/sci/ - Science & Math

Andrew Wiles discovered a truly marvelous proof, which this message board is too narrow to contain

his proof is one hundred pages of dense (very dense) mathematics. it tooks him six years and even then someone found a gap, which he filled.

I'm still waiting for an elementary proof.

Wiles used tools not available to Fermat (modularity theorem being the biggest), meaning that Fermat's proof looked totally different. Either that or Fermat's proof was erroneous or Fermat was the greatest troll ever.

>>4118372

>greatest troll

gets my vote

>>4118372
I'm sure there's an easier way to prove it, nothing says there's only one way to prove something.

>>4118391
>nothing says that there is only one way to prove something

0/10 <span class="math">you~are~a~giant~faggot[/spoiler]

so does this mean there is a pythagorean theorem-like theorem for all 3-dimensional pyramids?

>>4118398

Indeed. In a rectangular prism with sides of length a,b and c - and main diagonal of length d:

a^2 + b^2 + c^2 = d^2

And more generally, Pythagoras' Thm holds in any inner product space.

induction

>>4118395
>>4118395
You don't belong here, Please leave.

I really don't understand why this was so hard to prove... if you have a^x+b^x=c^x... and x has to be greater than two (though this doesn't really matter)... Can't you just go as:

a^x+b^x=c^x
a+b=c

And that's obviously possible, so it's true..

>>4118391
Actually, "elementary" does not always mean easier than "non-elementary."

>>4118470
>a^x+b^x=(a+b)^x
(╯°□°）╯︵ ┻━┻

>>4118482
Ok so
a^x+b^x=c^x
(a+b)^x=c^x
(a+b)=c
a+b=c

That's basic math... Sometimes I think people get so caught up in complexity that they overlook the really obvious.

>>4118484
>>4118470

>>4118484
what are you doing?
thats not math

>>4118496
Just cancelling exponents bro... ie if x^2=y^2, then x will always equal y. Did you guys not learn this? idk

>>4118501
Either you're an amazing troll or a fucking <span class="math">retard.[/spoiler]

>>4118484
Not sure if serious...
In general, <span class="math">a^n+b^n\ne (a+b)^n[/spoiler]. Only in very specific instances does a^n+b^n=c^n (e.g. a=0 or b=0). Although, now I am trying to work out where that statement is true in general.

>>4118522
>amazing troll
1/10 because i thought you were serious at first

>>4118522
Uh... Okay if I said 1+1=2 would you say I was trolling?

How about (x)^2=(y)^2 then x=y?

Then you have to admit (a+b)^n=c^n means a+b=c...

And since a^n+b^n equals (a+b)^n, I guess you have a problem now, huh? It's VERY basic algebra. Glad I finally have something to contribute to this board haha

>>4118528
>where that is true in general
>in a thread about Fermat's last theorem
Wow, I'm stupid sometimes.

>>4118533
15/10

>>4118537
>>4118533

this is some of the worse trolling i've seen in a while

i am dissapoint

Anybody want to explain to me why it's wrong, then? $10 says you can't

>>4118533
2^2 + 2^2 = (2+2)^2
8 = 16.

U srs bro? I come here specifically because I'm shit at maths and even I can see that 2^2+3^2=14 and (2+3)^2=25.

>>4118552
>>4118551
Yeah okay but fermat specifically said for n is larger than 2, dickheads. Learn to read

and they said trolling was dead

>>4118547
Suck my cock dude.

>>4118568
Trolling is dead ~ Nietzsche

>>4118559
This has nothing to do with fermat's theorem, we're talking about your statement that a^n + b^n = (a+b)^n.
2^3 + 2^3 = 4^3
16 = 64

0^n + 1^n = 1^n. For all n > 0.

Problem Fermat/Wiles?

>>4118570
Ok guys I don't get why everyone is getting angry at me. Fermat had some theory, and it's been proven a few times now (the really long way, but that guy idk what his name was) and the short way. Both are equially legitimate... if you're seriously arguing against my way of doing it, you're saying Fermat and the other guy was wrong too and I don't really think that's likely.

>>4118574
16 doesn't equal 64 dude, you're kinda making a fool of yourself.

>>4118533
Actually, "(a+b)^n=c^n means a+b=c" (the part where I assume you aren't trolling) isn't even true.
<span class="math">(a+b)^n=c^n \Rightarrow \exists m \in \mathbb{Z}/n\mathbb{Z} a+b=c \dcot exp \{ \frac{2im}{n}\}[/spoiler]. That is, a+b can be c times any nth root of unity. So if n=4 and c=3, a+b could be 3i.

As far as everything else goes, fuck off troll. You aren't clever.

>>4118578
Trying way too hard.

>>4118528

If x and y are elements of a commutative ring with characteristic p, where p is prime, then:

(x+y)^p = x^p + y^p

>>4118559
2^4+2^4 != (2+2)^4

>>4118606
Again dude, n LARGER THAN 2. Even if it doesn';t work, that doesn't mean the theorem is wrong - it's been proven, so it's obviously legit... you're sorta arguing a lost cause

>>4118610
>lrntobinomialtheorem

>>4118610
I don't whether you realize the stance you are taking is completely contrary to Fermat's last theorem.

>>4118621
How so?

>>4118629
Fermat's last theorem is that there are NO positive integer solutions to a^n+b^n=c^n for n>2. If your thing were true, there would be solutions.

>>4118371
He found the gap himself.
>>4118372
Obviously this is the case, what anyone would do if they couldn't think of a proof.
>>4118528
There is a concept called Freshman's Dream, as far as I know, where x^{p^r}+y^{p^r}=(x+y)^{p^r} where p is a prime number.

Pretty sure he used magnets