04:55 AM

Because no matter whether Fermat had a proof or not, the problem was still a valid one.

Wendell Wagner

10-30-2005, 05:20 AM

I think Dominic Mulligan was joking. (If you're not, Dominic Mulligan, please give a citation that he liked "winding people up.") I don't think that Pierre Fermat was known for making up fake theorems. What he was known for was coming up with conjectures or theorems which he claimed to have proved which were later confirmed to be true. Fermat's Last Theorem is so called because it was the only one of the theorems/conjectures that he wrote down which wasn't either proved or disproved within a few years after his death. But that's not the basic reason that it became famous. It's famous because it's a mathematically interesting theorem.

The general supposition among mathematicians for the past one hundred years or so is that Fermat thought he had a proof, but he made a mistake. Someone has even come up a supposed proof of the theorem (which is consistent with the mathematics that Fermat knew) that appears to prove the theorem but which has a subtle mistake in it. What's clear is that he couldn't possibly have come up with Wiles's proof of the theorem. That requires developing huge areas of mathematics that weren't created until centuries after Fermat died.

Capt. Ridley's Shooting Party

10-30-2005, 09:42 AM

Regarding Fermat as a practical joker, it seems that I was mistaken. I could have sworn that I had read it somewhere perhaps in the Simon Singh book?), but the best that I can do is offer this cite (http://groups.google.com/group/sci.math/browse_thread/thread/c7eb89d03682079b/18179e711d496494%2318179e711d496494?sa=X&oi=groupsr&start=0&num=3) (see Nat Silver's post) which states that it was his son who was a practical joker and all of Fermat's papers had passed through him before being published.

Little Nemo

10-30-2005, 10:02 AM

In my opinion, the most likely possibility was Fermat was thinking about the theorem one day and thought he'd invented a proof. He wrote down his note to remind himself. But later, he worked it out and realized his proof didn't work (there are several false proofs known). So to Fermat the note was an unimportant dead end and he never realized the number of people who would try to follow its lead. Keep in mind, Fermat lived another 27 years after writing his note, so he had ample opportunity to write out his complete proof if he had one.

Crowbar of Irony +3

10-30-2005, 10:20 AM

Keep in mind, Fermat lived another 27 years after writing his note, so he had ample opportunity to write out his complete proof if he had one.

My thoughts were that it was called "last theorem" because he died before he could write down the proof. It may be something to do with the word "last".... Why did they call it "Fermat's Last Theorem" ?

Thudlow Boink

10-30-2005, 10:25 AM

My friend and I were discussing Fermat's Last Theorem the other day, about how Fermat wrote in the margin of a book that "I have discoverd a truly remarkable proof of this thoerem which this margin is too small to contain". My friend was suggesting perhaps Fermat actually meant this to be a joke...If I understand correctly, Fermat never intended anyone else to see his marginal note. So if it was a joke, it would have been a very private one. (It would also explain why Fermat didn't go back and correct his claim if he later realized that his "proof" was flawed. i.e. basically what Little Nemo said.)

Exapno Mapcase

10-30-2005, 10:26 AM

Because they're proved all the other ones, and this was the last one remaining unproven.

ultrafilter

10-30-2005, 10:39 AM

There's also a relatively simple proof of FLT in the case that n = 3, and it's possible that Fermat may have discovered that and believed that it would generalize.

ITR champion

10-30-2005, 12:31 PM

It's worth noting that standards of proof were not as rigorous in Fermat's day as they are now. There are plenty of examples of papers from before the 20th century where mathematicians simply made huge leaps of logic or stated "this is obviously true". Such behavior would shock modern mathematicians.

Shagnasty

10-30-2005, 12:39 PM

I can't tell if some people in this thread are aware that Andrew Wiles solved Fermat's Last Theorem (http://www.pbs.org/wgbh/nova/proof/wiles.html) several years ago. In any case, he believes that Fermat was either kidding or joking because the proof was very long and difficult.

Dr_Paprika

10-30-2005, 12:44 PM

I've read Singh's book fairly recently. Fermat was well known for refusing to state proofs on his problems to rile other mathematicians, and did this on many occasions. But he was also an excellent mathematician and had actually worked out solutions to his other problems, even if he wouldn't publish them. All hsi other theorems did have solutions. FLT was likely intended to annoy, but that doesn't mean that Fermat hadn't worked out at least a partial solution to the problem. If he did so, there is no reason at all to believe his solution was anything close to Wiles -- I don't think anyone believes this to be the case.

chappachula

10-30-2005, 12:48 PM

related question:

the theorem has been solved, but by a modern method using 20th century math.So this proof is definitely not the one that Fermat himself may have found.

Are mathematicians satisfied by this? Is anybody still interested in finding Fermat's original proof, (if it existed?)

Exapno Mapcase

10-30-2005, 12:54 PM

I don't think any mathematicians exist who continue to think that Fermat had found a valid proof. Probably only amateurs are still looking for it.

It's well known what the proof he was referring to was likely to be, and its inadequacies are equally well known.

Dr_Paprika

10-30-2005, 12:59 PM

Here is a solution for n=3. I was disappointed that Singh's book did not include a discussion of this "simple" case -- not that I could have proved this myself given a million years... but I would have appreciated the insight.

http://meta-religion.com/Mathematics/Articles/fermats_last_theorem.htm

Walton Firm

10-30-2005, 01:03 PM

Are mathematicians satisfied by this? Is anybody still interested in finding Fermat's original proof, (if it existed?)Even if someone discovered a brilliantly simple proof using only concepts which were known in Fermat's time, it would be impossible to prove that Fermat found the same one.

During the centuries between Fermat scribbling his note and Wiles publicizing his proof, there have been lots of proposed proofs, all of which turned out to contain some subtle (or not-so-subtle) error. I think most mathematicians nowadays assume that Fermat found one of these.

On the other hand the theorem itself certainly looks simple enough that it seems as if there should be a straightforward proof, not requiring hundreds of pages of 20-th century math. I guess that's why it has attracted (and continues to attract) so many crackpots: it just seems like the kind of puzzle which an amateur with a decent mathematical intuition should be able to solve in an afternoon or so..

Hypnagogic Jerk

10-30-2005, 02:57 PM

I can't tell if some people in this thread are aware that Andrew Wiles solved Fermat's Last Theorem (http://www.pbs.org/wgbh/nova/proof/wiles.html) several years ago. In any case, he believes that Fermat was either kidding or joking because the proof was very long and difficult.

Look at Wendell Wagner's post (post #5). Most mathematicians today believe that Fermat thought he had a proof of the theorem, but later realised that he had make a mistake. He then started working on proofs of special cases of the theorem. There is no way he could have written Wiles's proof or anything similar.

Shagnasty

10-30-2005, 03:06 PM

Look at Wendell Wagner's post (post #5).

That post alluded to a solution with a mistake still outstanding. I wanted to make it clear that the proof is done now.

Wendell Wagner

10-30-2005, 03:35 PM

Shagnasty writes:

> That post alluded to a solution with a mistake still outstanding. I wanted to

> make it clear that the proof is done now.

I think you have misread my post. I thought I made it clear that Wiles's proof is a true proof. What I said was that long before Wiles announced his proof in 1993, other mathematicians had come up with supposed proofs which didn't quite work. They had subtle mistakes in them that it's possible that Fermat might have been fooled by, so perhaps one of them was the mistaken proof that Fermat thought of. What I said was that Wiles's true proof of the theorem could not possibly have been the proof that Fermat was thinking of. Wiles's proof requires math that Fermat couldn't possibly have known about.

spingears

10-30-2005, 07:32 PM

My friend and I were discussing Fermat's Last Theorem the other day, about how Fermat wrote in the margin of a book that "I have discoverd a truly remarkable proof of this thoerem which this margin is too small to contain". My friend was suggesting perhaps Fermat actually meant this to be a joke...

Had anyone else thought the same way too?

Fermats Last and Other Matters (http://www.pbs.org/wgbh/nova/proof/)

CalMeacham

10-31-2005, 07:09 AM

You fellas evidfently misdsed my old sig line (And I reprinted it a week or so ago in the Sig Line thread):

"I give up -- how do you keep a mathematician busy for 350 years?"

-- Pierrre de Fermat's friend.

..

wolf_meister

10-31-2005, 10:48 AM

From what I have heard of Pierre de Fermat, he was a mathematician whose insights greatly exceeded his (or a great many of his contemporaries) mathematical abilities.

In other words, he could propose theorems that were easily understood but exceedingly difficult to prove. The best example of which is the legendary "last theorem". I think I first heard of that when I was in the 9th grade. The statement:

An + B n = Cn, where A B C and n are integers, will only have solutions when n is no greater than 2

can be understood by a grammar school student . However, the proof, (as we know) is phenomenally difficult.

Another of his theorems,

22n+1 will yield prime numbers for all integer values of n

held true in his day, mainly because the first values 5 of n (from n=0 through 4) equal: 3 , 5 , 17 , 257 and 65,537 which were known to be primes.

The next number 4,294,967,297 (where n=5) couldn't be tested for primality in Fermat's day, so Pierre said that was also prime. AND when n=6 and larger the numbers become astronomically huge with no hope of testing their primality many centuries ago.

By the time Fermat was proven wrong on this theorem by the mathematician Euler (who was able to factorize 4,294,967,297), Pierre had long since shuffled off this mortal coil and so his reputation (while he was living) remained intact. As a matter of fact, the formula yields primes only for the values n=0 through 4.

It is because of these simple statements with mind-boggling proofs, that led one of Fermat's contemporaries to call him "that French bastard !!!"

Omphaloskeptic

10-31-2005, 11:44 AM

As a matter of fact, the formula [for Fermat numbers, 22n+1] yields primes only for the values n=0 through 4.This is not actually known to be true, though no larger values of n producing prime Fermat numbers are known.

Thudlow Boink

10-31-2005, 02:24 PM

In other words, he could propose theorems that were easily understood but exceedingly difficult to prove.This may be more a characteristic of Number Theory (http://en.wikipedia.org/wiki/Number_theory) (the area in which Fermat did much of his work) than of Fermat himself.

wolf_meister

10-31-2005, 11:37 PM

Thudlow

Thank you for that clarification. Still, you must admit that Fermat had a "knack" for formulating some very interesting theorems.

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