Who was Fermat and Why Was His Last Theorem So Significant?

  • Thread starter mathshead
  • Start date
  • Tags
    Theorem
In summary, Fermat's Last Theorem states that there are no solutions to the equation x^n + y^n = z^n for non-zero integers x, y, and z if n is an integer greater than 2. The theorem was first proposed by Fermat in the 17th century, but it was not proven until 1993 by Andrew Wiles. The importance of this proof lies in the fact that it led to the development of new branches of mathematics. Other famous theorems by Fermat include his method of infinite descent and his contributions to the development of calculus.
  • #1
mathshead
can someone tell what fermat's last thearom is? who prove it in 1993, and why it was a such great things to prove?
 
Mathematics news on Phys.org
  • #2
The theorem says that;

The equation x^n + y^n = z^n has no solution for non-zero integers x, y, and z if n is an integer greater than 2.

Fermat said he had a proof for this in the 17th Century but died before ever showing the proof. A guy called Andrew Wiles finally fully prooved it in 1993 after spending much of his life on it.

You'll find much more on google.
 
  • #3
Fermat probably lied, as Wiles' proof took mathematics it took hundreds of years to derive.
 
  • #4
Originally posted by FZ+
Fermat probably lied, as Wiles' proof took mathematics it took hundreds of years to derive.
I have a proof that Fermat lied, alas, I haven't the time in this thread to demonstrate it.
 
  • #5
*snicker*

Fermat's Last Theorem (FLT) itself isn't anything particularly special, it's just one of those "thorn in your side" type problems.

The reason why it's so great, though, is that entire branches of mathematics were invented in an attempt to prove it.

Wiles proof, in particular, is actually partial progress on one of the most fundamental conjectures in the study of elliptic curves, he proved that a certain type of "bad" elliptic curves cannot exist. It just so happens that a counterexample to FLT would allow one to construct one of those bad elliptic curves, so FLT is merely a rather minor corrolary to Wiles' theorem.

Hurkyl
 
  • #6
Boulderhead
I have a proof that Fermat lied, alas, I haven't the time in this thread to demonstrate it.
You Bould me over with your Wiles.
 
  • #7
can someone link me to page, that has a proof for it, what other famous did fermat have?
 
  • #8
A lot of the theorems in basic number theory are by Fermat. He invented the method of infinite descent, a kind of induction in reverse. In his time he was regarded as the best number theorist around, and everybody was eager to read his work when it was published. It was in the form of notes on Bachet's translation of Diophantus. Diophantus was an ancient Greek number theorist.

He is also one of the pre-inventors of the calculus. He did (simple) derivatives and integrals, but didn't see the point that they are inverse operations. Using this pre-calculus he proved Snell's law that when a light beam is refracted by a change of medium, the sines of the angles of incidence and refraction are in constant ratio depending on the media.
 

1. What is Fermat's Last Theorem?

Fermat's Last Theorem is a famous mathematical problem that was first proposed by French mathematician Pierre de Fermat in the 17th century. The theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two.

2. Why is Fermat's Last Theorem significant?

Fermat's Last Theorem is significant because it remained unsolved for over 350 years, despite many attempts by mathematicians to prove it. It has also sparked the development of new mathematical concepts and techniques, and the eventual proof of the theorem in 1994 by Andrew Wiles has been hailed as one of the greatest achievements in mathematics.

3. What is the proof of Fermat's Last Theorem?

The proof of Fermat's Last Theorem was provided by mathematician Andrew Wiles in 1994, building upon the work of other mathematicians such as Ernst Kummer and Gerhard Frey. Wiles' proof uses advanced mathematical concepts such as elliptic curves and modular forms. It is too complex to fully explain here, but it essentially shows that the equation an + bn = cn has no solutions for n > 2.

4. How did Fermat come up with his theorem?

Fermat's Last Theorem was first mentioned in a margin note in one of Fermat's copy of the ancient Greek text Arithmetica by Diophantus. It is believed that Fermat came up with the theorem while studying this text, which deals with equations involving integers. However, there is no concrete evidence of how Fermat arrived at his theorem.

5. Are there any real-world applications of Fermat's Last Theorem?

Fermat's Last Theorem may not have any direct real-world applications, but the techniques and concepts used to prove it have been applied in other areas of mathematics and science. For example, the proof of the theorem has led to a better understanding of elliptic curves and their applications in cryptography. It has also inspired further research in number theory and other mathematical fields.

Similar threads

B Have I proved some part of Fermat's last theorem?
    • General Math
Replies
15
Views
1K
A Prime Number Powers of Integers and Fermat's Last Theorem
    • General Math
Replies
1
Views
749
MHB Why isn't {0}^{3}+{0}^{3}={0}^{3} a proof for Fermat's Last Theorem?
    • General Math
Replies
3
Views
2K
B Fermat's Last Theorem; unacceptable proof, why?
    • General Math
Replies
12
Views
2K
On Fermat’s last theorem and others....
    • General Math
Replies
13
Views
1K
MHB Find Last Two Digits of ${2017}^{82}$
    • General Math
Replies
12
Views
3K
MHB How Should Fermat's Little Theorem be Introduced to Students?
    • General Math
Replies
1
Views
1K
I Proving Fermat's last theorem with easy math
    • General Math
Replies
2
Views
1K
I How to motivate the study of Fermat's Little Theorem
    • General Math
Replies
5
Views
1K
MHB Introducing Wilson's Theorem: Uses & Resources
    • General Math
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top