Wiles Proof of Fermat's Last Theorem

In summary, Wiles' proof of Fermat's Last Theorem is a mathematical proof published by Andrew Wiles in 1995. It shows that an + bn = cn has no non-zero integer solutions for n > 2. Wiles built upon previous work and spent seven years developing a new approach. His proof is considered one of the most important mathematical achievements of the 20th century and has opened up new areas of research. It has been accepted by the mathematical community and has had a significant impact on the field, inspiring others to tackle unsolved problems and showcasing the beauty of mathematics.
  • #1
fibonacci235
15
1
Just a quick question. What areas of mathematics would I have to study to understand Wiles' proof? I know his proof involves the Modularity Theorem, Elliptic Curves etc, but to really understand the proof what other topics would I need to master?
 
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  • #2
You need to know algebraic and arithmetic geometry quite well. Complex Analysis is probably also used.

Here are some nice books to get you started:
- Invitation to the mathematics of Fermat-Wiles by Hellegouarch
- Rational points on elliptic curves by Silverman and Tate
- Lectures on Curves, Surfaces and Projective Varieties by Beltrametti
 

Related to Wiles Proof of Fermat's Last Theorem

1. What is Wiles' proof of Fermat's Last Theorem?

Wiles' proof of Fermat's Last Theorem is a mathematical proof that was published in 1995 by Andrew Wiles. It demonstrates that for any integer value of n greater than 2, the equation an + bn = cn has no non-zero integer solutions for a, b, and c.

2. How did Wiles come up with this proof?

Wiles built upon the work of mathematicians who had attempted to prove Fermat's Last Theorem before him. He spent seven years working on a new approach, using techniques from algebraic geometry and number theory, before finally arriving at a proof.

3. How significant is Wiles' proof?

Wiles' proof of Fermat's Last Theorem is considered to be one of the most important mathematical achievements of the 20th century. It solved a problem that had puzzled mathematicians for over 300 years and has opened up new areas of research in number theory and algebraic geometry.

4. Has Wiles' proof been accepted by the mathematical community?

Yes, Wiles' proof of Fermat's Last Theorem has been thoroughly reviewed and accepted by the mathematical community. It has been published in respected mathematics journals and has been verified by other mathematicians.

5. What impact has Wiles' proof had on mathematics?

Wiles' proof has had a significant impact on mathematics, not only by solving a long-standing problem but also by introducing new techniques and ideas that have advanced the field. It has also inspired other mathematicians to tackle other unsolved problems and has shown the power and beauty of mathematics.

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