Mathhhhhh

[Sarah]

Anyone know about Cryptology and Fermat's Last Theorem? Is his theorem prooved.. its been told that it has been proved and disproved (is this even a word)... I have to write two page essays for each one for pre-calc. ~puke~ :crylaugh:

Anyone like math?

[Urd]

Yes, Fermat's Last Theorem was recently proven in 1994 using very advanced mathematics.

What kind of information are you exactly looking for?

[Pikachu]

That just blew over my head. But I sort of like math. At least, I like it more than I like Organic Chemistry..

[Sarah]

I just need information onhow FLt is used for math... basically I need to summarize what FLT is. I found an article about Taniyama-Shimura and she proved it... maybe that's what you are taking about.

I dunno what organic chemistry is but I do love chemistry

EDIT: Nevermind, it was recently A.Wiles suceeded in 1995.... Don't make fun of me but was is theorem proved wrong or right? :confused: :o

[Urd]

1995, eh? How strange. The textbook that I used last term said that Wiles proved it in '94.

He proved that "the result held", in mathematical terms.

[Sarah]

You're right it was proven November 1994. I guess that one site was just other proofs. I need to write a page typed and I somehow only have 3/4. I wrote a little about this background history and what was the Diophantine equation, and how Fermat proved it and then about A. Wiles.

-Pierre de Fermat was born near Montauban in 1601. He was a French lawyer who liked the subject mathematics and pursued it during his spare time. He was known to be one of the greatest mathematicians of all times. He really never wrote books (except one) but he was famous to write comments in margins of books. A few of his discoveries were analytic geometric, the theory of probability, and the Least Time Principle. He was most famous for his biggest discovery and proof yet which was called Fermat’s Last Theorem.
- He stated "I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain." He had discovered a proof that the Diophantine equation xn+yn = zn has no integer solutions for n>2. This became known as ‘Fermat’s Last Theorem.” For example, if n=3, his theorem would state that no natural numbers x, y, z exist such that x3+y3=z3. He gave a proof of the statement made by Diophantus that the sum of the squares of two integers cannot be of the form 4n – 1. He proved that x, y, z, and n are integers, has no nonzero solutions for n > 2.
- For hundreds of years, no one could prove it wrong except in 1993. What Fermat really meant was that the area of a right triangle cannot be a square. Clearly this means that a rational triangle cannot be a rational square. In symbols, there do not exist integers x, y, z with x2 + y2 = z2 such that xy/2 is a square. From this it is easy to deduce the n = 4 case of Fermat's theorem.
- Many mathematicians tried to solve this problem but no one seemed to prove it. The Shimura-Taniyama-Weil Conjecture asked some questions about elliptic curves and it turned out that it was unimportant. In 1993, A Wiles, a British mathematician working at Princeton in the USA, proved his theorem wrong with backed up information. An elliptic curves equation would look like y2 = x(x - an) (x + bn).
-It is now believed that Fermat's 'proof' was incorrect although it is impossible to be completely certain. Even A. Wiles was having a hard time and withdrew the claim that year since his proof was getting proved wrong. Finally in 1994, Wiles again claimed to have a correct proof which has now been accepted.

This is just a scratch copy and I will fix the grammatical errors later, but I need about two more paragraphs and do you know what I can add?

[Urd]

I'm at school right now, so I don't have access to my textbook. I'll get back to you later tonight (post-6pm on EST) when I'm back in my room. I will try to look for you on AIM.

Do you need anything on cryptography?

[JFA_bobguy]

Ah, Fermat's Last Theorem...I never studied that one in school but I've heard about it. But writing a 2-page essay on it? Well at least there's a reference. And Cryptology...assuming this means Cryptography, there are many ways to look at it. Caesar ciphers, monoalphabetic substitution, RSA enryption (which is used today I believe)...

[Kititt]

Ugh, that thread alone gave me a headache.

I can't help much with the mathmatical bit, but if you need help with editing, I'll look over grammar and such.

[Eric]

RSA is still used but not exactly the standard. Shit... I need to take cs crypto soon.

[Sarah]

I wrote a little about Cryptography but I dont think I did a great job I just wrote about the two types of cryptosystems (asymmetric and symmetric) and how its used today. If there is anything you guys know, please tell. RSA... I want to know more about that.

Urd- Thank you, I'll try to be on at that time.

Kititt- Are you good at grammar and sentence writing? I hate writing essays and since english was my second language, my grammar is very poor. Maybe I can give you my future essays about WWI (future=tomorrow) lol.. I'll create a thread for that.

[Urd]

The RSA scheme basically banks on the fact that large numbers are ridiculously difficult to factor. There are ways to go about finding primes and such by methods like sieve of eratosthenes, but, well...The sieve method gets out of hand when the numbers get big (like really, really big).

My textbook also covered cryptography stuff (which we went through in class).

[Eric]

However, that is a very big bank considering the strides made in distributed computing.

[Kititt]

Kititt- Are you good at grammar and sentence writing? I hate writing essays and since english was my second language, my grammar is very poor. Maybe I can give you my future essays about WWI (future=tomorrow) lol.. I'll create a thread for that.

Essays were always my forte. Send what you have, and I'll do what I can.

[Urd]

However, that is a very big bank considering the strides made in distributed computing.
Yeah. That is precisely why RSA Security has those challenges to see just how long it would take for people to factor out a very large number into two odd primes.

[Sarah]

Thanks you guys.

My paper is due tomorrow and I will be researching on RSA security.. what else should I write about?

[Urd]

Well, Fermat's Little Theorem is related to module numbers and prime numbers. You could tie that in with the RSA scheme's usage of modulo numbers. There's also probably a nice amount of information in regards to WWII cryptography out there like how Purple was broken.

[Kinael]

Purple was the Japanese's. Enigma was used by the Nazis.

[kyrien]

Alan Turing won a Nobel Peace Prize for helping crack Enigma. /random

[Kititt]

holy crap!

I'm watching Arjuna, right now. And they're talking about this. o.O; It's creepily ironic!